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Math Help - A few Pre-Calc problems in my AP Calc summer packet

  1. #1
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    A few Pre-Calc problems in my AP Calc summer packet

    Hey guys, my teacher said we could get help from anywhere and I figured this would be a good place.

    1. Let f(x) = 2x-3 [x less than or equal to 2] and x^2 + a [x greater than 2]

    Sketch the curve and find the value of "a" so that lim f(x) as x->2 = 1. I guess just find the value of "a"


    2. A piece of cardboard measures 20 by 35 inches. Two equal squaares are removed from the corners of a 20 inch side. Two equal rectangles are removed from the other corners so that the tabs can be folded to form a rectangular box with a lid.

    a. Write the forumla v(x) for the volume of the box.
    b. Fidn the domain of V for this problem. Express in interval notation (don't worry about end points)
    c. Find the maximum volume and the value of x that gives it. Justify your work.


    3. Find the solution(s) for the following system. Express your answer correctly to three decimal places (use your calculator).

    f(x)= (1/4) + sin((pi)(x))
    g(x)= 4^(-x)


    4. Let W(t) =95sqrt(t)(sin^2)(t/6). Find W(7) and W(10). For what value of "t" is W(t)= 0?


    Thanks.
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  2. #2
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    Have you tried these yourself?

    Please show your workings.
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    For the first one I graphed the 2x-3 part and have tried both positive and negative values for a. Nothing makes the limit as x approaches 2 = 1. Also, is there another way to solve it without graphing?

    For #2, I know the height is equal to x. The width is equal to 20-2x. I don't know what to put for the last one. I put 35-x-y but it didn't work for me.

    #3. I graphed it on my calculator. I need to look for where the two lines intersect, right?

    #4. I've never seen a problem like this and I'm not the greatest at functions. So no, I haven't attempted this last one
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  4. #4
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    Quote Originally Posted by INeedMathHelp33 View Post
    Hey guys, my teacher said we could get help from anywhere and I figured this would be a good place.

    1. Let f(x) = 2x-3 [x less than or equal to 2] and x^2 + a [x greater than 2]

    Sketch the curve and find the value of "a" so that lim f(x) as x->2 = 1. I guess just find the value of "a"

    With (2,1)

    f(x)= x^2+a

    1 = f(2)= 2^2+a\implies  a=-3


    Quote Originally Posted by INeedMathHelp33 View Post

    2. A piece of cardboard measures 20 by 35 inches. Two equal squaares are removed from the corners of a 20 inch side. Two equal rectangles are removed from the other corners so that the tabs can be folded to form a rectangular box with a lid.

    a. Write the forumla v(x) for the volume of the box.
    b. Fidn the domain of V for this problem. Express in interval notation (don't worry about end points)
    c. Find the maximum volume and the value of x that gives it. Justify your work.

    I think you are looking for

    v(x) = x(35-2x)(20-2x)





    Quote Originally Posted by INeedMathHelp33 View Post
    3. Find the solution(s) for the following system. Express your answer correctly to three decimal places (use your calculator).

    f(x)= (1/4) + sin((pi)(x))
    g(x)= 4^(-x)

    Yep calculator is best for this one.




    Quote Originally Posted by INeedMathHelp33 View Post

    4. Let W(t) =95sqrt(t)(sin^2)(t/6). Find W(7) and W(10). For what value of "t" is W(t)= 0?

    Thanks.

    W(7)= 95\sqrt{7}\times \sin ^2\frac{7}{6}= \dots

    W(10)= 95\sqrt{10}\times \sin ^2\frac{10}{6}= \dots

    W(t)= 0 \implies 0= 95\sqrt{t}\times \sin ^2\frac{t}{6} This is another job for your calculator.
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