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Math Help - more urgent areas and ratios

  1. #1
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    more urgent areas and ratios

    I do not understand most of these, Please help
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    Quote Originally Posted by sanee66 View Post
    I do not understand most of these, Please help
    To A

    the area of the rhombus is 4 \times _{area} \triangle UMW

    to find the area of the triangle use the \frac {1}{2} \cdot base \cdot height formula (note, you have to find the height, use Pythagoras' theorem

    got it?


    do you know what a rhombus is? do you know the properties of a rhombus? see here

    questions become easier when you know what you are dealing with
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    Quote Originally Posted by sanee66 View Post
    I do not understand most of these, Please help
    B is 81 \sqrt {3}

    but i think that's what you meant to type... right?

    double check question C. something is wrong with it


    D is correct


    clarify question E, what exactly is raised to the 4th power?


    To F.

    the circumference of a circle is given by:

    C = 2 \pi r

    For circle R, 12 \pi = 2 \pi r_R \implies \boxed { r_R = 6 }

    For circle S, 32 \pi = 2 \pi r_S \implies \boxed { r_S = 16 }

    Thus, the ratio of the radius of S to the radius of R is:

    r_S:r_R = \frac {r_S}{r_R} = \frac {16}{6} = \frac {8}{3} = 8:3
    Last edited by Jhevon; July 22nd 2007 at 02:56 PM.
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    Ratio of circumference of circle C to its radius is . Which is the area of the circle?
    Should be one of these



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    Quote Originally Posted by sanee66 View Post
    Ratio of circumference of circle C to its radius is . Which is the area of the circle?
    Should be one of these



    it seems you have some images missing, i can't see them. do you know how to use LaTex?
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    4pir4, I think the r is to the 4th and to the 6th for 16pir6.
    I have no clue about latex and there are no images with the other question

    Here is how it looks after finding the symbols
    Area of circle P is 4πr4 and area of circle Q is16πr6. Which is the ratio of a radius of Q to a radius of P
    The last 4 and the 6 are the powers and I think they go with the r.
    Last edited by sanee66; July 22nd 2007 at 03:14 PM. Reason: removing garbage
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    Quote Originally Posted by sanee66 View Post
    4pir4, I think the r is to the 4th and to the 6th for 16pir6.
    I have no clue about latex and there are no images with the other question

    Here is how it looks after finding the symbols
    [FONT='Times New Roman','serif']Area of circle P is 4πr4 and area of circle Q is16πr6. Which is the ratio of a radius of Q to a radius of P[/font]
    you could type, the first one for instance, as 4*pi*r^4

    doing that avoids confusion.
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    Quote Originally Posted by sanee66 View Post
    4pir4, I think the r is to the 4th and to the 6th for 16pir6.
    I have no clue about latex and there are no images with the other question

    Here is how it looks after finding the symbols
    Area of circle P is 4πr4 and area of circle Q is16πr6. Which is the ratio of a radius of Q to a radius of P
    The last 4 and the 6 are the powers and I think they go with the r.
    here it is:

    E

    Recall that the area of a circle is given by A = \pi r^2

    So, for P: P_{area} = 4 \pi r^4

    \Rightarrow 4 \pi r^4 = \pi r_P^2

    \Rightarrow 4r^4 = r_P^2

    \Rightarrow r_P = \sqrt {4 r^4} = 2r^2

    For Q: Q_{area} = 16 \pi r^6

    \Rightarrow 16 \pi r^6 = \pi r_Q^2

    \Rightarrow 16r^6 = r_Q^2

    \Rightarrow r_Q = \sqrt {16r^6} = 4r^3

    So the ratio of the radius of Q to the radius of P is:

    r_Q : r_P = \frac {r_Q}{r_P} = \frac {4r^3}{2r^2} = 2r
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    I want to thank you so much for this. You are GREAT! That just leaves A and C and I have tried to get them. I don't have any images for C just what I posted and those are the answers I can choose from. I think when I am trying to use the P theorem, I am putting the numbers in the wrong place in the formula for A.
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    Quote Originally Posted by sanee66 View Post
    I want to thank you so much for this. You are GREAT! That just leaves A and C and I have tried to get them. I don't have any images for C just what I posted and those are the answers I can choose from. I think when I am trying to use the P theorem, I am putting the numbers in the wrong place in the formula for A.
    i will look over C again and see if i can decipher what you want to say.

    to A

    see the diagram below:

    Pythagoras theorem says: If the sides of a right-triangle have lengths a, b and c, (where c is the hypotenuse), then the sides can be related as follows:

    a^2 + b^2 = c^2

    In the triangle below, c = 14, a = 10, we want to find b which is x on the diagram.

    a^2 + b^2 = c^2

    \Rightarrow b^2 = c^2 - a^2

    \Rightarrow b = \sqrt { c^2 - b^2 }

    \Rightarrow b = x = \sqrt {14^2 - 10^2} = \sqrt {96}

    So the area of the triangle is:

    A = \frac {1}{2}bh = \frac {1}{2} 10 \cdot \sqrt {96} = 5 \sqrt {96}

    the area of the rhombus is 4 times the area of one triangle.

    so area of rhombus is: A_R = 4 \times 5 \sqrt {96} = 20 \sqrt {96} = 80 \sqrt {6}
    Attached Thumbnails Attached Thumbnails more urgent areas and ratios-tri.gif  
    Last edited by Jhevon; July 22nd 2007 at 05:08 PM.
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    the ratio of the circumference of ANY circle to it's radius is 2 \pi -- always. so your question simply makes no sense
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    The only answers I can choose for the answer to the area of the rhombus are
    184.86
    195.96
    274.34
    276.34
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    Quote Originally Posted by sanee66 View Post
    The only answers I can choose for the answer to the area of the rhombus are
    184.86
    195.96
    274.34
    276.34
    it is 195.96

    that's the answer i gave you--or should be the answer, maybe i simplified incorrectly, let me check

    EDIT: yeah, my mistake. i forgot the 20 that was multiplying the 4*sqrt(6), i corrected it. the answer is 80*sqrt(6) = 195.96
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    Ratio of circumference of circle C to its radius is 12pi. Which is the area of the circle? 36pi,34pi,28pi, or 24pi
    I found a place that says
    The distance around a circle is called the circumference. The distance across a circle through the center is called the diameter. is the ratio of the circumference of a circle to the diameter. Thus, for any circle, if you divide the circumference by the diameter, you get a value close to .
    C=2*pi*r
    So 12pi=2*pi*r
    Then what?
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    Quote Originally Posted by sanee66 View Post
    Ratio of circumference of circle C to its radius is 12pi. Which is the area of the circle? 36pi,34pi,28pi, or 24pi
    I found a place that says
    The distance around a circle is called the circumference. The distance across a circle through the center is called the diameter. is the ratio of the circumference of a circle to the diameter. Thus, for any circle, if you divide the circumference by the diameter, you get a value close to .
    C=2*pi*r
    So 12pi=2*pi*r
    Then what?
    ratio means divide, not equate. the ratio of a circumference of a circle to it's radius is \frac {2 \pi r}{r} = 2 \pi always, 2 \pi cannot equal 12 \pi no matter what. so your question is off
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