## anonymous 3 years ago somebody please help me..got test tonight but still dunn how to solve this... The base of a triangle increases at the rate 2cm per second, and height decreases at the rate of 1/2cm per second.Find the rate of change f its area when the base and height are of length 5cm... ? T.T helpp

1. anonymous

anybody ??? :(

2. anonymous

you know agent00smith ?

3. agent0smith

hmm.... we know $A = 0.5 b h$ $\frac{ db }{ dt } = 2 (cm/s)$ $\frac{ dh }{ dt }= -0.5 (cm/s)$ We need $\frac{ dA }{ dt } = ?$

4. anonymous

chain rule ?

5. anonymous

but we have t differentiate A with respect to ??

6. agent0smith

Yeah that's what i'm trying to think of...

7. anonymous

o.O ok ... i really dunno how to relate that

8. zepdrix

Hmm are we assuming this is a right triangle? :o

9. zepdrix

I guess it would have to be, otherwise we need more information. :) Looks like agent was on the right track. Both $$\large b$$ and $$\large h$$ are variables. Just apply the product rule! :D

10. zepdrix

Differentiate with respect to time*

11. agent0smith

Yeah that's what I was thinking... differentiate A wrt t

12. anonymous

huh ??? yeahh differentiate wrt time . that is wwhat we want to find

13. anonymous

im not clear with that

14. agent0smith

But then that seems to make the actual values of the base and height unnecessary, but maybe that's okay.... $\frac{ dA }{ dt} = 0.5 \frac{ db }{ dt}\frac{ dh }{ dt}$

15. zepdrix

Woops, product rule! :O

16. zepdrix

$\large A=\frac{1}{2}bh$$\large A'=\frac{1}{2}b'h+\frac{1}{2}bh'$Something like that, yes? :D

17. anonymous

huhh ????? how can...i dont undrstand...

18. anonymous

urmmm let me try that

19. anonymous

wow.....yeahh!!! correct answer !!! greatt !! thank you so much guys ! love uollsz!! :D

20. zepdrix

yay team \:D/

21. anonymous

my mentors :)

22. agent0smith