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A woman’s glasses accidently fall off her face while she is looking out of a window in a tall building. The equation relating h , the height above the ground in feet, and t , the time in seconds her glasses have been falling, is h = 64 16 t 2 .

(a) How high was the woman’s face when her glasses fell off?

(b) How many seconds after the glasses fell did they hit the ground?

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Sample set b—type problems

The length of a rectangle is 6 feet more than twice its width. The area is 8 square feet. Find the dimensions.

length = 8 ; width = 1

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The length of a rectangle is 18 inches more than three times its width. The area is 81 square inches. Find the dimensions.

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The length of a rectangle is two thirds its width. The area is 14 square meters. Find the dimensions.

width = 21 length = 2 3 21

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The length of a rectangle is four ninths its width. The area is 144 square feet. Find the dimensions.

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The area of a triangle is 14 square inches. The base is 3 inches longer than the height. Find both the length of the base and height.

b = 7 ; h = 4

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The area of a triangle is 34 square centimeters. The base is 1 cm longer than twice the height. Find both the length of the base and the height.

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Sample set c—type problems

The product of two consecutive integers is 72. Find them.

9 , 8 or 8 , 9

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The product of two consecutive negative integers is 42. Find them.

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The product of two consecutive odd integers is 143. Find them. ( Hint: The quadratic equation is factorable, but the quadratic formula may be quicker.)

13 , 11 or 11 , 13

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The product of two consecutive even integers is 168. Find them.

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Three is added to an integer and that sum is doubled. When this result is multiplied by the original integer the product is 20. Find the integer.

n = 2 , 5

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Four is added to three times an integer. When this sum and the original integer are multiplied, the product is 1. Find the integer.

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Sample set d—type problems

A box with no top and a square base is to be made by cutting out 2-inch squares from each corner and folding up the sides of a piece of cardboard.The volume of the box is to be 25 cubic inches. What size should the piece of cardboard be?

4 + 12.5 inches

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A box with no top and a square base is to made by cutting out 8-inch squares from each corner and folding up the sides of a piece of cardboard. The volume of the box is to be 124 cubic inches. What size should the piece of cardboard be?

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Sample set e—type problems

A study of the air quality in a particular city by an environmental group suggests that t years from now the level of carbon monoxide, in parts per million, will be A = 0.1 t 2 + 0.1 t + 2.2.

(a) What is the level, in parts per million, of carbon monoxide in the air now?

(b) How many years from now will the level of carbon monoxide be at 3 parts per million?

(a) carbon monoxide now 2.2 parts per million
(b) 2.37 years

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A similar study to that of problem 21 suggests A = 0.3 t 2 + 0.25 t + 3.0.

(a) What is the level, in parts per million, of carbon monoxide in the air now?

(b) How many years from now will the level of carbon monoxide be at 3.1 parts per million?

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Sample set f—type problems

A contractor is to pour a concrete walkway around a wading pool that is 4 feet wide and 8 feet long. The area of the walkway and pool is to be 96 square feet. If the walkway is to be of uniform width, how wide should it be?

x = 2

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Astrophysical problem

A very interesting application of quadratic equations is determining the length of a solar eclipse (the moon passing between the earth and sun). The length of a solar eclipse is found by solving the quadratic equation

( a + b t ) 2 + ( c + d t ) 2 = ( e + f t ) 2

for t . The letters a , b , c , d , e , and f are constants that pertain to a particular eclipse. The equation is a quadratic equation in t and can be solved by the quadratic formula (and definitely a calculator). Two values of t will result. The length of the eclipse is just the difference of these t -values.

The following constants are from a solar eclipse that occurred on August 3, 431 B.C.

a = 619 b = 1438 c = 912 d = 833 e = 1890.5 f = 2
Determine the length of this particular solar eclipse.

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Exercises for review

( [link] ) Find the sum: 2 x + 10 x 2 + x 2 + x + 3 x 2 3 x + 2 .

3 x + 14 ( x + 2 ) ( x 2 )

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( [link] ) Solve the fractional equation 4 x + 12 + 3 x + 3 = 4 x 2 + 5 x + 6 .
( Hint: Check for extraneous solutions.)

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( [link] ) One pipe can fill a tank in 120 seconds and another pipe can fill the same tank in 90 seconds. How long will it take both pipes working together to fill the tank?

51 3 7

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( [link] ) Use the quadratic formula to solve 10 x 2 3 x 1 = 0.

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( [link] ) Use the quadratic formula to solve 4 x 2 3 x = 0.

x = 0 , 3 4

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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
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
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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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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