_________ is the form of nitrogen plants rely on most.

What is a primary cause of LO/TO accidents?

Bogdan [553]

Not doing any of this is why Preventing LO/TO accidents begins with training three groups of employees: Authorized employees generally include your electricians, maintenance personnel, and some machine operators.

7 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 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

How is federalism a tool for the protection against "majority tyranny" and therefore a protection for the minority?

sergejj [24]

Federalism means the way of government where there are various levels of government. As different level government system is more accessible for general people where they can say what they want or express their opinions about something being right or wrong. So in my opinion for the most part Federalism is a tool for the protection against "majority tyranny" and therefore a protection for the minority. To explain this in an example, if a state banns all the women to be employed at any level, the federal government will intervene and stop this unjust decision, or vice versa.

4 0

3 years ago

In Machiavelli's the prince, list 3 things rulers should avoid

NikAS [45]

Answer:

Explanation:

Which of the following is a precaution a worker should take to avoid on-the-job fall hazards?

8 0

3 years ago

In the statement "Critical thinking requires reasoned judgments," the word reasoned means

timama [110]

Answer:

In the statement "Critical thinking requires reasoned judgments," the word reasoned means logical and well thought out.

Explanation:

7 0

2 years ago