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Math Help - Advance Algebra. Plz HELP!

  1. #1
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    Exclamation Advance Algebra. Plz HELP!

    write an equation of a periodic function that has:

    a.) an amplitude of 200 units.

    b.) been moved to the left 20 degrees

    b.) been moved down 15 units

    d.) a period of Pi/4

    A parabola has intercepts at (-3,0), (1,0), and (0,6). find the exact equation for this parabola. Write the equation in both standard and graphing form

    I just placed $1000 in an account which earns 8%per year compounded annually. ow much money will be in the account in 10 years? how long will it take for this account to have $5000 in it?

    I cant seem to figure these out...

    Nvm i got it
    Last edited by takkun0486; May 23rd 2006 at 07:18 PM.
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  2. #2
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    Quote Originally Posted by takkun0486

    A parabola has intercepts at (-3,0), (1,0), and (0,6). find the exact equation for this parabola. Write the equation in both standard and graphing form
    The equation of parabola is,
    y=ax^2+bx+c.
    The points tell you that,
    0=a(-3)^2+b(-3)+c
    0=a(1)^2+b(1)+c
    6=a(0)^2+b(0)^2+c
    From here we have,
    \left\{ \begin{array}{c}9a-3b+c=0\\a+b+c=0\\c=6
    Hence, since you know the value of "c" you can use the first two equations,
    \left\{ \begin{array}{c}9a-3b+6=0\\a+b+6
    From these equation we can simply to,
    \left\{ \begin{array}{c}3a-b=-2\\a+b=-6
    Add them to get,
    4a=-8 thus, a=-2
    Finally, throw that value for "a" into second equation,
    -2+b=-6 thus, b=-4
    From here we have,
    y=-2x^2-4x+6
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  3. #3
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    Quote Originally Posted by takkun0486
    write an equation of a periodic function that has:

    a.) an amplitude of 200 units.

    b.) been moved to the left 20 degrees

    b.) been moved down 15 units

    d.) a period of Pi/4
    First convert 20 degrees into radians, \frac{\pi}{9}, also remember when you move something to the right you subtract and to the left you add.

    These are either,
    f(x)=200\cos \left( \frac{\pi}{4}x+\frac{\pi}{9}\right)-15
    f(x)=200\sin \left( \frac{\pi}{4}x+\frac{\pi}{9} \right)-15
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  4. #4
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    Quote Originally Posted by takkun0486

    I just placed $1000 in an account which earns 8%per year compounded annually. ow much money will be in the account in 10 years? how long will it take for this account to have $5000 in it?
    The formula is,
    A(t)=1000(1.08)^t
    In ten years gives,
    A(10)=1000(1.08)^{10}\approx 2,159.

    For the second part solve for t,
    1000(1.08)^t=5000
    Divide by 1000,
    (1.08)^t=5
    Take logarithms,
     \log 1.08^t=\log 5
    By exponents rule bring down the exponent,
    t \log 1.08=\log 5
    Thus,
    t=\frac{\log 5}{\log 1.08}\approx 20.91
    This means that 20 years is a little below, thus the next years is good. Thus answer is 21 years.
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