X is partly constant and partly varies directly with y. When x=9,y=5 and when x=34,y=10.
a. What is the formula connecting x and y
b. Find the value of x when y=7
X is partly constant and partly varies directly with y
----> x = ky + c
when x = 9, y = 5
9 = 5k + c
when x = 34 , y = 10
34 = 10k + c
subtruct them:
25 = 5k
k = 5
in 9 = 5k + c
9 = 25 + c
c = -16
x = 5y - 16
Felicity I gave you assignment and u came here we shall see in school , Go and practice
Felicity Runn
To find the formula connecting x and y, we need to determine the constant part and the part that varies directly.
Given that x is partly constant and partly varies directly with y, we can write the equation as follows:
x = cy + k
where c is the constant part and k is the constant term.
Now, let's solve for c and k using the given information:
When x = 9 and y = 5:
9 = 5c + k
When x = 34 and y = 10:
34 = 10c + k
We have a system of two equations with two variables. To solve for c and k, let's subtract the first equation from the second equation:
34 - 9 = 10c + k - 5c - k
25 = 5c
Divide both sides of the equation by 5:
5 = c
Now, substitute the value of c back into one of the equations to solve for k:
9 = 5(5) + k
9 = 25 + k
k = 9 - 25
k = -16
Therefore, the formula connecting x and y is:
x = 5y - 16
To find the value of x when y = 7, substitute y = 7 into the formula:
x = 5(7) - 16
x = 35 - 16
x = 19
Therefore, when y = 7, the value of x is 19.