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 = 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.
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
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