A craft store owner has 2,016 paint brushes if she wants to put them in packages of 28 how many packages can she make

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 NET DECREASE 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.

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

8 0

1 year ago

Why is the ending of Animal Farm ironic?

sleet_krkn [62]

Answer:

B because it's ironic for the animals to rebel against human when one of the animal acted just like a human in the end.

8 0

3 years ago

When you reflect on what you were reading in your history book and question how much of that information you remember or think i

tia_tia [17]

Answer:

A- Metacognition

Explanation:

The term metacognition refers to processes used to monitor and regulate one's thinking, understanding, and performance. It includes a critical awareness of one's thinking and learning and oneself as a thinker and learner. For example, you may be aware that you have trouble remembering people's names and remind yourself that you should try harder to remember the name of the person you met. Metacognitive strategies are often used to help students understand the way they learn and enhance their performance.

3 0

2 years ago

Your boss has asked you to e-mail a client to let her know that the company will be late in delivering a report she's requested.

Papessa [141]

inthink the answer is a

3 0

3 years ago

Read 2 more answers

1. How did Indian religion differ from the cultural traditions in China?

ra1l [238]

Answer:

The main religions of China were Confucianism, Taoism, and Legalism. The central religions in India were Hinduism and Buddhism. Both Ancient China and India had religious teachers that invented these prevalent religions. Confucius invented Confucianism, Lao Tzu invented Taoism, and Hsün Tzu invented Legalism in China.

Hope thsi Helps

Explanation:

8 0

2 years ago