## Related rates differentiation problem

35 * 4 = 140 for x, 25 * 4 = 100 for y; $\frac{-2(150-140)*35+2*100*25}{\sqrt{(150-140)^{2}+ 100^{2}}}$ = $\frac{-2*10*35 + 5000}{\sqrt{10^{2} + 100^{2}}}$ = $\frac{-700 + 5000}{\sqrt{10100}}$ = $\frac{4300}{10\sqrt{101}}$

Recognitions:
Homework Help
 Quote by frosty8688 35 * 4 = 140 for x, 25 * 4 = 100 for y; $\frac{-2(150-140)*35+2*100*25}{\sqrt{(150-140)^{2}+ 100^{2}}}$ = $\frac{-2*10*35 + 5000}{\sqrt{10^{2} + 100^{2}}}$ = $\frac{-700 + 5000}{\sqrt{10100}}$ = $\frac{4300}{10\sqrt{101}}$
Looks like you removed the 2 in the denominator, but never factored out or canceled the 2's in the numerator. Let's just forget about canceling out the 2. You should have written:
$$\frac{-2(150-140) \cdot 35+2 \cdot 100 \cdot 25}{2\sqrt{(150-140)^{2}+ 100^{2}}}$$
(Also, don't use "*" for multiplication in LaTeX. Use "\cdot" instead.)

 I see, my mistake. I must have missed the 2 in the denominator.
 It would be about 21.39 km/hr
 Recognitions: Homework Help That's what I got. You have to be careful with the algebra when solving Calculus problems. (Not easy -- I know.)