SOLUTION: Dear Sir/Madam, I am confronted with the following problem: "T varies directly as the cube of a and inversely as the square root of d. If T = 4 when a = 2 and d = 9, find T w

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations -> SOLUTION: Dear Sir/Madam, I am confronted with the following problem: "T varies directly as the cube of a and inversely as the square root of d. If T = 4 when a = 2 and d = 9, find T w      Log On

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Question 6483: Dear Sir/Madam,
I am confronted with the following problem:
"T varies directly as the cube of a and inversely as the square root of d. If T = 4 when a = 2 and d = 9, find T when a = -1 and d = 4."
I really don't know how to approach this question. Can you help me?
Best regards,
-Mike
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
in terms of maths we have T alpha a%5E3%2Fsqrt%28d%29 or converting to an equation,

T+=+ka%5E3%2Fsqrt%28d%29 where k is the constant of proportionality.

So, now we need to find the value of k. For this we need to know T, a and d --> which we do from the question. So put the values into the equation to find k:

4+=+k2%5E3%2Fsqrt%289%29
4+=+8k%2F3
4%2A3%2F8+=+k

--> k = 3%2F2

so the equation is now: T+=+3a%5E3%2F2sqrt%28d%29

And now we have it, we can do the final part: "find T when a=-1 and d=4"

T+=+3%28-1%29%5E3%2F2sqrt%284%29
T+=+3%28-1%29%2F%282%2A2%29
T+=+-3%2F4

jon.