A quantity, W, is directly proportional to X and the square Y, and inversely proportional to the cube of Z. W=3 when X=4, Y=2 and Z=4. What is the value of W when X=8, Y=9 and Z= 6? Give answer to 3 decimal places.
Thanks in advance! I appreciate all the help! :)
if you know what direct and inverse variations are, then you know that
w = kxy^2/z^3
plug in w,x,y,z to get k:
3=k(4)(4)/64
3 = k/16
k=48 so,
w = 48xy^2/z^3
Now plug in the new x,y,z to get w, since we now know k.
To solve this problem, we need to apply the concept of direct and inverse proportionality. Let's break down the given information:
1. The quantity W is directly proportional to X and the square of Y. This means that we can express it as W = k * X * Y^2, where k is a constant of proportionality.
2. The quantity W is inversely proportional to the cube of Z. This implies that we can write it as W = k / Z^3.
To find the value of W when X = 8, Y = 9, and Z = 6, we can use the given information W = 3 when X = 4, Y = 2, and Z = 4. Let's start by finding the constant of proportionality, k.
Using the initial values W = 3, X = 4, Y = 2, and Z = 4, we can substitute these values into the equation for direct proportionality: W = k * X * Y^2.
3 = k * 4 * 2^2
3 = k * 4 * 4
3 = 16k
We can solve for k by dividing both sides by 16:
k = 3 / 16
k = 0.1875
Now that we have the constant of proportionality, we can substitute the given values X = 8, Y = 9, and Z = 6 into the equation for W = k * X * Y^2 / Z^3:
W = (0.1875) * (8) * (9^2) / (6^3)
W = 0.1875 * 8 * 81 / 216
W = 0.1875 * 648 / 216
W = 1.78125
Therefore, the value of W when X = 8, Y = 9, and Z = 6 is approximately 1.781 to 3 decimal places.
I hope this helps! Let me know if you have any other questions.