anonymous
  • anonymous
The value of y varies directly with x2, and y = 36 when x = 3. What is the value of y when x = 5?
Mathematics
katieb
  • katieb
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Nnesha
  • Nnesha
what is the equation for direct variation ?
radar
  • radar
A direct variation means (when using y and x for the variable labels) When x increases so does y and vice versa, when x decreases so does y. For the given problem it would appears as:\[y= kx ^{2}. \]First step is to solve for k from the info given.
anonymous
  • anonymous
so the equation would be like 36=k3^2? or 36=k5^2

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radar
  • radar
Your are on the right track, from what is given 36 = k x^2, to solve for k substitute the value given for x. The value was (according to the problem) a 3 Sooo k 3^2 = 36 or 9k = 36 or k=36/9 k=??
radar
  • radar
That value of k will remain the same for all values of x, so it is important to get the correct value. k is called the "constant of proportionally"
anonymous
  • anonymous
so if you do k=36/9 k would equal 4?
radar
  • radar
Yes k=4 so now you can proceed with the new value of x which is given as 5, use k and plug in the value of 5 for x, and don't forget it is x^2 which is used to solve for y.
anonymous
  • anonymous
what would the equation look like again?
radar
  • radar
y=kx^2
anonymous
  • anonymous
so y=4 5^2 or i keep the 36 in the y place
radar
  • radar
No, ditch the 36 that was when x = 3. This is a new situation (except for k) when x = 5.
anonymous
  • anonymous
i got 100 as my answer cause 5^2 is 25 and 4 * 25 is 100
radar
  • radar
Great, sorry with the slow response, I had visitors. You are correct.
radar
  • radar
As always, good luck with your studies.

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