If R1 and R2 are increasing at rates of 0.3 Ω/s and 0.2 Ω/s, respectively, how fast is R changing when R1 = 70 Ω and R2 = 110 Ω? (Round your answer to three decimal places.)

1/R=1/R1+1/R2

Question

If R1 and R2 are increasing at rates of 0.3 Ω/s and 0.2 Ω/s, respectively, how fast is R changing when R1 = 70 Ω and R2 = 110 Ω? (Round your answer to three decimal places.)

1/R=1/R1+1/R2

anonymous · Answer

They want you to use implicit differentiation.

anonymous · Answer

$$
\frac{d}{dt}\frac1R=-\frac{dR/dt}{R^2}
$$

anonymous · Answer

So $$
-\frac{R'}{R^2}=-\left(\frac{R_1'}{R_1^2}+\frac{R_2'}{R_2^2}\right)
$$

anonymous · Answer

R1 = 70 Ω and R2 = 110 Ω?

 R1 and R2 are increasing at rates of 0.3 Ω/s and 0.2 Ω/s,

anonymous · Answer

Plug them in.

anonymous · Answer

i got .000000042

anonymous · Answer

Okay, check in the back of the book?

anonymous · Answer

its online. nothing in the back of the book

anonymous · Answer

I get $R=42.7$

anonymous · Answer

http://www.wolframalpha.com/input/?i=%281%2F%281%2F70%2B1%2F110%29%29%5E2+%280.3%2F70%5E2%2B0.2%2F110%5E2%29

anonymous · Answer

$R' \approx  0.142$