anonymous
  • anonymous
x^2+y=120 find y. what is the max area? (the problem is this: a rectangle and a fence to cover 3 sides, find area of the longest side.) (120 is the amount of fencing needed for all 3 sides)
Mathematics
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anonymous
  • anonymous
x^2+y=120 find y. what is the max area? (the problem is this: a rectangle and a fence to cover 3 sides, find area of the longest side.) (120 is the amount of fencing needed for all 3 sides)
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
is the equation you mentioned is equation of area ?
anonymous
  • anonymous
yes
anonymous
  • anonymous
rearrange the equation, y=120-x^2 to find critical point, you have to take the first derivative equals to 0. dy/dx = -2x =0 thus x=0. so now we have a critical point that we don't know it's a max or min point. since you're having a quadratic equation with negative coefficient in front of x^2, generally we know the curve and the critical point you got is a maximum point. to find max area, pluck in the value of x=0 into your equation and you'll get y=120 which is the maximum area.

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anonymous
  • anonymous
so y=120, which is also the max, area?
anonymous
  • anonymous
i forgot to ask, is y the variable that represent the area this problem?
anonymous
  • anonymous
*area of this problem
anonymous
  • anonymous
well the problem is laid out like this: a mall wants to add a restaurant to its outside in a rectangular shape. so 3 sides (one long side is against building so you dont use it. and they want to put fencing around the 3 sides which requires 120 feet of fencing. you have to find: 1)length of all sides which mean find the y (which i am using as the one long side) and you have to find: 2)the maximum area.
anonymous
  • anonymous
does that make sense?
anonymous
  • anonymous
ah-ha. so y is the length of all sides. i think it should be 2x+y=120. area of the restaurant =xy
anonymous
  • anonymous
Oh yeah I think so! but can you compute that?
anonymous
  • anonymous
rearrange the length equation, y=120-2x, substitute the y above into equation of area, A= x(120-2x) = 120x -2x^2 now differentiate A with respect to x, dA/dx = 120 -4x =0, now you have a critical point, x=30. again we have a quadratic point with negative coefficient on x^2. x is maximum. to find maximum area, pluck in x=30 into the equation of area and you'll get 1800.
anonymous
  • anonymous
so the max area is 1800 feet? and y=60?
anonymous
  • anonymous
yep :)
anonymous
  • anonymous
thanks so much!!
anonymous
  • anonymous
do you know this: how many integer values of (a) can x^2+ax+6 be factored? what are they?
anonymous
  • anonymous
the highest order of x is two. it's a quadratic function. is the value of a given in the question ?

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