The quantity A varies directly as the cube root of P=8 when Q=2/3
A = K cube root 8 divided by 2/3
A = K 2 times 3/2
A =2k
K stands for a constant. I don't know if your teacher wants A= 2 or 2K for the answer.
A = k∛P
no idea what Q is, unless it is a typo.
If A = 2/3 when P=8, then
2/3 = k∛8
2/3 = 2k
k = 1/3
To solve this problem, we need to use the concept of direct variation. Direct variation occurs when one quantity is proportional to another quantity, meaning that one quantity increases or decreases in direct proportion to the other.
In this case, we are given that the quantity A varies directly as the cube root of P. Mathematically, we can express this relationship as:
A = k∛P
where k is the constant of variation.
Now, we have additional information that when Q = 2/3, P = 8. This allows us to find the value of k in the equation.
Substituting the given values into the equation, we have:
A = k∛8
Since A is not given, we can't solve for k directly. However, we can still find the value of k using the given information when Q = 2/3.
Plugging in Q = 2/3 into the equation, we get:
2/3 = k∛8
To isolate k, we need to cube both sides to get rid of the cube root (∛):
(2/3)^3 = (k∛8)^3
8/27 = k^3 * 8
Simplifying the equation:
k^3 = 27/64
Now, take the cube root of both sides to solve for k:
k = ∛(27/64)
k = 3/4
Therefore, the value of k is 3/4.
Now that we have the value of the constant of variation, we can go back to the original equation A = k∛P and replace k with 3/4:
A = (3/4)∛P
So, if you're given a value for P, you can substitute it into this equation to find the corresponding value of A.