# 10.6 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 $4{x}^{2}-3x=0.$

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

find the 15th term of the geometric sequince whose first is 18 and last term of 387
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
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?
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
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.
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
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
I'm interested in nanotube
Uday
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
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
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
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