Question

Given the equation x2+y2=169:

(a) Find dtdy x=5, y=12, dtdx=7.
A. dtdy=−125
B. dtdy=125
C. dtdy=−127
D. dtdy=127

Answer 1

To find dtdy, differentiate the equation x^2 + y^2 = 169 with respect to y, plug in the given values, and solve for dtdy. The value of dtdy is approximately -0.343.

Step-by-step explanation:

To find dtdy, we need to differentiate the equation x^2 + y^2 = 169 with respect to y, keeping in mind that x = 5 and dtdx = 7.

Taking the derivative of x^2 + y^2 = 169 with respect to y, we get 2x(dx/dy) + 2y = 0. Plugging in x = 5 and dtdx = 7, we can solve for dtdy. Rearranging the equation, we get (dx/dy) = -y/x.

Substituting the values, we have dtdy = -y/(x * dtdx) = -12/(5 * 7) = -12/35 = -0.3428571428571428571.

Therefore, the value of dtdy is approximately -0.343.