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Math Help - Are these correct?

  1. #1
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    Are these correct?

    1) Find f(2+h), f(x+h), and (f(x+h) - f(x))/h
    f(x)= x/(x+1)
    My answers: f(2+h) = (2+h)/(3+h)
    f(x+h)= (x+h)/(x+h+1)
    (f(x+h) - f(x))/h= 1/[(x+1)(x+h+1)]

    2) The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs in one day and $4800 to produce 300 chairs in one day.
    (a) Express the cost as a function of the number of chairs produced, assuming that it is linear.
    (b) what is the slope of the graph and what does it represent?
    (c) what is the y-intercept of graph and what does it represent?
    My answers:
    (a) c(x)=13x+900
    (b) slope is 13 which represents the price to produce each chair
    (c)the y-intercept is 900 which represents the cost function when x=0
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  2. #2
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    Quote Originally Posted by yoman360 View Post
    1) Find f(2+h), f(x+h), and (f(x+h) - f(x))/h
    f(x)= x/(x+1)
    My answers: f(2+h) = (2+h)/(3+h) CORRECT!
    f(x+h)= (x+h)/(x+h+1) CORRECT!
    (f(x+h) - f(x))/h= 1/[(x+1)(x+h+1)]
    \frac{f(x+h) - f(x)}{h}
    \begin{aligned}<br />
&= \frac{\frac{x + h}{x + h + 1} - \frac{x}{x + 1}}{h} \\<br />
&= \frac{\frac{(x+h)(x + 1) - x(x + h + 1)}{(x + 1)(x + h + 1)}}{h} \\<br />
&= \frac{\frac{x^2 + hx + x + h - x^2 - hx - x}{(x + 1)(x + h + 1)}}{h} \\<br />
&= \frac{\frac{h}{(x + 1)(x + h + 1)}}{h}<br />
\end{aligned}
    \begin{aligned}<br />
&= \frac{h}{(x + 1)(x + h + 1)}\cdot \frac{1}{h} \\<br />
&= \frac{1}{(x + 1)(x + h + 1)}<br />
\end{aligned}

    CORRECT!


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  3. #3
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    Thanks!
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  4. #4
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    Quote Originally Posted by yoman360 View Post
    1) Find f(2+h), f(x+h), and (f(x+h) - f(x))/h
    f(x)= x/(x+1)
    My answers: f(2+h) = (2+h)/(3+h)
    f(x+h)= (x+h)/(x+h+1)
    (f(x+h) - f(x))/h= 1/[(x+1)(x+h+1)]
    As yeongil said, your answers are correct.

    2) The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs in one day and $4800 to produce 300 chairs in one day.
    (a) Express the cost as a function of the number of chairs produced, assuming that it is linear.
    (b) what is the slope of the graph and what does it represent?
    (c) what is the y-intercept of graph and what does it represent?
    My answers:
    (a) c(x)=13x+900[/quote]
    Important point! An answer like this is meaningless if you don't specify what your variables mean! You must say "x is the number of chairs produced in one day and c(x) is the cost, in dollars, to produce those chairs".

    Given that, is your "c(x)= 13x+ 900" correct? It's easy to check. If x= 100, then c(x)= 13(100)+ 900= 1300+ 900= 2200 (dollars). If x= 300, then c(x)= 13(300)+ 900= 3900+ 900= 4800 (dollars). Those are the numbers we are given so your formula is correct!

    (b) slope is 13 which represents the price to produce each chair
    Yes, that is correct.

    (c)the y-intercept is 900 which represents the cost function when x=0
    That is also known as "overhead", the cost that cannot be attributed to individual chairs, such as rental for the building, equipment you bought to make the chairs, things you have to pay for whether you make chairs or not.
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