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Math Help - Binomial expansion and exponential

  1. #1
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    Binomial expansion and exponential

    1.Expand the expression using the Binomial Theorem:
    ________________

    2.Suppose p varies inversely as the square root of q. If p=-7 when q=9, what is p if q is 6?
    p=_____

    3.The stopping distance d of an automobile is directly proportional to the square of its speed v. A car required 50 feet to stop when its speed was 80 miles per hour. Find a mathematical model that gives the stopping distance d in terms of its speed v.
    Your answer is d=_____
    Estimate the stopping distance if the brakes are applied when the car is traveling at 62 miles per hour.
    Your answer is_____.

    4.If the point is on the unit circle in quadrant IV, then y=___.

    For number five, let me know if these are right.

    5.= sqrt(3)/2
    =0
    =sqrt3
    = sqrt(3)/3
    =-1
    =2/sqrt(2)
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  2. #2
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    Hello, badandy328!

    Do you know the Binomial Theorem?
    . . If you do, exactly where is your difficulty?


    1. Expand the expression using the Binomial Theorem:
    . . (4x - 2)^5

    (4x-2)^5\;=\;\binom{5}{5}(4x)^5(-2)^0 + \binom{5}{4}(4x)^5(-2)^1 + \binom{5}{3}(4x)^3(-2)^2

    . . . . . . . .  + \binom{5}{2}(4x)^2(-2)^3 + \binom{5}{1}(4x)^1(-2x)^4 + \binom{5}{0}(4x)^0(-2)^5


    . . = \;1(1024x^5)(1) + 5(256x^4)(-2) + 10(64x^3)(4) +  10(16x^2)(-8) + 5(4x)(16) + 1(1)(-32)


    . . = \;1024x^5 - 2560x^4 + 2560x^3 - 1280x^2 + 210x - 32

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  3. #3
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    Oh i see what i did wrong. I didn't keep track of the negatives. Thanks. What about the others though? #2 i got -4.7 but that seems to be wrong. #3 I'm completely lost. #4 i got y=3/5 which is wrong. #5 i think is all right just want to make sure.
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  4. #4
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    Quote Originally Posted by badandy328 View Post
    5.= sqrt(3)/2
    =0
    =sqrt3
    = sqrt(3)/3
    =-1
    =2/sqrt(2)
    I'd suggest re-checking the following:

    cot(2Pi/3)

    The rest look good to me.
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  5. #5
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    Quote Originally Posted by Soroban View Post
    Hello, badandy328!

    Do you know the Binomial Theorem?
    . . If you do, exactly where is your difficulty?



    (4x-2)^5\;=\;\binom{5}{5}(4x)^5(-2)^0 + \binom{5}{4}(4x)^5(-2)^1 + \binom{5}{3}(4x)^3(-2)^2

    . . . . . . . .  + \binom{5}{2}(4x)^2(-2)^3 + \binom{5}{1}(4x)^1(-2x)^4 + \binom{5}{0}(4x)^0(-2)^5


    . . = \;1(1024x^5)(1) + 5(256x^4)(-2) + 10(64x^3)(4) +  10(16x^2)(-8) + 5(4x)(16) + 1(1)(-32)


    . . = \;1024x^5 - 2560x^4 + 2560x^3 - 1280x^2 + 210x - 32

    Minor error; 5(4x)(16) = 320x, not 210x
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