Question

W is partly constant and partly varies as the square of x when x=3,w=18 and when x=5,w=169.find w in terms of x

Answer 1

The equation describing the relationship between w and x is:

w = ax + bx^2

Substitute the provided values for x and w into the equation.

When x = 3, w = 18:
18 = 3a + 9b

When x = 5, w = 169:
169 = 5a + 25b

Now solve these two equations simultaneously to find the values of a and b.

Subtract the first equation from the second:
151 = 2a + 16b

Now, divide this equation by 2 to simplify it:
75.5 = a + 8b

We can also write the answer in the form of a matrix:

[3 9] [a] = [18]
[5 25] [b] [169]

Next, multiply the first equation by 5 and the second by 3:

15a + 45b = 90
15a + 75b = 507

Now, subtract the first equation from the second:

30b = 417
b = 13.9

Now plug the value of b back into the previous equation to solve for a:

a + 8(13.9) = 75.5
a = - 1.7

So, the equation that describes the relationship between w and x is:

w = -1.7x + 13.9x^2

Therefore, w in terms of x is:

w = -1.7x + 13.9x^2