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mathematics
precalculus
Precalculus 9th edition Michael Sullivan - Solutions
Tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. 10z2 + z
Tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. 2y3 – √2
Tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. 3/x + 2
Tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. 3x2 – 5/x
Tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. -π
Tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. 5
Tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. 1 - 4x
Tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. 3x2 – 5
whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial, state why not. 3x2 + 4
whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial, state why not. x2 + 2x – 5
whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial, state why not. 2x2 x + 1
whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial, state why not. 8x x? - 1
whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial, state why not. 6x5 – 8x2
whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial, state why not. -2x3 + 5x2
whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial, state why not. -2x-3
whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial, state why not. 8/x
whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial, state why not. -4x2
whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial, state why not. 2x3
True or False.3x3 – 2x2 – 6x + 4 = (3x - 2)( x2 + 2)
True or FalseThe polynomial x2 + 4 is prime.
To complete the square of the expression x2 + 5x, you _______ would the number ________ .
If factored completely, 3x3 – 12x = __________.
To check division, the expression that is being divided, the dividend, should equal the product of the________and the _________plus the________.
True or False. (x + a)(x2 + ax + a) = x3 + a3
True or False.-4x-2 is a monomial of degree -2.
(x – 2)(x2 + 2x + 4) = ______.
(x2 – 4)(x2+ 5)= _____.
The polynomial 3x4 – 2x3 + 13x2 – 5 is of degeree_____. The leading coefficient is _____.
The Gibb’s Hill Lighthouse, Southampton, Bermuda, in operation since 1846, stands 117 feet high on a hill 245 feet high, so its beam of light is 362 feet above sea level. A brochure states that the light itself can be seen on the horizon about 26 miles from the lighthouse.Verify the correctness
You have 1000 feet of flexible pool siding and wish to construct a swimming pool. Experiment with rectangularshaped pools with perimeters of 1000 feet. How do their areas vary? What is the shape of the rectangle with the largest area? Now compute the area enclosed by a circular pool with a
Suppose that m and n are positive integers with m > n. If a = m2 – n2, b = 2mm and c = m2 + n2 show that a, b, and c are the lengths of the sides of a right triangle. (This formula can be used to find the sides of a right triangle that are integers, such as 3, 4, 5; 5, 12, 13; and so on. Such
Use the facts that the radius of Earth is 3960 miles and 1 mile = 5280 feet. The deck of a destroyer is 100 feet above sea level. How far can a person see from the deck? How far can a person see from the bridge, which is 150 feet above sea level?
Use the facts that the radius of Earth is 3960 miles and 1 mile = 5280 feet. A person who is 6 feet tall is standing on the beach in Fort Lauderdale, Florida, and looks out onto the Atlantic Ocean. Suddenly, a ship appears on the horizon. How far is the ship from shore?
Use the facts that the radius of Earth is 3960 miles and 1 mile = 5280 feet. The conning tower of the U.S.S. Silversides, a World War II submarine now permanently stationed in Muskegon, Michigan, is approximately 20 feet above sea level. How far can you see from the conning tower?
Karen is doing research on the Bermuda Triangle, which she defines roughly by Hamilton, Bermuda; San Juan, Puerto Rico; and Fort Lauderdale, Florida. On her atlas Karen measures the straight-line distances from Hamilton to Fort Lauderdale, Fort Lauderdale to San Juan, and San Juan to Hamilton to be
The ancient Greek philosopher Thales of Miletus is reported on one occasion to have visited Egypt and calculated the height of the Great Pyramid of Cheops by means of shadow reckoning. Thales knew that each side of the base of the pyramid was 252 paces and that his own height was 2 paces. He
A circular swimming pool, 20 feet in diameter, is enclosed by a wooden deck that is 3 feet wide. What is the area of the deck? How much fence is required to enclose the deck? 20' II
A Norman window consists of a rectangle surmounted by a semicircle. Find the area of the Norman window shown in the illustration. How much wood frame is needed to enclose the window? 6' 4'
Refer to the figure. Square has an area of 100 square feet; square has an area of 16 square feet. What is the area of the triangle CGF? A
In the figure shown, is a square, with each side of length 6 feet. The width of the border (shaded portion) between the outer square and is 2 feet. Find the area of the border. A B 6 ft 2 ft н ш
How many revolutions will a circular disk with a diameter of 4 feet have completed after it has rolled 20 feet?
How many feet does a wheel with a diameter of 16 inches travel after four revolutions?
The pair of triangles are similar. Find the missing length x and the missing angles A, B, and C. 10 -125° 50° 50 5°. -B х
The pair of triangles are similar. Find the missing length x and the missing angles A, B, and C. 20 /60° 95° 45 25° 30 х
The pair of triangles are similar. Find the missing length x and the missing angles A, B, and C. 30° 16 V75° 12 75° х
The pair of triangles are similar. Find the missing length x and the missing angles A, B, and C. 60° .06 4 30° 8
Find the area of the shaded region. 2 2.
Find the area of the shaded region. 2.
Find the area of the shaded region. 2
Find the area of the shaded region. 2 2.
Find the volume V and surface area S of a right circular cylinder with radius 8 inches and height 9 inches.
Find the volume V and surface area S of a right circular cylinder with radius 9 inches and height 8 inches.
Find the volume V and surface area S of a sphere of radius 3 feet.
Find the volume V and surface area S of a sphere of radius 4 centimeters.
Find the volume V and surface area S of a rectangular box with length 9 inches, width 4 inches, and height 8 inches.
Find the volume V and surface area S of a rectangular box with length 8 feet, width 4 feet, and height 7 feet.
Find the area A and circumference C of a circle of radius 2 feet.
Find the area A and circumference C of a circle of radius 5 meters.
Find the area A of a triangle with height 9 centimeters and base 4 centimeters.
Find the area A of a triangle with height 4 inches and base 2 inches.
Find the area A of a rectangle with length 9 centimeters and width 4 centimeters.
Find the area A of a rectangle with length 4 inches and width 2 inches.
The lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 5, 4, 7
The lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 6, 4, 3
The lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 10, 24, 26
The lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 7, 24, 25
The lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 2, 2, 3
The lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 4, 5, 6
The lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 6, 8, 10
The lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 3, 4, 5
The lengths of the legs of a right triangle are given. Find the hypotenuse. a = 14, b = 48
The lengths of the legs of a right triangle are given. Find the hypotenuse. a = 7, b = 24
The lengths of the legs of a right triangle are given. Find the hypotenuse. a = 4, b = 3
The lengths of the legs of a right triangle are given. Find the hypotenuse. a = 10, b = 24
The lengths of the legs of a right triangle are given. Find the hypotenuse. a = 6, b = 8
The lengths of the legs of a right triangle are given. Find the hypotenuse. a = 5, b = 12
True or False.The triangles shown are similar. 3 120° 120° 3. 2.
True or False.The triangles shown are similar. 25 25° 100° 100°
True or False.The triangles shown are congruent. 10 30 30 29 29 10
True or False.The volume of a sphere of radius r is 4/3πr2.
True or False.The triangle with sides of length 6, 8, and 10 is a right triangle.
True or False.In a right triangle, the square of the length of the longest side equals the sum of the squares of the lengths of the other two sides.
Two triangles are________ if corresponding angles are equal and the lengths of the corresponding sides are proportional.
The formula for the circumference C of a circle of radius r is _______.
For a triangle with base b and altitude h, a formula for the area A is _______.
A(n)_______ triangle is one that contains an angle of 90 degrees. The longest side is called the _________ .
Give a reason why statement 5 < 8 is true.
I’m thinking of a number! It lies between 1 and 10; its square is rational and lies between 1 and 10. The number is larger than π. Correct to two decimal places (that is, truncated to two decimal places) name the number. Now think of your own number, describe it, and challenge a fellow student
Is there a positive real number “closest” to 0?
Does 2/3 equal 0.666? If not, which is larger? By how much?
Does 1/3 equal 0.333? If not, which is larger? By how much?
Normal human body temperature is 98.6 F. A temperature x that differs from normal by at least 1.5 F is considered unhealthy. A formula that describes this is |x - 98.6| ≤ 1.5(a) Show that a temperature of 97°F is unhealthy.(b) Show that a temperature of 100°F is not unhealthy.
The FireBall Company manufactures ball bearings for precision equipment. One of its products is a ball bearing with a stated radius of 3 centimeters (cm). Only ball bearings with a radius within 0.01 cm of this stated radius are acceptable. If x is the radius of a ball bearing, a formula describing
In some countries, normal household voltage is 220 volts. It is acceptable for the actual voltage x to differ from normal by at most 8 volts. A formula that describes this is |x - 220| ≤ 8(a) Show that a voltage of 214 volts is acceptable.(b) Show that a voltage of 209 volts is not
In the United States, normal household voltage is 110 volts. It is acceptable for the actual voltage x to differ from normal by at most 5 volts. A formula that describes this is |x - 110| ≤ 5(a) Show that a voltage of 108 volts is acceptable.(b) Show that a voltage of 104 volts is not
Write an inequality using an absolute value to describe each statement.x is more than 5 units from 2.
Write an inequality using an absolute value to describe each statement.x is at least 6 units from 4.
At the beginning of the month, Mike had a balance of $210 in his checking account. During the next month, he deposited $80, wrote a check for $120, made another deposit of $25, and wrote two checks: one for $60 and the other for $32. He was also assessed a monthly service charge of $5. What was his
The weekly production cost C of manufacturing x watches is given by the formula C = 4000 + 2x where the variable C is in dollars. (a) What is the cost of producing 1000 watches? (b) What is the cost of producing 2000 watches?
Express each statement as an equation involving the indicated variables.The surface area S of a cube is 6 times the square of the length x of a side.
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