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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

if 6x=-2 find value of 6/x
issaya Reply
if sin15°=√p, express the following in terms of p
Norman Reply
prove sin²x+cos²x=3+cos4x
Kiddy Reply
the difference between two signed numbers is -8.if the minued is 5,what is the subtrahend
jeramie Reply
the difference between two signed numbers is -8.if the minuend is 5.what is the subtrahend
jeramie
what are odd numbers
micheal Reply
numbers that leave a remainder when divided by 2
Thorben
1,3,5,7,... 99,...867
Thorben
7%2=1, 679%2=1, 866245%2=1
Thorben
the third and the seventh terms of a G.P are 81 and 16, find the first and fifth terms.
Suleiman Reply
if a=3, b =4 and c=5 find the six trigonometric value sin
Martin Reply
ask
Ans
pls how do I factorize x⁴+x³-7x²-x+6=0
Gift Reply
in a function the input value is called
Rimsha Reply
how do I test for values on the number line
Modesta Reply
if a=4 b=4 then a+b=
Rimsha Reply
a+b+2ab
Kin
commulative principle
DIOSDADO
a+b= 4+4=8
Mimi
If a=4 and b=4 then we add the value of a and b i.e a+b=4+4=8.
Tariq
what are examples of natural number
sani Reply
an equation for the line that goes through the point (-1,12) and has a slope of 2,3
Katheryn Reply
3y=-9x+25
Ishaq
show that the set of natural numberdoes not from agroup with addition or multiplication butit forms aseni group with respect toaaddition as well as multiplication
Komal Reply
x^20+x^15+x^10+x^5/x^2+1
Urmila Reply
Practice Key Terms 7

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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