y varies jointly as X and Z. y=64 when x=4 and z=8. Find y when x=8 and z=6
y = k ∙ x ∙ z
When x = 4 , y = 64 and z = 8:
y = k ∙ x ∙ z
64 = k ∙ 4 ∙ 8
64 = 32 k
Divide both sides by 32
64 / 32 = k
2 = k
k = 2
When x = 8 and z = 6:
y = k ∙ x ∙ z
y = 2 ∙ x ∙ z
y = 2 ∙ 8 ∙ 6
y = 2 ∙ 48
y = 96
y = kxz
so, y/(xz) = k, a constant
You want y such that
y/(8*6) = 64/(4*8)
y/48 = 2
y = 96
Well, if y varies jointly as X and Z, we can write the equation as y = k*X*Z, where k is a constant.
To find the value of k, we can use the given information. When x = 4 and z = 8, y = 64. So we can substitute these values into the equation:
64 = k*4*8
Now let's solve for k:
64 = 32k
k = 64/32
k = 2
So our equation is y = 2*X*Z.
Now, let's plug in x = 8 and z = 6 to find y:
y = 2*8*6
y = 96
So when x = 8 and z = 6, y is equal to 96.
To solve this problem, we can use the concept of joint variation, where y varies directly with both x and z. In mathematical terms, this can be represented as:
y = k * x * z
where k is the constant of variation.
To find the value of k, we can use the given information that y = 64 when x = 4 and z = 8. Substituting these values into the equation, we get:
64 = k * 4 * 8
Simplifying the equation, we have:
256 = 32k
Dividing both sides by 32, we can find the value of k:
k = 256 / 32
k = 8
Now, we can use the value of k to find y when x = 8 and z = 6. Substituting these values into the equation, we get:
y = 8 * 8 * 6
y = 384
Therefore, when x = 8 and z = 6, the value of y is 384.
To find the value of y when x=8 and z=6, you need to use the joint variation equation.
Joint variation means that y varies directly with both x and z, so we can express this relationship mathematically by the equation:
y = k * x * z
where k is the constant of variation.
To find the value of k, we can use the information given. We are told that y=64 when x=4 and z=8. Plugging these values into the equation, we get:
64 = k * 4 * 8
Simplifying, we have:
64 = 32k
Dividing both sides by 32, we find:
k = 2
Now that we know the value of k, we can substitute it back into the equation. Therefore:
y = 2 * x * z
To find the value of y when x=8 and z=6, we can plug these values into the equation:
y = 2 * 8 * 6
Simplifying, we have:
y = 96
Therefore, when x=8 and z=6, the value of y is 96.