# 8.11 Exercise supplement

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${\left(x-7\right)}^{4}÷\frac{{\left(x-7\right)}^{3}}{x+1}$

$\left(x-7\right)\left(x+1\right)$

${\left(4x+9\right)}^{6}÷\frac{{\left(4x+9\right)}^{2}}{{\left(3x+1\right)}^{4}}$

$5x+\frac{2{x}^{2}+1}{x-4}$

$\frac{7{x}^{2}-20x+1}{\left(x-4\right)}$

$2y+\frac{4{y}^{2}+5}{y-1}$

$\frac{{y}^{2}+4y+4}{{y}^{2}+10y+21}÷\left(y+2\right)$

$\frac{\left(y+2\right)}{\left(y+3\right)\left(y+7\right)}$

$2x-3+\frac{4{x}^{2}+x-1}{x-1}$

$\frac{3x+1}{{x}^{2}+3x+2}+\frac{5x+6}{{x}^{2}+6x+5}-\frac{3x-7}{{x}^{2}-2x-35}$

$\frac{5{x}^{3}-26{x}^{2}-192x-105}{\left({x}^{2}-2x-35\right)\left(x+1\right)\left(x+2\right)}$

$\frac{5a+3b}{8{a}^{2}+2ab-{b}^{2}}-\frac{3a-b}{4{a}^{2}-9ab+2{b}^{2}}-\frac{a+5b}{4{a}^{2}+3ab-{b}^{2}}$

$\frac{3{x}^{2}+6x+10}{10{x}^{2}+11x-6}+\frac{2{x}^{2}-4x+15}{2{x}^{2}-11x-21}$

$\frac{13{x}^{3}-39{x}^{2}+51x-100}{\left(2x+3\right)\left(x-7\right)\left(5x-2\right)}$

## Rational equations ( [link] )

For the following problems, solve the rational equations.

$\frac{4x}{5}+\frac{3x-1}{15}=\frac{29}{25}$

$\frac{6a}{7}+\frac{2a-3}{21}=\frac{77}{21}$

$a=4$

$\frac{5x-1}{6}+\frac{3x+4}{9}=\frac{-8}{9}$

$\frac{4y-5}{4}+\frac{8y+1}{6}=\frac{-69}{12}$

$y=-2$

$\frac{4}{x-1}+\frac{7}{x+2}=\frac{43}{{x}^{2}+x-2}$

$\frac{5}{a+3}+\frac{6}{a-4}=\frac{9}{{a}^{2}-a-12}$

$a=1$

$\frac{-5}{y-3}+\frac{2}{y-3}=\frac{3}{y-3}$

$\frac{2m+5}{m-8}+\frac{9}{m-8}=\frac{30}{m-8}$

No solution; $m=8$ is excluded.

$\frac{r+6}{r-1}-\frac{3r+2}{r-1}=\frac{-6}{r-1}$

$\frac{8b+1}{b-7}-\frac{b+5}{b-7}=\frac{45}{b-7}$

No solution; $b=7$ is excluded.

Solve $z=\frac{x-\overline{x}}{x}\text{\hspace{0.17em}for\hspace{0.17em}}s.$

Solve $A=P\left(1+rt\right)\text{\hspace{0.17em}for\hspace{0.17em}}t.$

$t=\frac{A-P}{Pr}$

Solve $\frac{1}{R}=\frac{1}{E}+\frac{1}{F}\text{\hspace{0.17em}for\hspace{0.17em}}E.$

Solve $Q=\frac{2mn}{s+t}\text{\hspace{0.17em}for\hspace{0.17em}}t.$

$t=\frac{2mn-Qs}{Q}$

Solve $I=\frac{E}{R+r}\text{\hspace{0.17em}for\hspace{0.17em}}r.$

For the following problems, find the solution.

When the same number is subtracted from both terms of the fraction $\frac{7}{12},$ the result is $\frac{1}{2}.$ What is the number?

2

When the same number is added to both terms of the fraction $\frac{13}{15},$ the result is $\frac{8}{9}.$ What is the number?

When three fourths of a number is added to the reciprocal of the number, the result is $\frac{173}{16}.$ What is the number?

No rational solution.

When one third of a number is added to the reciprocal of the number, the result is $\frac{-127}{90}.$ What is the number?

Person A working alone can complete a job in 9 hours. Person B working alone can complete the same job in 7 hours. How long will it take both people to complete the job working together?

$3\frac{15}{16}\text{\hspace{0.17em}hrs}$

Debbie can complete an algebra assignment in $\frac{3}{4}$ of an hour. Sandi, who plays her radio while working, can complete the same assignment in $1\frac{1}{4}$ hours. If Debbie and Sandi work together, how long will it take them to complete the assignment?

An inlet pipe can fill a tank in 6 hours and an outlet pipe can drain the tank in 8 hours. If both pipes are open, how long will it take to fill the tank?

24 hrs

Two pipes can fill a tank in 4 and 5 hours, respectively. How long will it take both pipes to fill the tank?

The pressure due to surface tension in a spherical bubble is given by $P=\frac{4T}{r},$ where $T$ is the surface tension of the liquid, and $r$ is the radius of the bubble.
(a) Determine the pressure due to surface tension within a soap bubble of radius $\frac{1}{2}$ inch and surface tension 22.
(b) Determine the radius of a bubble if the pressure due to surface tension is 57.6 and the surface tension is 18.

(a) 176 units of pressure; (b) $\frac{5}{4}$ units of length

The equation $\frac{1}{p}+\frac{1}{q}=\frac{1}{f}$ relates an objects distance $p$ 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 8 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 10 inches and the image distance is 10 inches.
(c) Determine how far an object will be from a lens that has a focal length of $1\frac{7}{8}$ cm and the object distance is 3 cm away from the lens.

## Dividing polynomials ( [link] )

For the following problems, divide the polynomials.

${a}^{2}+9a+18$ by $a+3$

$a+6$

${c}^{2}+3c-88$ by $c-8$

${x}^{3}+9{x}^{2}+18x+28$ by $x+7$

${x}^{2}+2x+4$

${y}^{3}-2{y}^{2}-49y-6$ by $y+6$

${m}^{4}+2{m}^{3}-8{m}^{2}-m+2$ by $m-2$

${m}^{3}+4{m}^{2}-1$

$3{r}^{2}-17r-27$ by $r-7$

${a}^{3}-3{a}^{2}-56a+10$ by $a-9$

${a}^{2}+6a-2-\frac{8}{a-9}$

${x}^{3}-x+1$ by $x+3$

${y}^{3}+{y}^{2}-y$ by $y+4$

${y}^{2}-3y+11-\frac{44}{y+4}$

$5{x}^{6}+5{x}^{5}-2{x}^{4}+5{x}^{3}-7{x}^{2}-8x+6$ by ${x}^{2}+x-1$

${y}^{10}-{y}^{7}+3{y}^{4}-3y$ by ${y}^{4}-y$

${y}^{6}+3$

$-4{b}^{7}-3{b}^{6}-22{b}^{5}-19{b}^{4}+12{b}^{3}-6{b}^{2}+b+4$ by ${b}^{2}+6$

${x}^{3}+1$ by $x+1$

${x}^{2}-x+1$

${a}^{4}+6{a}^{3}+4{a}^{2}+12a+8$ by ${a}^{2}+3a+2$

${y}^{10}+6{y}^{5}+9$ by ${y}^{5}+3$

${y}^{5}+3$

how can chip be made from sand
is this allso about nanoscale material
Almas
are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
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
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
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
Difference between extinct and extici spicies
While the American heart association suggests that meditation might be used in conjunction with more traditional treatments as a way to manage hypertension
Eleven fifteenths of two more than a number is eight.
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