Please help me with this question: W is directly proportional to the cube root of X is increased by 50. what is the percentage increase in W
The answer is 14.47%, but i'm not sure how
lol
Well, my dear friend, it's time to put on our thinking caps and solve this mathematical riddle with a touch of humor. Now, let's dive in!
If we say that W is directly proportional to the cube root of X, we can write it as:
W ∝ (∛X)
Now, the question tells us that X is increased by 50. In other words, X' = X + 50. So, let's see how this affects W:
W' ∝ (∛X')
But wait, we need to find the percentage increase in W, so we need to compare W and W'.
To calculate the percentage increase, we'll use this dandy formula: Percentage Increase = ((W' - W) / W) * 100
Now, let's substitute the values we've got:
Percentage Increase = ((W' - W) / W) * 100
But since W and W' are directly proportional, we can say that:
(W' - W) / W = k
where k is a constant. So, the percentage increase becomes:
Percentage Increase = k * 100
Now, since W ∝ (∛X), we can say that there's another constant, let's call it m, such that:
W = m * (∛X)
And similarly, for W':
W' = m * (∛X')
But we know that X' = X + 50, so:
W' = m * (∛(X + 50))
Now, let's substitute these little fellas back into our percentage increase formula:
Percentage Increase = ((W' - W) / W) * 100
Percentage Increase = ((m * (∛(X + 50))) - (m * (∛X))) / (m * (∛X))) * 100
My friend, I think it's time for a little joke to keep our spirits high. Did you hear about the mathematician who's afraid of negative numbers? He'll stop at nothing to avoid them!
Now let's continue our calculation:
Percentage Increase = (∛(X + 50) - (∛X)) / (∛X) * 100
Well, my friend, it looks like we've done all we can. Unfortunately, without specific values for X and m, we can't calculate the exact percentage increase in W. But don't worry, I hope this little mathematical clown show brought a smile to your face!
To calculate the percentage increase in W when the cube root of X is increased by 50, we first need to understand the relationship between W and X.
According to the given information, W is directly proportional to the cube root of X. This means that as the cube root of X increases, W also increases, and their relationship can be expressed as:
W = k * (X)^(1/3)
where k is the constant of proportionality.
Now, let's consider the increase in the cube root of X. Let's call the original cube root of X as C, and the increased value as C + 50.
So, we have:
W2 = k * (C + 50)^(1/3) (where W2 is the new value of W)
To determine the percentage increase in W, we need to calculate the difference between W2 and the original value of W (let's call it W1), and then express that difference as a percentage of W1.
Percentage Increase = (W2 - W1) / W1 * 100
We need the values of W1 and C to calculate the exact percentage increase.
W=x hk
Fπ34
Gsk
impossible,
w = x^.3 + 50
say x = 1
w = 1 + 50 = 51, % = 100(51/50)
say x = 27
w = 3 + 50 = 53 , % = 100 (53/50)