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Math Help - calculus

  1. #1
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    calculus

    These problems involve advanced Algebra II problems. I am 100% clueless on all four of these problems... I am in Algebra II honors, top of the class.

    I would VERY much appreciate it, if you uploaded your work via a scanner or w/e, so I can view it. If you can't do that, I need you to explain your answers.

    Problems:

    7. If 1200 cm^2 of material is available to make a box with a square base and an open top. Find the largest possible volume of the box. Use the following steps:
    a.) Draw a picture
    b) Find the volume in terms of x and h
    c) Find the surface area in terms of x and h. Then solve for h in terms of x.
    d) Find the volume in terms of x
    e) To find max, solve the following equation derived from calculus: 1200-3x^2=0
    f) Find h
    g) Find V

    Here is the other three problems in image form:
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  2. #2
    Senior Member vincisonfire's Avatar
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    7. b)  V = x^2h Simply base area times height.
    c)  S = x^2+4xh Base area plus 4 times the side area.
    d)  h = \frac{S-x^2}{4x} Isolate h taking care of priority of operations.
    e)  V = x^2h=x^2\frac{S-x^2}{4x} = x(S-x^2) Replace in V.
     \frac{dV}{dx} = 0 = S-3x^2 Solve for x.
     x = \sqrt{\frac{S}{3}}
    You should be able to do the rest.
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  3. #3
    Senior Member vincisonfire's Avatar
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    10 : Put divide by 4\pi to get \sqrt{r^2-x^2} -\frac{x^2}{\sqrt{r^2-x^2}}+x=0 Then multiply by  \sqrt{r^2-x^2} to get  r^2-x^2 -x^2 +x\sqrt{r^2-x^2}=0
     r^2-2x^2= -x\sqrt{r^2-x^2} Square both sides  r^4-4x^2r^2 + 4x^4= x^2r^2-x^4
     r^4-5x^2r^2 + 5x^4= 0
    Put x^2 = u and use the formula to solve quadratic equations.
    Exercice #11 is pretty much like #7. You should be able to work it out once you've understood #7.
    12 : g o f = g(f(x)) and f o g = f(g(x)) Use either f(x) or g(x) as variable.
    e.g.  g(f(x)) = \frac{x+\frac{1}{x}+1}{x + \frac{1}{x}+2} Simplify by multiplying by  \frac{x}{x} .
    Last edited by vincisonfire; January 19th 2009 at 06:40 PM.
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  4. #4
    Senior Member mollymcf2009's Avatar
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    See if this helps you with #7. It is a Word document. Good luck! Molly

    square open top box.doc
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