Given that y is directly proportional to x√3 such that y=kx√3, where k is a constant, and y = 6 when x = 8, find(a) the value of k,(b) the value of x when y = 15.

(a) To find the value of k, we can use the given values of y and x in the equation y = kx√3.

Substitute y = 6 and x = 8 into the equation:

6 = k * 8√3

To isolate k, divide both sides of the equation by 8√3:

k = 6 / (8√3)

Simplify the right side of the equation to get the value of k:

k = 0.433

(b) To find the value of x when y = 15, we can substitute these values into the equation y = kx√3:

15 = 0.433 * x√3

To isolate x, divide both sides of the equation by 0.433√3:

x = 15 / (0.433√3)

Simplify the right side of the equation to get the value of x:

x = 19.4