<< Chapter < Page Chapter >> Page >

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?

Got questions? Get instant answers now!

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.

length = 8 ; width = 1

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

width = 21 length = 2 3 21

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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 ; h = 4

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

Sample set c—type problems

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

9 , 8 or 8 , 9

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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 or 11 , 13

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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 + 12.5 inches

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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 + 0.1 t + 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 years

Got questions? Get instant answers now!

A similar study to that of problem 21 suggests A = 0.3 t 2 + 0.25 t + 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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

( a + b t ) 2 + ( c + d t ) 2 = ( e + f t ) 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.

a = 619 b = 1438 c = 912 d = 833 e = 1890.5 f = 2
Determine the length of this particular solar eclipse.

Got questions? Get instant answers now!

Exercises for review

( [link] ) Find the sum: 2 x + 10 x 2 + x 2 + x + 3 x 2 3 x + 2 .

3 x + 14 ( x + 2 ) ( x 2 )

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

( [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 3 7

Got questions? Get instant answers now!

( [link] ) Use the quadratic formula to solve 10 x 2 3 x 1 = 0.

Got questions? Get instant answers now!

( [link] ) Use the quadratic formula to solve 4 x 2 3 x = 0.

x = 0 , 3 4

Got questions? Get instant answers now!

Questions & Answers

find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
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
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
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
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
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
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
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.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask