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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

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
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fine, how about you?
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hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
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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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