Question

A particle moves along the graph of x y=x+10 so that d x/d t=4 x+4. What is d y/d t when x=2 ?

Answer 1

To find dy/dt when x = 8, we differentiate y^2 = x + 1 implicitly with respect to t and solve for dy/dt. Substituting x = 8, we find that dy/dt = 6.

Step-by-step explanation:

To find dy/dt when x = 8, we need to differentiate the equation y^2 = x + 1 implicitly with respect to time t and solve for dy/dt. Let's start by differentiating both sides:

2y(dy/dt) = 1(dx/dt)

Since we are given that dx/dt = 4x + 4, we can substitute this value in the equation:

2y(dy/dt) = 1(4x + 4)

Now we can substitute x = 8 and solve for dy/dt:

2y(dy/dt) = 1(4(8) + 4)

2y(dy/dt) = 36

dy/dt = 36/(2y)

Since y^2 = x + 1, we can substitute x = 8 to find the value of y:

y^2 = 8 + 1

y^2 = 9

y = 3

Now we can substitute y = 3 in the equation for dy/dt:

dy/dt = 36/(2*3)

dy/dt = 6

Complete Question:

A particle moves on the graph of y^2 = x + 1 so that dx/dt = 4x +4. What is dy/dt when x =8 ?