X is partly constant and partly varies as y. When y is 5,x is 7 and when y is 7 x is 8. Find the law of the variation and find x when y is 11
(7,5), (8,7), (x,11).
Slope = (7-5)/(8-7) = 2.
Slope = (11-7)/(x-8) = 2.
2x-16 = 4.
X = 10.
To find the law of variation, we need to analyze the relationship between the variables X and Y.
Given that X is partly constant and partly varies as Y, it can be expressed as:
X = a + bY
Where "a" is the constant term and "b" is the coefficient of variation.
Now, let's use the given information to solve for the values of "a" and "b":
When Y is 5, X is 7:
7 = a + 5b ---(1)
When Y is 7, X is 8:
8 = a + 7b ---(2)
To solve these two equations, we can either use substitution or elimination method. Let's use substitution:
From Equation (1), we have:
a = 7 - 5b
Substituting this value of "a" in Equation (2), we get:
8 = (7 - 5b) + 7b
8 = 7 + 2b
2b = 8 - 7
2b = 1
b = 1/2
Now, substitute the value of "b" back into Equation (1) or (2) to solve for "a":
Using Equation (1):
7 = a + 5(1/2)
7 = a + 5/2
14/2 - 5/2 = a
9/2 = a
a = 9/2
So, the law of variation is:
X = (9/2) + (1/2)Y
To find X when Y is 11, substitute the value of Y into the equation:
X = (9/2) + (1/2)(11)
X = (9/2) + (11/2)
X = (20/2)
X = 10
Therefore, when Y is 11, X is equal to 10.