please solve w fair is partly x and partly as the square of x when x is equals to 3 w is equals 18 and when x equals to 5 w is equals to 165 find w in terms of x
You don't need an answer , you need to know how to do this type of question.
But first of all, fix your post, since
"..solve w fair is partly x and partly as the square of x.." makes no sense to me.
poor dictation
"w fair is " probably means "w varies"
so, now it appears that
w = ax + bx^2
and thus that
3a+9b = 18
5a+25b = 165
Now just solve for and a and b as usual
To find an expression for w in terms of x, we need to determine the relationship between w and x. Let's analyze the given information.
We are given that w is partly x and partly the square of x. We can express this relationship mathematically as:
w = ax + bx^2
Now, we need to find the values of a and b. We have two data points: when x = 3, w = 18, and when x = 5, w = 165. We can use these data points to create a system of equations to solve for a and b.
1) When x = 3, w = 18:
18 = 3a + 9b
2) When x = 5, w = 165:
165 = 5a + 25b
Now, we have a system of two equations. We can solve this system of equations using any preferred method, such as substitution or elimination.
Let's use the method of substitution to solve this system:
From the first equation,
3a + 9b = 18 (divide both sides by 3)
a + 3b = 6 (equation A)
From the second equation,
5a + 25b = 165 (divide both sides by 5)
a + 5b = 33 (equation B)
Subtracting equation A from equation B:
(a + 5b) - (a + 3b) = 33 - 6
2b = 27
b = 27 / 2
b = 13.5
Substituting the value of b back into equation A:
a + 3(13.5) = 6
a + 40.5 = 6
a = 6 - 40.5
a = -34.5
Therefore, the values of a and b are a = -34.5 and b = 13.5.
Now, we can substitute these values back into our original equation:
w = ax + bx^2
w = (-34.5)x + (13.5)x^2
So, the expression for w in terms of x is:
w = 13.5x^2 - 34.5x