Y is inversely proportional to d^2 When d=10 y=4 D is directly proportional to x^2 When x=2, d=24 Find a formula for y in terms of x?

y = 1.44x⁴

Step-by-step explanation:

From the question,

Y∝d²

To remove the proportionality sign we introduce a constant.

Y = kd² Equation 1

make k the subject of the equation

k = Y/d² Equation 2

Given: Y = 4, d = 10

Substitute these values into equation 2

k = 4/10²

k = 4/100

k = 0.04

Substitute these value of k in equation 1

Y = 0.04d² Equation 3

Similarly,

d∝x²,

d = Cx²

make C the subject of the equation

C = d/x² Equation 4

Given:  d = 24, x = 2

Substitute into equation 4

C = 24/2²

C = 24/4

C = 6

Hence,

d = 6x² Equation 5

Substitute the value of d in equation 5 into equation 3

y = 0.04(6x²)²

y = 0.04(36x⁴)

y = 1.44x⁴

Hence the formula for y in terms of x is y = 1.44x⁴