If (x+3) varies directly as you and x= 3 when y= 12
Find the ;
i)relationship between x and y
ii) value of x when you = 8
Please proofread and repost.
you must have meant:
If (x+3) varies directly as y
then,
x+3 = ky
when x=3, y=12, so
6 = 12k
k = 6/12 = 1/2
then x+3 = (1/2)y
or
2x + 6 = y
when "you" = 8
2x+6=8
2x=2
x = 1
i) In this problem, (x+3) varies directly as you. This means that as the value of you increases or decreases, the value of (x+3) will increase or decrease proportionally.
By setting up a proportion, we can find the relationship between x and y. From the given information, we have x = 3 when y = 12.
(x+3) / y = k, where k is the constant of proportionality.
Substituting the given values, we get (3+3)/12 = k.
Simplifying, we get 6/12 = k.
Therefore, k = 1/2.
The relationship between x and y is (x+3) = (1/2)y.
ii) To find the value of x when you = 8, we can use the relationship between x and y that we found in the previous step.
Substitute you = 8 and solve for x:
(x+3) = (1/2) * 8
x+3 = 4
x = 4-3
x = 1
Therefore, when you = 8, x = 1.
To find the relationship between x and y in a direct variation, we can use the formula:
y = kx
Where y is the dependent variable, x is the independent variable, and k is the constant of variation.
We are given that (x+3) varies directly as you. So, we can write the equation as:
(x+3) = k * you
Now, let's solve for k. We are given that when x = 3, y = 12. Plugging these values into our equation, we get:
(3+3) = k * 12
6 = 12k
Dividing both sides by 12, we find:
k = 6/12
k = 1/2
So, the relationship between x and y is:
y = (1/2) * (x+3)
Now, let's find the value of x when you = 8. We can substitute the given values into the equation:
y = (1/2) * (x+3)
8 = (1/2) * (x+3)
Multiplying both sides by 2:
16 = x + 3
Subtracting 3 from both sides:
13 = x
Therefore, when you = 8, x = 13.