Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The amount of a particular pollutant $p$ from a power plant in the air above the plant depends on the wind speed $s$ , among other things, with the relationship between $p$ and $s$ approximated by $p=18-0.02s^{2}$ , with $s$ in miles per hour. $\newline$ a. Find the value(s) of $s$ that will make $p=0$ . $\newline$ b. What does $p=0$ mean in this application? $\newline$ c. What solution to $0=18-0.02s^{2}$ makes sense in the context of this application?

View step-by-step help

View step-by-step help

Evaluate a linear function: word problems

Full solution

Q. The amount of a particular pollutant

p

from a power plant in the air above the plant depends on the wind speed

s

, among other things, with the relationship between

p

and

s

approximated by

p=18-0.02s^{2}

, with

s

in miles per hour.

\newline

a. Find the value(s) of

s

that will make

p=0

.

\newline

b. What does

p=0

mean in this application?

\newline

c. What solution to

0=18-0.02s^{2}

makes sense in the context of this application?

Isolate $s^2$ term: To find the value(s) of $s$ that will make $p=0$ , we need to solve the equation $0=18-0.02s^{2}$ for $s$ .
Divide by $0.02$ : Rearrange the equation to isolate the $s^2$ term. This gives us $0.02s^{2} = 18$ .
Calculate $s^2$ : Divide both sides of the equation by $0.02$ to solve for $s^2$ . This gives us $s^{2} = \frac{18}{0.02}$ .
Take square root: Calculate the right side of the equation to find the value of $s^2$ . This gives us $s^{2} = 900$ .
Calculate $s$ : Take the square root of both sides to solve for $s$ . This gives us $s = \pm\sqrt{900}$ .
Consider positive value: Calculate the square root of $900$ to find the values of $s$ . This gives us $s = \pm30$ .
Interpret $p=0$ : In the context of this application, negative wind speed does not make sense. Therefore, we only consider the positive value of $s$ . This gives us $s = 30$ mph.
Confirm solution: Interpret the result of $p=0$ in this context. A pollutant level of zero means that there is no pollutant from the power plant in the air above the plant at this wind speed.
Confirm solution: Interpret the result of $p=0$ in this context. A pollutant level of zero means that there is no pollutant from the power plant in the air above the plant at this wind speed.Confirm that the solution makes sense in the context of the application. A wind speed of $30$ mph is a reasonable and possible value, and it would be the wind speed at which the pollutant level is reduced to zero due to dispersion.

More problems from Evaluate a linear function: word problems

Question

Igbo uploaded a funny video of his cat onto a website.

\newline

The relationship between the elapsed time,

d

, in days, since the video was first uploaded, and the total number of views,

V(d)

, that the video received is modeled by the following function.

\newline

V(d)=10^{1.5 d}

\newline

How many days will it take for the video to receive

1,000,000

views? Round your answer, if necessary, to the nearest hundredth.

\newline

Posted 3 months ago

Question

Hannah reads at a constant rate of

3

8

\newline

Write an equation that shows the relationship between

p

, the number of pages she reads, and

m

, the number of minutes she spends reading.

\newline

Do NOT use a mixed number.

Posted 3 months ago

Question

20 l+25 g-10

gives the number of dollars that Josie makes from mowing

l

lawns and raking

g

\newline

How many dollars does Josie make from raking

4

gardens and mowing

3

\newline

Posted 3 months ago

Question

The population of a town grows at a rate of

r(t)

people per year (where

t

is time in years).

\newline

\int_{2}^{4} r(t) d t

\newline

1

\newline

(A) The change in number of people between the second and the fourth year.

\newline

(B) The time it took for the town to grow from a population of

2

people to a population of

4

\newline

(C) The number of people in the town on the fourth year.

\newline

(D) The average rate at which the population grew between the second and the fourth year.

Posted 3 months ago

Question

The cumulative profit a business has earned is changing at a rate of

r(t)

dollars per day (where

t

is the time in days). In the first

30

days, the business earned a cumulative profit of

\$ 1700

\newline

1700+\int_{30}^{90} r(t) d t

\newline

1

\newline

(A) The time it takes for the cumulative profit to increase another

\$ 1700

after the first

30

\newline

(B) The cumulative profit the business has earned as of day

90

\newline

(C) The rate at which the cumulative profit was increasing when

t=90

\newline

(D) The change in the cumulative profit between days

30

90

Posted 3 months ago

Question

A habitat of prairie dogs can support

m

\newline

The habitat's population,

p

, grows proportionally to the product of the current population and the difference between

m

p

\newline

Which equation describes this relationship?

\newline

1

\newline

\frac{d p}{d t}=k p(m-p)

\newline

\frac{d p}{d t}=\frac{k m}{m-p}

\newline

\frac{d p}{d t}=\frac{k p}{m-p}

\newline

\frac{d p}{d t}=k m(m-p)

Posted 3 months ago

Question

A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. After

11

months, he weighed

140

kilograms. He gained weight at a rate of

5.5

kilograms per month.

\newline

y

represent the sumo wrestler's weight (in kilograms) after

x

\newline

Complete the equation for the relationship between the weight and number of months.

\newline

y=\square

Posted 2 months ago

Question

Seb bikes at a constant rate of

20

kilometers per hour.

1

. Write an equation that represents the distance, in kilometers, Seb travels

(b)

based on how many hours he bikes

(t)

2

. How far will Seb travel if he bikes at this rate for

3

\_

Posted 2 months ago

Question

\newline

\frac{1}{2}

\newline

\newline

\omega=\sqrt{\frac{k}{m}}

. This is the formula for the angular frequency

\newline

\omega

\newline

m

suspended from a spring of spring constant

\newline

k

. Solve this formula for

\newline

k

\newline

\newline

Posted 2 months ago

Question

Consider the following quadratic function.

\newline

f(x)=-2 x^{2}-8 x-13

\newline

(a) Write the equation in the form

f(x)=a(x-h)^{2}+k

. Then give the vertex of its graph.

Posted 6 hours ago