How many minutes are students given to complete the evidence-based reading section of the PSAT?A. 45B. 30C. 60D. 35

Describe Yahoo's homepage as a source of information

Gwar [14]

Unreliable........lol

4 0

3 years ago

If Congress passes a law that conflicts with the Constitution, which one are we required to follow: the law or the Constitution?

Ostrovityanka [42]

Answer:

The constitution

Explanation:

the constitution is the whole basis for our rights and freedoms as humans. Congress SHOULDN'T ever pass anything that goes against it, but if they were to, you always follow thee constitution unless they want to work on amending it.

6 0

2 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>

8 0

1 year ago

The following was a government response to the growing interest in socialist and communist movements.

Alenkasestr [34]

Answer:

A. LaborUnions, Legislation on labor and work reform

Explanation:

Unionized labor often improves the wages corporations pay across the committee to their workers. ... Collective agreement arrangements generate significant advantages for workers who may not be interested in raising production because they earn a higher salary.

The Labor Reform Act of 1977 was a recommended United States Act of Congress on US labor legislation that never came into dominance. It would have modified the labor law to bring it in line with modern advancements and global standards, by eliminating obstacles from employers to unions structure in the workplace.

6 0

2 years ago

The second derivative of x<img src="https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2By%5E%7B2%7D%20%3D25" id="TexFormula1" title="x^{2}

Gala2k [10]

Hahahahaha so i was that a hahahahaha amp u owy owas was my time amp what i is a great amp thank you:)

7 0

2 years ago