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Given that the equation connecting x and y is y2 = kx, where k is a constant, and y = 15 when x = 5, find(a) the value of k,(b) the value of x when y = 90.

Question

Given that the equation connecting x and y is y2=kxy^2 = kx, where k is a constant, and y=15y = 15 when x=5x = 5, find:

(a) the value of k,

(b) the value of x when y=90y = 90.

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Solution

(a) To find the value of k, we can substitute the given values of x and y into the equation y^2 = kx.

Given y = 15 and x = 5, the equation becomes:

(15)^2 = k * 5 225 = 5k

To solve for k, divide both sides of the equation by 5:

k = 225 / 5 k = 45

(b) To find the value of x when y = 90, we substitute y = 90 and k = 45 into the equation y^2 = kx:

(90)^2 = 45x 8100 = 45x

To solve for x, divide both sides of the equation by 45:

x = 8100 / 45 x = 180

This problem has been solved

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