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kodGreya [7K]
3 years ago
9

Let f(x) = x2 − 3x − 7. Find f(−3)

Mathematics
1 answer:
uranmaximum [27]3 years ago
3 0
Substituting -3 for x, we have:  (-3)^2-3*-3-7.  This simplifies to 9+9-7, or 11.
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Answer:

The tip of the man shadow moves at the rate of \frac{20}{3} ft.sec

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Let's draw a figure that describes the given situation.

Let "x" be the distance between the man and the pole and "y" be distance between the pole and man's shadows tip point.

Here it forms two similar triangles.

Let's find the distance "y" using proportion.

From the figure, we can form a proportion.

\frac{y - x}{y} = \frac{6}{15}

Cross multiplying, we get

15(y -x) = 6y

15y - 15x = 6y

15y - 6y = 15x

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y = \frac{15x}{9\\} y = \frac{5x}{3}

We need to find rate of change of the shadow. So we need to differentiate y with respect to the time (t).

\frac{dy}{t} = \frac{5}{3} \frac{dx}{dt} ----(1)

We are given \frac{dx}{dt} = 4 ft/sec. Plug in the equation (1), we get

\frac{dy}{dt} = \frac{5}{3} *4 ft/sect\\= \frac{20}{3} ft/sec

Here the distance between the man and the pole 45 ft does not need because we asked to find the how fast the shadow of the man moves.

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