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 ≈ 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 ≈ 105.78.

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y = kxz

33 =k *9* 12
33 = 108k
k = 33/108

y = (33/108)(16)(22)

y = 242/3