I am also having trouble with this one, thanks!

If y varies jointly as x and the cube root of z, and y=120 when x=3 and z=8, find y when x=4 and z=27.

y=k*x*cubroot z

120=k*3*2 find k, then put that k in to
y=k*x*cubroot z to solve the last.

Y = K * X * ∛Z

120= K (3)(2)...CUBE ROOT OF 8 IS 2
120= 6 K
120/6 =K
20= K

Y= (20)(4)(3)...CUBE ROOT OF 27 IS 3
Y= 240

Well, it seems like we have a joint party here with x, y, and the cube root of z! The equation tells us that y varies jointly as x and the cube root of z. So, let's throw a little math comedy into the mix to solve this problem.

First, we need to find the constant of variation. Let's call it k, which stands for "kooky constant." So, we have an equation:

y = k * (x * ∛z)

Now, we're told that when x equals 3 and z equals 8, y is 120. So, let's plug those values in and do some math.

120 = k * (3 * ∛8)

Now, let's simplify this equation and find the value of our kooky constant.

120 = k * 3 * 2

120 = 6k

To find k, we divide both sides by 6:

k = 20

Great! The kooky constant is 20. Now, we can use it to find y when x equals 4 and z equals 27.

y = 20 * (4 * ∛27)

Now, let's put on our math clown noses and do some calculations.

y = 20 * (4 * 3)

y = 20 * 12

y = 240

So, when x is 4 and z is 27, y is 240! Ta-da! I hope this math circus performance brought a smile to your face.

To solve this problem, we need to use the concept of joint variation. When a variable varies jointly as two or more other variables, it means that the variable is directly proportional to the product of those variables raised to certain exponents.

In this case, we are given that y varies jointly as x and the cube root of z. Mathematically, we can represent this relationship as:

y = k * x * (z^(1/3))

Here, k is a constant of variation.

To find the value of k, we can use the given information. We are told that when x = 3 and z = 8, y = 120. Substituting these values into the equation, we get:

120 = k * 3 * (8^(1/3))

Now we can solve for k:

k = 120 / (3 * (8^(1/3)))

To evaluate (8^(1/3)), we need to find the cube root of 8. The cube root of a number is the number that, when multiplied by itself three times, gives the original number. In this case, the cube root of 8 is 2, since 2 * 2 * 2 = 8.

Substituting this into the equation, we have:

k = 120 / (3 * 2)
k = 120 / 6
k = 20

So, the constant of variation is 20.

Now that we know the value of k, we can use it to find y when x = 4 and z = 27. Substituting these values into the equation, we get:

y = 20 * 4 * (27^(1/3))

To evaluate (27^(1/3)), we need to find the cube root of 27. The cube root of 27 is 3, since 3 * 3 * 3 = 27.

Substituting this into the equation, we have:

y = 20 * 4 * 3
y = 240

Therefore, when x = 4 and z = 27, y = 240.