Một ô tô đi từ A đến B với vận tốc 45 km/h. Sau
Một ô tô đi từ A đến B với vận tốc 45 km/h. Sau đó 1 thời gian ô tô thứ 2 cũng đi từ A với vận tốc 60 km/h và nếu không có gì thay đuổi thì đuổi kịp ô tô thứ nhất tại B. Nhưng ngay sau khi đi được nửa quãng đường AB, ô tô thứ nhất giảm bớt vận tốc 5 km/h nên 2 xe gặp nhau tại C cách B 30 km. Tính quãng đường AB.
Câu trả lời (1)
-
ta có hpt :\(\left\{{}\begin{matrix}\dfrac{s}{45}-\dfrac{s}{60}=t\\\dfrac{s-30}{45}-\left(\dfrac{\dfrac{S}{2}}{60}+\dfrac{\dfrac{s}{2}-30}{55}\right)=t\end{matrix}\right.\)
t là thời thời gian giữa hai xe xuất phát
tự giải đi
\(\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{ }{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{ }{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{ }{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{ }{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{ }{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{ }{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{ }{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{ }{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }\dfrac{ }{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{ }{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }\dfrac{ }{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{ }{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}}{ }}{ }}{ }\dfrac{ }{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{ }{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{ }{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{ }{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{ }{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{ }{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{ }{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{ }{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{ }{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }\dfrac{ }{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{ }{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }\dfrac{ }{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{ }{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}}{ }}{ }}{ }\dfrac{ }{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{ }{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}{ }}\)
bởi Nguyễn Thị Kim Nguyên 20/07/2018Like (0) Báo cáo sai phạm
Nếu bạn hỏi, bạn chỉ thu về một câu trả lời.
Nhưng khi bạn suy nghĩ trả lời, bạn sẽ thu về gấp bội!
Lưu ý: Các trường hợp cố tình spam câu trả lời hoặc bị báo xấu trên 5 lần sẽ bị khóa tài khoản
Các câu hỏi mới
-
Hình bình hành ABCD có góc A = 60 . lấy E thuộc AD và F thuộc CD sao cho DE = CF. gọi K là điểm đối xứng với F qua BC . chứng minh EK // AB
25/11/2022 | 0 Trả lời
-
phân tích đa thức thành nhân tử:
27+27x+9x^2+x^3
x^2-5x-y^2+5y
4x^2-12x+9-y^229/11/2022 | 0 Trả lời
-
cho tam giác ABC cân tại A, đường cao AD. O là trung điểm AC. E đối xứng với B qua O
a) chứng minh: AECD là hình chữ nhật
b) gọi I là trung điểm AD. chứng minh I là trung điểm BE
c) cho AB=10cm, BC=12cm. Tính diện tích tam giác OAD
d) đường thẳng OI cách AB tại K. tìm điều kiện của tam giác ABC để tứ giác AEDK là hình thang cân30/11/2022 | 0 Trả lời
-
VIDEOYOMEDIA
Tìm GTLN:
1) A= -x^2+4x+4
2) B= -x^2+6x-1
3) C= -2x^2+4x-5
4) D= -2x^2+8x-2
5) E= -3x^2+6x-2
6) F= -3x^2+2x-1
30/11/2022 | 0 Trả lời
-
cho tứ giác abcd có e,f,g,h là trung điểm ab,ac,cd,ad. tìm điều kiện của tứ giác abcd để efgh là a,hinh chữ nhật b, hình thoi c, hình vuông. vẽ hình viết giả thiết, kết luận trước mới giải
02/12/2022 | 0 Trả lời
-
(3x-1)-2x(4x-3)=5
07/12/2022 | 0 Trả lời
-
tìm x : (x – 5)^2 = 4x^2
b) 7x^2 – 16x = 2x^3 – 56
c) – 4x^2 + 28x = 0
d) x(x + 6) -7x -42 = 0
e) (x - 4)^2 – 36 = 0
f) 3x^2 + 5y – 3xy – 5x
08/12/2022 | 0 Trả lời
-
\({\left( {x + 5} \right)^2} + {\left( {x - 2} \right)^2} = 2\left( {x + 1} \right)\left( {x - 1} \right)\)
09/12/2022 | 0 Trả lời
-
cho tam giác ABC cân tại A đường cao AH gọi M là trung điểm AC,E đối xứng với H qua M.
a)chứng minh AECH là hình chữ nhật
b)ABHE là hình gì? Vì sao?
c)tính AECHbiết BC=12cm,AH=8cm
d)tam giác ABC cần thêm điều kiện gì để tứ giác ABHE là hình vuông
13/12/2022 | 0 Trả lời
-
5x(3x-2)
13/12/2022 | 2 Trả lời
-
Cho Tam giác ABC cân tại A, gọi D,E,F lần lượt là t/đ của AB,AC,BC
a.C/m t/g DECF là hbh
b.Gọi K là điểm đối xứng của F qua E. C/m t/g AKCF là hcn
c. Gọi H là điểm đối xứng của A qua K. Vẽ AI vuông góc với CH tại I. Tính số đo KIF
16/12/2022 | 0 Trả lời
-
(x-3)^2-(x-1)(x+1)=10
16/12/2022 | 1 Trả lời
-
x2 - 4 = 3(x-2)2
tìm x
16/12/2022 | 1 Trả lời
-
Bài 1: Thực hiện phép tính:
a, (3x+4x2-2)(-x2+1)
b,(x+2)(x-1)-x(x+3)
c,(x+3)(x2+3x-5)
d,(2x-1)(3x+2)(3-x)
17/12/2022 | 1 Trả lời
-
a) Tìm giá trị nhỏ nhất của biểu thức : P= x4 + x2 - 6x+9
b) chứng minh rằng n2+11n+39 không chia hết cho 49 với mọi số tự nhiên n
18/12/2022 | 0 Trả lời
-
Cho ABC, trung tuyến AM. Gọi I là trung điểm của AC. Gọi K là điểm đối xứng với M qua I
. a.Chứng minh : Tứ giác ABMK là hình bình hành.
b.Tìm điều kiện của tam giác ABC để AMCK là hình thoi.
20/12/2022 | 0 Trả lời
-
Cho tam giác ABC vuông tại A, đường trung tuyến AM. Gọi O là trung điểm của AC, N là điểm đối xứng với M qua O
a) Chứng minh tứ giác AMCN là hình thoi
b)Cho AB= 14cm, AC= 8cm, Tính diện tích tâm giác COM
c) Tam giác ABC caand điều kiện gì thì tứ giác AMCN là hình vuông?20/12/2022 | 0 Trả lời
-
Cho hình bình hành ABCD có AB=2BC.Gọi M và N lần lượt theo thứ tự là trung điểm của AB và CD
a/ Chứng minh tứ giác ABCD là hình bình hành
b/ tứ giác AMND là hình gì
c/ gọi I là giao điểm của AN và DM, K là giao điểm của BN và CM. Chứng minh tứ giác MKNI là hình chữ nhật
d/hình bình hành ABCD có thêm điều kiện gì để tứ giác MKNI là hình vuông
28/12/2022 | 0 Trả lời
-
Tính GTNN của: (x2+2x+3)/(x2+2x+7)
28/12/2022 | 0 Trả lời
-
tìm x, biết rằng:(x+2) ^2-(x-2)(x+2) =0
31/12/2022 | 2 Trả lời
-
x³ – 2x²y + xy² – x
01/01/2023 | 0 Trả lời
-
Bài 4: Cho hình thoi ABCD, O là giao điểm hai đường chéo. Vẽ đường thẳng qua B và song song với AC, vẽ đường thẳng qua C và song song với BD, hai đường thẳng đó cắt nhau tại K.
a) Tứ giác OBKC là hình gì? Vì sao?
b) Chứng minh: AB = OK.
c) Tìm điều kiện của tứ giác ABCD để tứ giác OBKC là hình vuông.
hép miii
03/01/2023 | 0 Trả lời
-
Toán 7 oki nhé giúp zới help
03/01/2023 | 0 Trả lời
-
Kết quả phân tích đa thức -x2 + 4x - 4 là
04/01/2023 | 1 Trả lời
-
cho hình bình hành ABCD, trên CDvà BClấy M,N sao cho BM=DN. gọi I là giao điểm của BM và DN.
a. chứng minh SABM=SABN.
b. Chứng minh: IA là phân giác góc DIB
15/01/2023 | 0 Trả lời