Answer;
dy/dx = - or + 4 and y = 8
Explanation;
x² + y² = 100
when y = 8
Then, x² + 8² = 100
thus; x² = 100 - 64 = 36
x² = 36
therefore; x = + 6 or -6
2x (dx/dt) + 2y (dy/dt) = 0
x(dx/dt) + y (dy/dt) =0
When dy/dt = 3
= (- or + 6) dx/dt + 8 (3) = 0
thus; dx/dt = - 8 (3/6)
= + or - 4.
Answer; y = 8 and dx/dy = - or + 4
If x^2 + y^2 = 100 and dy/dt = 3The value of dx/dt when y = 8 is -4
Given the function x^2 + y^2 = 100
Differentiating the equation implicitly with respect to "t" as shown:
2xdx/dt + 2y dy/dt = 0
Divide through by 2
xdx/dt + y dy/dt = 0
Given the following parameters
y = 8
dy/dt = 3
Get the value of x
Recall that x^2 + y^2 = 100
x^2 + 8^2 = 100
x^2 + 64 = 100
x^2 = 100 - 64
x^2 = 36
x = 6
Get the measure of dx/dt
xdx/dt + y dy/dt = 0
6 dx/dt + 8(3) = 0
6 dx/dt = -24
dx/dt = -24/6
dx/dt = -4
Hence the value of dx/dt when y = 8 is -4
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