Formular.

V=a+bu
Question
W varies partly as x and partly as the x square of x when x=3, w=18 and when x=5, w=169.
A. Find w interms of x.

1 answer

To find the relationship between w and x, we need to set up the equation using the given information.

Let the relationship between W and x be represented as:
W = ax + bx^2

Using the initial conditions when x=3, w=18:
18 = 3a + 9b (1)

Using the second conditions when x=5, w=169:
169 = 5a + 25b (2)

Now, we can solve these two simultaneous equations to find the values of a and b.

From equation (1), we can rewrite it as:
3a + 9b = 18
Dividing by 3, we get:
a + 3b = 6 (3)

From equation (2), we can rewrite it as:
5a + 25b = 169
Dividing by 5, we get:
a + 5b = 33.8 (4)

Now, we can solve equations (3) and (4) simultaneously to find the values of a and b.

Subtracting equation (3) from (4), we get:
2b = 27.8
b = 13.9

Substitute b = 13.9 into equation (3) to find the value of a:
a + 3(13.9) = 6
a + 41.7 = 6
a = -35.7

Therefore, the relationship between W and x is:
W = -35.7x + 13.9x^2

So, W varies partly as x and partly as the square of x when x=3, w=18 and when x=5, w=169 is given by:
W = -35.7(3) + 13.9(3)^2
W = -107.1 + 41.7
W = -65.4

Therefore, the formula for W in terms of x is:
W = -35.7x + 13.9x^2