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Alja [10]
3 years ago
8

WILL MARK YOU BRAINLIEST! Hurry please im on a time limit (answer only if you know!)

Advanced Placement (AP)
1 answer:
yaroslaw [1]3 years ago
4 0

Answer:

Uh, what's the question? What do you need help with?..

Explanation:

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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>

8 0
2 years ago
How did the Sudan Refugee Crisis begin?
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1938 hitler demanded self-determination for all Germans in Austria
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3 years ago
From 2010 through 2017 there was a large increase in the number of migrants from Africa to Europe. Which of the following explai
postnew [5]

The impact of migration from 2010 to 2017 created a large increase in immigrants in the continents of Africa and Europe.

During 2010-17 due to the expansion of population there was growth of slums and asylums.

  • Most of the sub-Saharan moved to the European Union nations such as Norway and Sweden. Thus an over a seven-year period these refugees Most of the migrants came from Nigeria, Ghana, and Kenya.
  • The possible impacts that the migrants made were seen in terms of financial support and gains.

Hence option B is correct, as more emigrants sent money home, this money helped in the growth of their country of origin.

Learn more about the From 2010 through 2017 there was a large increase in the number of migrants from Africa to Europe.

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6 0
2 years ago
The energy in fossil fuels is derived from the energy stored in plant and animal matter. Please select the best answer from the
Elis [28]
<h3><u>Answer;</u></h3>

The above statement is True

The energy in fossil fuels is derived from the energy stored in plant and animal matter.

<h3><u>Explanation;</u></h3>
  • Fossil fuels are sources of energy that have developed within the earth over millions of years. Because fossil fuels - oil, natural gas, and coal - take so long to form, they are considered nonrenewable.
  • Fossil fuels are a great source of energy because they originate from living things. Plants and trees use sunlight to make food from carbon dioxide and water, using the process called photosynthesis. The energy from the sun gets stored in the plants and transferred to any animal that eats the plants.
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4 years ago
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A semiarid climate is BEST suited for what type of agriculture?
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<span>C) Herding animals
 The  asals are  ideal for pastoralist activities. The rotational nature that semi arid areas demand is only ideal with herding activities.  In as much as the ecosystem is balanced, the areas are viable options for herdsmen.
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6 0
4 years ago
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