# 8.7 Applications  (Page 4/4)

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An inlet pipe can fill a tank in $a$ units of time. An outlet pipe can empty the tank in $b$ units of time. If both pipes are open, how many units of time are required to fill the tank? Are there any restrictions on $a$ and $b$ ?

A delivery boy, working alone, can deliver all his goods in 6 hours. Another delivery boy, working alone, can deliver the same goods in 5 hours. How long will it take the boys to deliver all the goods working together?

$2\frac{8}{11}\text{\hspace{0.17em}hours}$

A Space Shuttle astronaut can perform a certain experiment in 2 hours. Another Space Shuttle astronaut who is not as familiar with the experiment can perform it in $2\frac{1}{2}$ hours. Working together, how long will it take both astronauts to perform the experiment?

One person can complete a task 8 hours sooner than another person. Working together, both people can perform the task in 3 hours. How many hours does it take each person to complete the task working alone?

First person: 12 hours; second person: 4 hours

Find two consecutive integers such that two thirds of the smaller number added to the other yields 11.

Find two consecutive integers such that three fourths of the smaller number added to the other yields 29.

$16,17$

The width of a rectangle is $\frac{2}{5}$ its length. Find the dimensions if the perimeter is 42 meters.

The width of a rectangle is $\frac{3}{7}$ the length. Find the dimensions if the perimeter is 60 feet.

$\begin{array}{lll}\text{width}=9\text{\hspace{0.17em}ft;}\hfill & \hfill & \text{length}=21\text{\hspace{0.17em}ft}\hfill \end{array}$

Two sides of a triangle have the same length. The third side is twice as long as either of the other two sides. The perimeter of the triangle is 56 inches. What is the length of each side?

In a triangle, the second side is 3 inches longer than first side. The third side is $\frac{3}{4}$ the length of the second side. If the perimeter is 30 inches, how long is each side?

$\begin{array}{lllll}\text{side\hspace{0.17em}}1=9\text{\hspace{0.17em}inches};\hfill & \hfill & \text{side\hspace{0.17em}}2=12\text{\hspace{0.17em}inches};\hfill & \hfill & \text{side\hspace{0.17em}}3=9\text{\hspace{0.17em}inches}\hfill \end{array}$

The pressure due to surface tension in a spherical drop of liquid is given by $P=\frac{2T}{r},$ where $T$ is the surface tension of the liquid and $r$ is the radius of the drop. If the liquid is a bubble, it has two surfaces and the surface tension is given by

$P=\frac{2T}{r}+\frac{2T}{r}=\frac{4T}{r}$
(a) Determine the pressure due to surface tension within a soap bubble of radius 2 inches and surface tension 28.
(b) Determine the radius of a bubble if the pressure due to surface tension is 52 and the surface tension is 39.

The equation $\frac{1}{p}+\frac{1}{q}=\frac{1}{f}$ relates the distance $p$ of an object from a lens and the image distance $q$ from the lens to the focal length $f$ of the lens.

(a) Determine the focal length of a lens in which an object 10 feet away produces an image 6 feet away.
(b) Determine how far an object is from a lens if the focal length of the lens is 6 inches and the image distance is 10 inches.
(c) Determine how far an image will be from a lens that has a focal length of $4\frac{4}{5}$ cm and the object is 12 cm away from the lens.

(a) $f=\frac{15}{4}\text{\hspace{0.17em}ft}$  (b) $p=15\text{\hspace{0.17em}inches}$  (c) $q=8\text{\hspace{0.17em}cm}$

Person A can complete a task in 4 hours, person B can complete the task in 6 hours, and person C can complete the task in 3 hours. If all three people are working together, how long will it take to complete the task?

Three inlet pipes can fill a storage tank in 4, 6, and 8 hours, respectively. How long will it take all three pipes to fill the tank?

$\text{1}\frac{11}{13}\text{\hspace{0.17em}hours}$

An inlet pipe can fill a tank in 10 hours. The tank has two drain pipes, each of which can empty the tank in 30 hours. If all three pipes are open, can the tank be filled? If so, how long will it take?

An inlet pipe can fill a tank in 4 hours. The tank has three drain pipes. Two of the drain pipes can empty the tank in 12 hours, and the third can empty the tank in 20 hours. If all four pipes are open, can the tank be filled? If so, how long will it take?

$\text{30\hspace{0.17em}hours}$

## Exercises for review

( [link] ) Factor $12{a}^{2}+13a-4.$

( [link] ) Find the slope of the line passing through the points $\left(4,-3\right)$ and $\left(1,-6\right).$

$m=1$

( [link] ) Find the quotient: $\frac{2{x}^{2}-11x-6}{{x}^{2}-2x-24}÷\frac{2{x}^{2}-3x-2}{{x}^{2}+2x-8}.$

( [link] ) Find the difference: $\frac{x+2}{{x}^{2}+5x+6}-\frac{x+1}{{x}^{2}+4x+3}.$

0

( [link] ) Solve the equation $\frac{9}{2m-5}=-2.$

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
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
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?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
how did you get the value of 2000N.What calculations are needed to arrive at it
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