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Rate of Change? (The maximum speed of a truck up a steep hill is 50 mph)..?

The maximum speed of a truck up a steep hill is 50 mph with no cargo. With 20 tons of cargo, its maximum speed is 40 mph.

a. Calculate the rate of change and explain the meaning of this rate of change in the context. (Hint: use the information to write 2 points (x1, y1) and (x2, y2), then calculate the rate of change)

b. Write the equation of this function. Define the variables.

c. For what weight of cargo does the equation predict a maximum speed of 0 mph?

1 Answer

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    The maximum speed of a truck up a steep hill is 50 mph with no cargo.

    suggests the point (0,50)

    and

    With 20 tons of cargo, its maximum speed is 40 mph.

    suggests the point (20,40)

    Now

    a. Calculate the rate of change and explain the meaning of this rate of change in the context. (Hint: use the information to write 2 points (x1, y1) and (x2, y2), then calculate the rate of change)...........................................................................................................

    ............................................................................................................................................

    ...y2-1.....50-40...10................................

    m=▬▬ =▬▬ = ▬ = -2.....................................................................................................

    .....x2-x1...0-20....-20..............................................................................................

    That slope is m=-2

    b. Write the equation of this function. Define the variables.

    x = weight of truck in tons

    y = speed of truck in mph

    note: units must be included in definition of variable

    as shown above for full credit.

    We can use point slope form or slope intercept form

    to solve for the unknown equation. I will do it the

    slope-intercept way.

    y = mx b

    y = -2x b

    now substitute in a point

    50 = -2(0) b makes 50 the y intercept

    so

    y = -2x 50

    c. For what weight of cargo does the equation predict a maximum speed of 0 mph

    solution

    0 = -2x 50

    so

    2x = 50 → x = 25

    so the answer is 25 tons.

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