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VLD [36.1K]
3 years ago
11

PLEASE HELP! I will give brainliest! If an object is dropped from a tall building, then the distance (in feet) it has fallen aft

er t seconds is given by the function d(t)=16t^2.
Determine the average speed (rate of change) between 3 and 8 seconds.
Mathematics
1 answer:
siniylev [52]3 years ago
8 0

Answer:

160ms^{-1}

Step-by-step explanation:

d(t)=16t^2\\

To work out rate of change of a function, you must differentiate it.

\frac{\Delta d(t)}{\Delta t} =32t

d'(8)-d'(3)=32*8 - 32*3=32*5=160ms^{-1}

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Step-by-step explanation:

This seems to be calculus 1.

<u>Question a</u>

We have -2x^3 + 5x^2 + 9

m = slope = derivative

Find the derivative / slope of -2x^3 + 5x^2 + 9

We do this by differentiating the polynomials. There are a few methods to do this but I am going to use the power rule, which we multiply the constant by the exponent on the variable and subtract one from the exponent.

\frac{d}{dx}(-2x^3 + 5x^2 + 9)

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<em>Now that we have this information, we can answer question b</em>

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<u>The tangent line for Point (1, 12)</u>

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Find the slope at the point.

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y(x) - 13 = -4(x - 2)

y(x) = -4x + 21


Now graph the lines, which I have done and you can see by viewing the image I have attached.


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