Question

(a) Find dy for 6y - 7xy + 4x = 0.

(b) Evaluate dy for x = 0 and dx = 0.03.
A) (a) dy = -4dx; (b) dy = 0
B) (a) dy = 0; (b) dy = -4dx
C) (a) dy = 0; (b) dy = 4dx
D) (a) dy = -4dx; (b) dy = -4dx

Answer 1

To find dy for the equation 6y - 7xy + 4x = 0, differentiate both sides with respect to x. Then, evaluate dy for x = 0 and dx = 0.03 which gives dy = -0.04.

Step-by-step explanation:

To find dy for the equation 6y - 7xy + 4x = 0, we differentiate both sides of the equation with respect to x. This gives us:

6dy/dx - 7xdy/dx - 7y + 4 = 0

Simplifying this equation, we get:

dy/dx = (7y - 4)/(6 - 7x)

To evaluate dy when x = 0 and dx = 0.03, we substitute these values into the equation we found in part (a):

dy = (7(0) - 4)/(6 - 7(0)) * 0.03 = -0.04

Therefore, the correct answer is:

(a) dy = (7y - 4)/(6 - 7x), (b) dy = -0.04