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2 years ago

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An ice-hockey puck is slid along ice in a straight line. The puck travels at a steady speed of 20 ms^-1 and experiences no frict

ional force. How far does the puck travel in 2.5 s?
a. 5 m
b. 8 m
c. 25 m
d. 50 m

1 answer:

laila [671]2 years ago

7 0

Answer:

d. 50 m

Step-by-step explanation:

1. You have the following information given in the problem above:

- The speed of the puck is 20 $\frac{m}{s}$ and experiences no frictional force.

- The time is 2.5 seconds.

2. Then, to calculate the distance, you must apply the following formula:

$d=Vt$

Where $d$ is the distance, $V$ is the speed and $t$ is the time.

3. Now, you must substitute values into the formula, as below:

$d=(20\frac{m}{s})(2.5s)$

4. Therefore, the result is:

$d=50m$

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2 years ago

Determine the area (in units2) of the region between the two curves by integrating over the x-axis. y = x2 − 24 and y = 1

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Answer:

The area of the region between the two curves by integration over the x-axis is 9.9 square units.

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This case represents a definite integral, in which lower and upper limits are needed, which corresponds to the points where both intersect each other. That is:

$x^{2} - 24 = 1$

Given that resulting expression is a second order polynomial of the form $x^{2} - a^{2}$ , there are two real and distinct solutions. Roots of the expression are:

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$x^{2} - 24 > 0$

$x^{2} > 24$

$x < -4.899$ and $x > 4.899$ .

Therefore, exists two sub-intervals: $[-5, -4.899]$ and $\left[4.899,5\right]$ . Besides, $x^{2} - 24 > y = 1$ in each sub-interval. The definite integral of the region between the two curves over the x-axis is:

$A = \int\limits^{-4.899}_{-5} [{1 - (x^{2}-24)]} \, dx + \int\limits^{4.899}_{-4.899} \, dx + \int\limits^{5}_{4.899} [{1 - (x^{2}-24)]} \, dx$

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$A = 25\cdot x \right \left|\limits_{-5}^{-4.899} -\frac{1}{3}\cdot x^{3}\left|\limits_{-5}^{-4.899} + x\left|\limits_{-4.899}^{4.899} + 25\cdot x \right \left|\limits_{4.899}^{5} -\frac{1}{3}\cdot x^{3}\left|\limits_{4.899}^{5}$

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The area of the region between the two curves by integration over the x-axis is 9.9 square units.

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