Y is partly constant and partly varies as the square if X giveb that Y=16 when X=3 and Y=12 when X=2,

Question

a) Write down an equation connecting X and Y
b) Find Y when X=15

Answer 1

a) Let the constant part be k and the varying part be mx^2. Thus, we have:

Y = k + mx^2

Using the two given data points, we can create a system of equations:

16 = k + 9m
12 = k + 4m

Subtracting the second equation from the first, we get:

4 = 5m

Solving for m, we get:

m = 4/5

Substituting this back into one of the equations, we can solve for k:

16 = k + 9(4/5)
16 = k + 7.2
k = 8.8

Therefore, the equation connecting X and Y is:

Y = 8.8 + (4/5)x^2

b) To find Y when X = 15, we simply plug it into the equation we found:

Y = 8.8 + (4/5)(15^2)
Y = 8.8 + 360
Y = 368.8

Therefore, when X = 15, Y = 368.8.