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The force exerted by the wind on a plane surface varies jointly with the square of the velocity of the wind and with the area of the plane surface. If the area of the surface is 40 square feet surface and the wind velocity is 20 miles per hour, the resulting force is 15 pounds. Find the force on a surface of 65 square feet with a velocity of 30 miles per hour.

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The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute (rpm) and the cube of the diameter. If the shaft of a certain material 3 inches in diameter can transmit 45 hp at 100 rpm, what must the diameter be in order to transmit 60 hp at 150 rpm?

2.88 inches

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The kinetic energy K of a moving object varies jointly with its mass m and the square of its velocity v . If an object weighing 40 kilograms with a velocity of 15 meters per second has a kinetic energy of 1000 joules, find the kinetic energy if the velocity is increased to 20 meters per second.

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Chapter review exercises

Quadratic Functions

For the following exercises, write the quadratic function in standard form. Then give the vertex and axes intercepts. Finally, graph the function.

f ( x ) = x 2 4 x 5

f ( x ) = ( x 2 ) 2 9 vertex   ( 2 , –9 ) ,   intercepts   ( 5 , 0 ) ;   ( –1 , 0 ) ;   ( 0 , –5 )

Graph of f(x)=x^2-4x-5.

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f ( x ) = 2 x 2 4 x

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For the following exercises, find the equation of the quadratic function using the given information.

The vertex is ( 2 , 3 ) and a point on the graph is ( 3 , 6 ) .

f ( x ) = 3 25 ( x + 2 ) 2 + 3

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The vertex is ( 3 , 6.5 ) and a point on the graph is ( 2 , 6 ) .

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For the following exercises, complete the task.

A rectangular plot of land is to be enclosed by fencing. One side is along a river and so needs no fence. If the total fencing available is 600 meters, find the dimensions of the plot to have maximum area.

300 meters by 150 meters, the longer side parallel to river.

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An object projected from the ground at a 45 degree angle with initial velocity of 120 feet per second has height, h , in terms of horizontal distance traveled, x , given by h ( x ) = 32 ( 120 ) 2 x 2 + x . Find the maximum height the object attains.

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Power Functions and Polynomial Functions

For the following exercises, determine if the function is a polynomial function and, if so, give the degree and leading coefficient.

f ( x ) = 4 x 5 3 x 3 + 2 x 1

Yes, degree = 5, leading coefficient = 4

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f ( x ) = 5 x + 1 x 2

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f ( x ) = x 2 ( 3 6 x + x 2 )

Yes, degree = 4, leading coefficient = 1

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For the following exercises, determine end behavior of the polynomial function.

f ( x ) = 2 x 4 + 3 x 3 5 x 2 + 7

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f ( x ) = 4 x 3 6 x 2 + 2

As x , f ( x ) , as x , f ( x )

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f ( x ) = 2 x 2 ( 1 + 3 x x 2 )

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Graphs of Polynomial Functions

For the following exercises, find all zeros of the polynomial function, noting multiplicities.

f ( x ) = ( x + 3 ) 2 ( 2 x 1 ) ( x + 1 ) 3

–3 with multiplicity 2, 1 2 with multiplicity 1, –1 with multiplicity 3

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f ( x ) = x 5 + 4 x 4 + 4 x 3

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f ( x ) = x 3 4 x 2 + x 4

4 with multiplicity 1

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For the following exercises, based on the given graph, determine the zeros of the function and note multiplicity.

Graph of an even-degree polynomial with two turning points.

1 2 with multiplicity 1, 3 with multiplicity 3

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Use the Intermediate Value Theorem to show that at least one zero lies between 2 and 3 for the function f ( x ) = x 3 5 x + 1

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Questions & Answers

what is math number
Tric Reply
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
Need help solving this problem (2/7)^-2
Simone Reply
x+2y-z=7
Sidiki
what is the coefficient of -4×
Mehri Reply
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
Alfred Reply
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
Kala Reply
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
Moses Reply
12, 17, 22.... 25th term
Alexandra Reply
12, 17, 22.... 25th term
Akash
College algebra is really hard?
Shirleen Reply
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
I'm 13 and I understand it great
AJ
I am 1 year old but I can do it! 1+1=2 proof very hard for me though.
Atone
hi
Adu
Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
Vedant
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
If f(x) = x-2 then, f(3) when 5f(x+1) 5((3-2)+1) 5(1+1) 5(2) 10
Augustine
how do they get the third part x = (32)5/4
kinnecy Reply
make 5/4 into a mixed number, make that a decimal, and then multiply 32 by the decimal 5/4 turns out to be
AJ
how
Sheref
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
hi
Ayuba
Hello
opoku
hi
Ali
greetings from Iran
Ali
salut. from Algeria
Bach
hi
Nharnhar
Practice Key Terms 7

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Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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