A ball thrown in the air has a height of y = – 16x² + 50x + 3 feet after x seconds. a) What are the units of measurement for the rate of cha

Question

A ball thrown in the air has a height of y = – 16x² + 50x + 3 feet after x seconds. a) What are the units of measurement for the rate of change of y? b) Find the rate of change of y between x = 0 and x = 2?

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Minh Khuê 2 weeks 2021-09-02T19:55:59+00:00 1 Answers 0 views 0

Answers ( )

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    2021-09-02T19:57:09+00:00

    Answer:

    (a) ft/s

    (b) 1ft/s

    Step-by-step explanation:

    Given equation;

    y = (- 16x² + 50x + 3)ft       ————-(i)

    Where;

    y is measured in feet(ft)

    x is measured in seconds(s).

    (a) The rate of change of y with respect to x is found by dividing the total change in y by the total change in x. i.e

    Δy / Δx

    Where;

    Δy = y₂ – y₁  

    Δx = x₂ – x₁

    ∴ Δy / Δx = \frac{y_2 - y_1}{x_2 - x_1}              ————–(ii)

    Since y is measured in feet, Δy will also be measured in feet.

    Also, since x is measured in seconds, Δx will also be measured in seconds.

    Therefore, the rate of change of y with respect to x (Δy / Δx) will be measured in feet per second (ft/s)

    (b) The rate of change of y between x  = 0 and x = 2 can be found by using equation (ii)

    Where;

    y₂ is the value of y at x = 2 found by substituting x = 2 into equation (i)

    y₁ is the value of y at x = 0 found by substituting x = 0 into equation (i)

    => y₂ =  – 16(2)² + 50(2) + 3 = 39

    => y₁ =  – 16(1)² + 50(1) + 3 = 37

    Now, substitute the values of y₂, y₁, x₂ and x₁  into equation (ii)

    Δy / Δx = \frac{39 - 37}{2 - 0}  

    Δy / Δx = \frac{2}{2}

    Δy / Δx = 1

    Therefore, the rate of change of y is 1 ft/s

     

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