# 3.3 Quadratic equations: applications  (Page 4/4)

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A woman’s glasses accidently fall off her face while she is looking out of a window in a tall building. The equation relating $h$ , the height above the ground in feet, and $t$ , the time in seconds her glasses have been falling, is $h=64-16{t}^{2}.$

(a) How high was the woman’s face when her glasses fell off?

(b) How many seconds after the glasses fell did they hit the ground?

## Sample set b—type problems

The length of a rectangle is 6 feet more than twice its width. The area is 8 square feet. Find the dimensions.

$\text{length}=8;\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{width}=1$

The length of a rectangle is 18 inches more than three times its width. The area is 81 square inches. Find the dimensions.

The length of a rectangle is two thirds its width. The area is 14 square meters. Find the dimensions.

$\text{width}=\sqrt{21}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{length}=\text{\hspace{0.17em}}\frac{2}{3}\sqrt{21}$

The length of a rectangle is four ninths its width. The area is 144 square feet. Find the dimensions.

The area of a triangle is 14 square inches. The base is 3 inches longer than the height. Find both the length of the base and height.

$b=7;\text{\hspace{0.17em}}\text{\hspace{0.17em}}h=4$

The area of a triangle is 34 square centimeters. The base is 1 cm longer than twice the height. Find both the length of the base and the height.

## Sample set c—type problems

The product of two consecutive integers is 72. Find them.

$-9,-8\text{\hspace{0.17em}}\text{or}\text{\hspace{0.17em}}8,9$

The product of two consecutive negative integers is 42. Find them.

The product of two consecutive odd integers is 143. Find them. ( Hint: The quadratic equation is factorable, but the quadratic formula may be quicker.)

$-13,-11\text{\hspace{0.17em}}\text{or}\text{\hspace{0.17em}}11,13$

The product of two consecutive even integers is 168. Find them.

Three is added to an integer and that sum is doubled. When this result is multiplied by the original integer the product is 20. Find the integer.

$n=2,-5$

Four is added to three times an integer. When this sum and the original integer are multiplied, the product is $-1.$ Find the integer.

## Sample set d—type problems

A box with no top and a square base is to be made by cutting out 2-inch squares from each corner and folding up the sides of a piece of cardboard.The volume of the box is to be 25 cubic inches. What size should the piece of cardboard be?

$4+\sqrt{12.5}\text{\hspace{0.17em}}\text{inches}$

A box with no top and a square base is to made by cutting out 8-inch squares from each corner and folding up the sides of a piece of cardboard. The volume of the box is to be 124 cubic inches. What size should the piece of cardboard be?

## Sample set e—type problems

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, will be $A=0.1{t}^{2}+0.1t+2.2.$

(a) What is the level, in parts per million, of carbon monoxide in the air now?

(b) How many years from now will the level of carbon monoxide be at 3 parts per million?

(a) carbon monoxide now $2.2$ parts per million
(b) $2.37\text{\hspace{0.17em}}\text{years}$

A similar study to that of problem 21 suggests $A=0.3{t}^{2}+0.25t+3.0.$

(a) What is the level, in parts per million, of carbon monoxide in the air now?

(b) How many years from now will the level of carbon monoxide be at 3.1 parts per million?

## Sample set f—type problems

A contractor is to pour a concrete walkway around a wading pool that is 4 feet wide and 8 feet long. The area of the walkway and pool is to be 96 square feet. If the walkway is to be of uniform width, how wide should it be?

$x=2$

## Astrophysical problem

A very interesting application of quadratic equations is determining the length of a solar eclipse (the moon passing between the earth and sun). The length of a solar eclipse is found by solving the quadratic equation

${\left(a+bt\right)}^{2}+{\left(c+dt\right)}^{2}={\left(e+ft\right)}^{2}$

for $t$ . The letters $a,b,c,d,e,$ and $f$ are constants that pertain to a particular eclipse. The equation is a quadratic equation in $t$ and can be solved by the quadratic formula (and definitely a calculator). Two values of $t$ will result. The length of the eclipse is just the difference of these $t$ -values.

The following constants are from a solar eclipse that occurred on August 3, 431 B.C.

$\begin{array}{ccccccc}a& =& -619& & b& =& 1438\\ c& =& 912& & d& =& -833\\ e& =& 1890.5& & f& =& -2\end{array}$
Determine the length of this particular solar eclipse.

## Exercises for review

( [link] ) Find the sum: $\frac{2x+10}{{x}^{2}+x-2}+\frac{x+3}{{x}^{2}-3x+2}.$

$\frac{3x+14}{\left(x+2\right)\left(x-2\right)}$

( [link] ) Solve the fractional equation $\frac{4}{x+12}+\frac{3}{x+3}=\frac{4}{{x}^{2}+5x+6}.$
( Hint: Check for extraneous solutions.)

( [link] ) One pipe can fill a tank in 120 seconds and another pipe can fill the same tank in 90 seconds. How long will it take both pipes working together to fill the tank?

$51\frac{3}{7}$

( [link] ) Use the quadratic formula to solve $10{x}^{2}-3x-1=0.$

( [link] ) Use the quadratic formula to solve $4{x}^{2}-3x=0.$

$x=0,\frac{3}{4}$

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
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
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
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
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
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?
what is a peer
What is meant by 'nano scale'?
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 ?
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?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
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