Suppose 4x2 + 16y2 = 100, where x and y are functions of t.(a)If dydt = 14, find dxdt when x = 3 and y = 2.

Question

(a) If $\frac{dy}{dt} = 14$ , find $\frac{dx}{dt}$ when $x = 3$ and $y = 2$ .

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To solve this problem, we first need to differentiate the given equation with respect to t.

The given equation is 4x^2 + 16y^2 = 100.

Differentiating both sides with respect to t, we get:

8x(dx/dt) + 32y(dy/dt) = 0.

We are given that dy/dt = 14, x = 3, and y = 2.

Substitute these values into the differentiated equation:

83(dx/dt) + 32214 = 0,

24*(dx/dt) + 896 = 0.

Solving for dx/dt, we get:

dx/dt = -896 / 24 = -37.33.

So, when x = 3 and y = 2, dx/dt = -37.33.

This problem has been solved

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