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2 years ago

One of the illegal drugs that some top Olympic athletes have been caught using is

Advanced Placement (AP)

1 answer:

Harman [31]2 years ago

5 0

Answer:

Red blood cells can increase stamina and can boost the energy within the athlete.

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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!

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:

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

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):

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

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

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 NET DECREASE of people at the movie theater of around 20.823 (21) people per hour.

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.

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

8 0

1 year ago

A market economy is regulated by the interactions between which two things

antiseptic1488 [7]

I just took both AP micro and macro. I don't think any answer would be more appropriate than suppliers and demanders.

3 0

2 years ago

Read 2 more answers

You must use headlights when driving

Ulleksa [173]

Answer:

False

Explanation:

Headlights are only required when it's dark and when it's raining.

6 0

2 years ago

Tama O Mali (ESP talaga to wla kasi subject eh)

kow [346]

1. Tama

2.Tama

3.Tama

4.Mali

5.Tama

6.Tama

Brainliest Please

7 0

2 years ago

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Which list places the layers of the sun in the correct order from outermost to innermost?

miss Akunina [59]

(A) Corona, chromosphere, photosphere

Explanation:

Photosphere - it is the Sun’s deepest layer, and the layer visible to human eyes directly from the Earth. It is also called the solar surface

Chromosphere - This layer of the Sun is located between 250 miles and 1300 miles above the photosphere. The chromosphere has temperatures around 4000K at the base, and 8000K at the top.

Transition Region - This layer is very thin with a size of about 60 miles, and it is present between corona and the chromosphere.

Corona - This layer is the Sun’s outermost layer. It starts at roughly 1300 miles over the photosphere and it has no upper limit. Its temperature is between 500,000 K to 1 million K.

8 0

3 years ago