Find an equation of variation in which y varies jointly as x and z, and y=4 when x=4 and z=1. Simplify

y = kxz

4 = k*4*1
k = 1

y = xz

Well, let's start by writing the equation of variation in its general form:

y = kxz

Now, we can use the given values of y, x, and z to solve for the constant of variation, k. Plug in y = 4, x = 4, and z = 1:

4 = k(4)(1)
4 = 4k

Divide both sides by 4:

1 = k

So, the equation of variation can be simplified to:

y = xz

Therefore, y varies jointly as x and z, and the equation of variation is y = xz.

To find an equation of variation where y varies jointly as x and z, we can use the formula:

y = k * x * z

where k is the constant of variation.

Given that y = 4 when x = 4 and z = 1, we can substitute these values into the equation:

4 = k * 4 * 1

Simplifying this equation gives us:

4 = 4k

Dividing both sides of the equation by 4, we find:

k = 1

Now that we know the value of k, we can substitute it back into the equation:

y = 1 * x * z

Simplifying further, we get:

y = xz

Therefore, the equation of variation in which y varies jointly as x and z, simplified, is y = xz.

To find an equation of variation in which y varies jointly as x and z, we can use the equation:

y = k * x * z,

where k is the constant of variation.

To find the value of k, we can substitute the given values of y, x, and z:

4 = k * 4 * 1.

Simplifying this equation, we have:

4 = 4k.

Dividing both sides of the equation by 4, we get:

k = 1.

Now that we know the value of k is 1, we can substitute it back into the original equation:

y = 1 * x * z.

Simplifying further, we have:

y = xz.

Thus, the equation of variation in which y varies jointly as x and z is y = xz.