## anonymous one year ago Related Rates Question Help!?!?! The base of a triangle is decreasing at the rate of 1 ft/sec, while the height is increasing at the rate of 2 ft/sec. At what rate is the area of the triangle changing when the base is 10 ft and the height is 70 ft? a)25 b)-45 c)-50 d)45

1. anonymous

only need help on this one and then i can do a whole bunch that are alike!!

2. phi

|dw:1438197781116:dw|

3. phi

the area of the triangle is $A = \frac{1}{2} x y$ take the derivative with respect to t: $\frac{dA}{dt} = \frac{1}{2}\left( x \frac{dy}{dt}+ y \frac{dx}{dt}\right)$

4. anonymous

wouldn't the x and y disappear ?

5. anonymous

and also the .5

6. phi

both x and y are variables and you must use the product rule

7. anonymous

lovely okay got it thank you very much!

8. phi

d u v = u dv + v du if you have a constant, it can "go out front"

9. phi

10. anonymous

wait would it be x dy/dt wouldn't it be x dx/dt

11. anonymous

okay nvm product rule forgot

12. phi

the rule is d (uv) = u * dv + v * du or with x and y d/dt (xy)= x d/dt y + y * d/dt x

13. anonymous

what are you getting?

14. anonymous

im getting -25

15. phi

dx/dt= -1 dy/dt= 2 x=10 y=70 x dy/dt + y dx/dt = 10*2 + 70*-1 = 20-70= -50 then multiply by 1/2 to get -25 sq ft/ sec

16. anonymous

-25 is an answer choice though. wheres the problem?

17. phi

which one ?

18. anonymous

oh woops a should be a -25

19. anonymous

sorry abut that :(

20. anonymous

Thank you very much !!

21. phi

good luck on the other problems