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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 + 0.1 t + 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

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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.
    A rectangle with side length forty plus two x and width of twenty plus two x with an inner rectangle x units from the outside rectangle throughout. The length of the inner rectangle is labeled as forty and the width is labeled as twenty.
     (Area of pool and walkway) — (area of pool) = (area of walkway)
      ( 20 + 2 x ) ( 40 + 2 x ) 20 · 40 = 544
Step 3: ( 20 + 2 x ) ( 40 + 2 x ) 20 · 40 = 544 800 + 120 x + 4 x 2 800 = 544 120 x + 4 x 2 = 544 4 x 2 + 120 x 544 = 0 Divide each term by 4 . x 2 + 30 x 136 = 0 Solve by factoring . ( x 4 ) ( x + 34 ) = 0 (This is difficult to factor so we may  wish to use the quadratic formula .) 
      x 4 = 0 or x + 34 = 0 x = 4 or x = 34  has no physical meaning .
Check a width of 4 feet as a solution.
      Step 4: Area of pool and walkway  = ( 20 + 2 · 4 ) ( 40 + 2 · 4 ) = ( 28 ) ( 48 ) = 1344
     Area of pool = (20)(40) = 800
     Area of walkway = 1344 800 = 544 Yes, this is correct .
     This solution checks.
Step 5:  The contractor should make the walkway 4 feet wide.

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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

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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 = 22 x x 2 . At what price should the manufacturer price the injectors so that 112 of them are sold?

$ 8 or $ 14

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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 = 21 x x 2 . At what price should the shop buyer price the glass so that 162 sell?

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

P = t 2 15 t + 12 , 036

(a) What is the population now?

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

(a)  12 , 036   (b)  3  and  12  years from now

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

P = t 2 16 t + 24 , 060

(a) What is the population now?

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

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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 + 32 t 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 .)

(a)  48  feet  (b) 64 feet  (c)  t = 3

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Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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