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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

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.

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

$ 8 or $ 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 = 21 x 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 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

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?

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

Questions & Answers

how can chip be made from sand
Eke Reply
are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Selected topics in algebra. OpenStax CNX. Sep 02, 2015 Download for free at http://legacy.cnx.org/content/col11877/1.2
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