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jenyasd209 [6]
3 years ago
11

Match each force with the correct description. 1. a force that opposes motion electrical force 2. equal and opposite forces appl

ied to the ends of an object normal force 3. affects objects moving through air friction 4. press the surfaces of static, or unmoving, objects together air resistance 5. force of attraction between masses gravity 6. force which involve charged atoms tension
Advanced Placement (AP)
1 answer:
lesya [120]3 years ago
5 0

1. a force that opposes motion = friction

2. equal and opposite forces applied to the ends of an object = normal force

3. affects objects moving through air = air resistance

4. press the surfaces of static, or unmoving, objects together = tension

5. force of attraction between masses = gravity

6. force which involve charged atoms = electrical force

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C.25% of children are in someone else's home
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3 years ago
1. The rate at which people enter a movie theater on a given day is modeled by the function S defined by S(t) = 80 -12 cos 6 The
Arlecino [84]

Hi there!

a.

To find the total amount of people that have ENTERED by t = 20, we must take the integral of the appropriate function.

\text{Amount that entered} = \int\limits^{20}_{10} {S(t)} \, dt \\\\ = \int\limits^{20}_{10} {80 - 12cos(\frac{t}{5})} \, dt

Evaluate using a calculator:

= 899.97 \approx \boxed{900\text{ people}}

b.

To solve, we can find the total amount of people that have entered of the interval and subtract the total amount of people that have left from this value.

In other terms:
\text{Amount of people} = \int\limits^{20}_{10} {S(t)} \, dt - \int\limits^{20}_{10} {R(t)} \, dt

We can evaluate using a calculator (math-9 on T1-84):


\text{\# of people} = \int\limits^{20}_{10} {80-12cos(\frac{t}{5})} \, dt - \int\limits^{20}_{10} {12e^{\frac{t}{10}}+20} \, dt

= 899.97 - 760.49 = 139.47 \approx \boxed{139 \text{ people}}

c.

If:
P(t) = \int\limits^t_{10} {S(t) - R(t)} \, dt

Then:

\frac{dP}{dt}  = P'(t)= \frac{d}{dt}\int\limits^t_{10} {S(t) - R(t)} \, dt  = S(t) - R(t)

Evaluate at t = 20:


S(20) = 80 - 12cos(\frac{20}{5}) = 87.844\\\\R(20) = 12e^{\frac{20}{10}} + 20 = 108.669

S(20) - R(20) = 87.844 - 108.669 = -20.823

This means that at t = 20, there is a <u>NET DECREASE</u> of people at the movie theater of around 20.823 (21) people per hour.

d.

To find the maximum, we must use the first-derivative test.

Set S(t) - R(t) equal to 0:

80 - 12cos(\frac{t}{5}) - 12e^{\frac{t}{10}} - 20 = 0\\\\60 - 12(cos(\frac{t}{5}) + e^{\frac{t}{10}})= 0

Graph the function with a graphing calculator and set the function equal to y = 0:

According to the graph, the graph of the first derivative changes from POSITIVE to NEGATIVE at t ≈ 17.78 hours, so there is a MAXIMUM at this value.

<u>Thus, at t = 17.78 hours, the amount of people at the movie theater is a MAXIMUM.</u>

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the way the Constitution is interpreted.

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Can someone please explain this to me please?
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Answer:

Explanation:

14)  Horrible English.

You can't have more than 2600 lbs on the elevator

or

You can have no more than 2600 lbs on the elevator.

"Can't have no more" is a double negative and quite confusing. It actually mean you Must have more than 2600 lbs on the elevator.

500 + 140x ≤ 2600

500 - 500 + 140x ≤ 2600 - 500

140x ≤ 2100

140x/140 ≤ 2100/140

x ≤ 15 people

15)  $2.49(1.80) = $4.48

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