W varies partly as x and partly as the x square of x when x =3, w=18, and when x=5, w=169. Find w interm of x

Answer 1

To solve for w in terms of x, we can set up a system of equations based on the information given:

w = k*x + m*x^2

Using the first set of data: x=3, w=18
18 = 3k + 9m

Using the second set of data: x=5, w=169
169 = 5k + 25m

Now we can solve these two equations simultaneously to find the values of k and m.

From equation 1:
18 = 3k + 9m
=> 2k + 6m = 12

From equation 2:
169 = 5k + 25m
=> k + 5m = 33

Solving these two equations simultaneously, we get:
k = 3
m = 2

Therefore, w = 3x + 2x^2 = x(3+2x)

So, w in terms of x is w = x(3+2x)