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Math Help - Two Word Problems

  1. #1
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    Two Word Problems

    A contractor purchases a piece of equipment for $36,500 that costs an average of $9.25 per hour for fuel and maintenance. The equipment operator is paid $13.50 per hour, and customers are charged $30 per hour.

    Write an equation for the cost C of operating this equipment for t hours.

    Write an equation for the revenue R derived from t hours of use.

    Find the break-even point for this equipment by finding the time at which R = C.


    AND

    A large room contains two speakers that are 4 meters apart. The sound intensity I of one speaker is k times that of the other, as indicated in the attached image.

    Find the equation of all locations (x,y) where one could stand and receive equal amounts of sound from both speakers. (I have the feeling that it's a circle but I don't know where to start)

    Graph the equation for the case k = 3.

    Describe the set of locations of equal sound as k becomes very large.
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  2. #2
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    Quote Originally Posted by superfly8912 View Post
    A contractor purchases a piece of equipment for $36,500 that costs an average of $9.25 per hour for fuel and maintenance. The equipment operator is paid $13.50 per hour, and customers are charged $30 per hour.

    Write an equation for the cost C of operating this equipment for t hours.

    C(t) = 36500 + 9.25t + 13.50t = 36500 + 22.75t

    Write an equation for the revenue R derived from t hours of use.

    R(t) = 30t

    Find the break-even point for this equipment by finding the time at which R = C.

    do it


    AND

    A large room contains two speakers that are 4 meters apart. The sound intensity I of one speaker is k times that of the other, as indicated in the attached image.

    Find the equation of all locations (x,y) where one could stand and receive equal amounts of sound from both speakers. (I have the feeling that it's a circle but I don't know where to start)

    Graph the equation for the case k = 3.

    Describe the set of locations of equal sound as k becomes very large.

    you want to find the set of points (x,y) such that the distance from (x,y) to (4,0) is 3 times greater than the distance from (x,y) to the origin.

    distance from (x,y) to the origin is \textcolor{red}{\sqrt{x^2+y^2}}

    distance from (x,y) to the point (4,0) is \textcolor{red}{\sqrt{(x-4)^2 + y^2}}

    \textcolor{red}{3\sqrt{x^2+y^2} = \sqrt{(x-4)^2 + y^2}}
    ...
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