If y varies jointly as x and z, and y = 33 when x = 9 and z = 12, find y and x = 16 and = 22.
To solve this problem, we need to use the concept of joint variation. If y varies jointly as x and z, we can express this relationship using the equation:
y = kxz
where k is the constant of variation.
Given that y = 33 when x = 9 and z = 12, we can substitute these values into the equation to find the value of k.
33 = k * 9 * 12
Dividing both sides of the equation by (9 * 12):
k = 33 / (9 * 12)
Simplifying this expression, we get:
k = 33 / 108
Now that we know the value of k, we can find y when x = 16 and z = 22 by substituting these values into the equation:
y = k * x * z
Substituting the given values:
y = (33 / 108) * 16 * 22
Calculating this expression:
y â 18.81
Therefore, when x = 16 and z = 22, y is approximately equal to 18.81.
To find the value of y when x = 16 and z = 22, we need to use the joint variation equation.
First, let's write the joint variation equation: y = k * x * z, where k is the constant of variation.
To find the constant of variation, we can use the initial values given in the problem.
When y = 33, x = 9, and z = 12, we can substitute these values into the equation:
33 = k * 9 * 12
Now we can solve for k:
33 = 108k
Dividing both sides by 108 gives:
k = 33/108
k = 11/36
Now that we have the value of k, we can find y when x = 16 and z = 22 by substituting them into the equation:
y = (11/36) * 16 * 22
y = (11/36) * 352
y = 105.78 (approximately)
Therefore, when x = 16 and z = 22, y â 105.78.
Ask ur grand father!!!
ðððððĪŠ
y = kxz
33 =k *9* 12
33 = 108k
k = 33/108
y = (33/108)(16)(22)
y = 242/3