# 10.6 Applications  (Page 3/4)

 Page 3 / 4

## Practice set e

A study of the air quality in a particular city by an environmental group suggests that $t$ years from now the level of carbon monoxide, in parts per million, in the air will be

$A=0.2{t}^{2}+0.1t+5.1$

(a) What is the level, in parts per million, now?

(b) How many years from now will the level of carbon monoxide be at 8 parts per million? Round to the nearest tenth.

(a). $5.1$ parts per million (b). $3.6$ years

## Sample set f

A contractor is to pour a concrete walkway around a swimming pool that is 20 feet wide and 40 feet long. The area of the walkway is to be 544 square feet. If the walkway is to be of uniform width, how wide should the contractor make it?

Step 1:  Let $x$ = the width of the walkway.
Step 2:  A diagram will help us to get the equation.

(Area of pool and walkway) — (area of pool) = (area of walkway)
$\left(20+2x\right)\left(40+2x\right)-20·40=544$
$\begin{array}{lllllll}\text{Step\hspace{0.17em}3:}\hfill & \hfill & \hfill \left(20+2x\right)\left(40+2x\right)-20·40& =\hfill & 544\hfill & \hfill & \hfill \\ \hfill & \hfill & \hfill 800+120x+4{x}^{2}-800& =\hfill & 544\hfill & \hfill & \hfill \\ \hfill & \hfill & \hfill 120x+4{x}^{2}& =\hfill & 544\hfill & \hfill & \hfill \\ \hfill & \hfill & \hfill 4{x}^{2}+120x-544& =\hfill & 0\hfill & \hfill & \text{Divide\hspace{0.17em}each\hspace{0.17em}term\hspace{0.17em}by\hspace{0.17em}4}.\hfill \\ \hfill & \hfill & \hfill {x}^{2}+30x-136& =\hfill & 0\hfill & \hfill & \text{Solve\hspace{0.17em}by\hspace{0.17em}factoring}.\hfill \\ \hfill & \hfill & \hfill \left(x-4\right)\left(x+34\right)& =\hfill & 0\hfill & \hfill & \begin{array}{l}\text{(This\hspace{0.17em}is\hspace{0.17em}difficult\hspace{0.17em}to\hspace{0.17em}factor\hspace{0.17em}so\hspace{0.17em}we\hspace{0.17em}may\hspace{0.17em}}\\ \text{wish\hspace{0.17em}to\hspace{0.17em}use\hspace{0.17em}the\hspace{0.17em}quadratic\hspace{0.17em}formula}\text{.)\hspace{0.17em}}\end{array}\hfill \end{array}$
$\begin{array}{lllll}x-4=0\hfill & \hfill & \text{or}\hfill & \hfill & x+34=0\hfill \\ x=4\hfill & \hfill & \text{or}\hfill & \hfill & x=-34\text{\hspace{0.17em}has\hspace{0.17em}no\hspace{0.17em}physical\hspace{0.17em}meaning}\text{.}\hfill \end{array}$
Check a width of 4 feet as a solution.
$\begin{array}{lllll}\text{Step\hspace{0.17em}4:}\hfill & \hfill & \text{Area\hspace{0.17em}of\hspace{0.17em}pool\hspace{0.17em}and\hspace{0.17em}walkway\hspace{0.17em}}\hfill & =\hfill & \left(20+2·4\right)\left(40+2·4\right)\hfill \\ \hfill & \hfill & \hfill & =\hfill & \left(28\right)\left(48\right)\hfill \\ \hfill & \hfill & \hfill & =\hfill & 1344\hfill \end{array}$
Area of pool = (20)(40) = 800
Area of walkway = $\begin{array}{ccc}1344-800=544& & \text{Yes,\hspace{0.17em}this\hspace{0.17em}is\hspace{0.17em}correct}\text{.}\end{array}$
This solution checks.
Step 5:  The contractor should make the walkway 4 feet wide.

## Practice set f

A contractor is to pour a concrete walkway around a swimming pooi that is 15 feet wide and 25 feet long. The area of the walkway is to be 276 square feet. If the walkway is to be of uniform width, how wide should the contractor make it?

3 ft wide

## Exercises

Some of the following problems have actual applications and some are intended only as logic developers. A calculator may be helpful. The problems appear in groups and correspond to the noted Sample Set problem.

## Sample set a—type problems

The manufacturer of electronic fuel injectors determines that the number $N$ of injectors sold is related to the price $x$ per injector by $N=22x-{x}^{2}.$ At what price should the manufacturer price the injectors so that 112 of them are sold?

$8\text{\hspace{0.17em}}\text{or}\text{\hspace{0.17em}}14$

The owner of a stained-glass shop determines that the number $N$ of pieces of a particular type of glass sold in a month is related to the price $x$ per piece by $N=21x-{x}^{2}.$ At what price should the shop buyer price the glass so that 162 sell?

It is estimated that $t$ years from now the population of a certain city will be

$P={t}^{2}-15t+12,036$

(a) What is the population now?

(b) How many years from now will the population be 12,000?

$\text{(a)\hspace{0.17em}}12,036\text{\hspace{0.17em}\hspace{0.17em}(b)\hspace{0.17em}}3\text{\hspace{0.17em}and\hspace{0.17em}}12\text{\hspace{0.17em}years\hspace{0.17em}from\hspace{0.17em}now}$

It is estimated that $t$ years from now the population of a certain city will be

$P={t}^{2}-16t+24,060$

(a) What is the population now?

(b) How many years from now will the population be 24,000?

If an object is thrown vertically upward, its height $h$ , above the ground, in feet, after $t$ seconds is given by $h={h}_{0}+{v}_{0}t-16{t}^{2}$ , where ${h}_{0}$ is the initial height from which the object is thrown and ${v}_{0}$ is the initial velocity of the object. Using this formula and an approach like that of Sample Set A, solve this problem.

A ball thrown vertically into the air has the equation of motion $h=48+32t-16{t}^{2}.$

(a) How high is the ball at $t=0$ (the initial height of the ball)?

(b) How high is the ball at $t=1$ (after 1 second in the air)?

(c) When does the ball hit the ground? ( Hint: Determine the appropriate value for $h$ then solve for $t$ .)

$\text{(a)\hspace{0.17em}}48\text{\hspace{0.17em}feet\hspace{0.17em}\hspace{0.17em}(b)\hspace{0.17em}64\hspace{0.17em}feet\hspace{0.17em}\hspace{0.17em}(c)\hspace{0.17em}}t=3$

can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
im not good at math so would this help me
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!