Question

You are given the parametric equations x=7−t² and y=t³ −9t.
(a). Find dy/dx in terms of t.

Answer 1

To find dy/dx given the parametric equations x=7-t² and y=t³-9t, first compute the derivatives dy/dt and dx/dt, then divide dy/dt by dx/dt to get dy/dx = (3t² - 9) / (-2t).

Step-by-step explanation:

The question requires finding the derivative of y with respect to x (dy/dx) given the parametric equations x=7-t² and y=t³-9t. To find dy/dx, we need to calculate dy/dt and dx/dt separately, and then divide the former by the latter.

First, let's find dy/dt:

• dy/dt = 3t² - 9

Now let's find dx/dt:

• dx/dt = -2t

To find dy/dx, we divide dy/dt by dx/dt:

dy/dx = (3t² - 9) / (-2t)

Remember that for values of t where dx/dt is zero, dy/dx is undefined as you cannot divide by zero.