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mathematics
calculus

Questions and Answers of Calculus

1. A snow globe has a diameter of 6 inches. Find its exact volume. Then approximate its volume using 3.14 for Ï€.2. The face of a circular watch has a diameter of 2 centimeters. What is its
Find the area of each geometric figure. If the figure is a circle, give an exact area and then use the given approximation for p to approximate the area.1.2. Use 22/7 for Ï€.
1. Mount Fuji, in Japan, is considered the most beautiful composite volcano in the world. The mountain is in the shape of a cone whose height is about 3.5 kilometers and whose base radius is about 3
The Space Cube is supposed to be the world's smallest computer, with dimensions of 2 inches by 2 inches by 2.2 inches. Find the surface area of the Space Cube.
Given the following situations, tell whether you are more likely to be concerned with area or perimeter. 1. ordering grass seed to plant in a yard 2. buying gutters to install on a house 3. ordering
1. Find the approximate area of the state of Utah.2. The Adler Museum in Chicago has a planetarium, its StarRider Theater, that has a diameter of 55 feet. Find the surface area of its hemispheric
The largest pumpkin pie on record was made in New Breman, Ohio, by the New Breman Giant Pumpkin Growers, in September 2010. The pie had a diameter of 240 inches. Find the exact area of the top of the
Find the area of each figure. If needed, use Ï€ ‰ˆ 3.14 and round results to the nearest tenth.1.2. Do two rectangular solids with the same volume have the same surface area? To
Determine whether the measurement in each statement is reasonable. 1. A window measures 1 meter by 0.5 meter. 2. A window measures 1 meter by 0.5 meter. 3. A model's hair is 30 centimeters long.
Estimate each sum or difference. 1. Using a unit other than the meter, write a length that is equivalent to 7 meters. 2. Explain why conversions in the metric system are easier to make than
Convert each measurement as indicated 1. 3.8 mi to feet 2. 7216 yd to mi (Write answer as a decimal.) 3. 129 in. to ft (Write answer as a decimal.)
Convert each measurement as indicated. 1. 84 in. to feet 2. 18 yf to feet 3. 36,960 ft to miles 4. 12 1/2ft to inches 5. 25 ft to yards
Perform each indicated operation. Simplify the result if possible. 1. 12 ft 7 in. +9 ft 11 in. 2. 16 yd 2 ft + 8 yd 2 ft 3. 15 ft 5 in. - 8 ft 2 in.
Perform each indicated operation. Simplify the result if possible. 1. 14 ft 8 in. - 3 ft 11 in. 2. 34 ft 6 in.÷ 2 3. 15 yd 1 ft × 8
Convert as indicated 1. 46 m to centimeters 2. 14 mm to centimeters 3. 400 m to kilometers 4. 6400 mm to meters 5. 6400 cm to meters
Convert as indicated. 1. 0.95 km to centimeters 2. 5 km to meters 3. 4.6 cm to millimeters 4. 140.2 mm to decimeters 5. 0.2 m to millimeters
Perform each indicated operation. Remember to insert units when writing your answers. 1. 14.1 cm + 3.96 cm 2. 30 cm + 8.9 m 3. 45.3 m - 2.16 dam
Perform each indicated operation. Remember to insert units when writing your answers. 1. 14 cm - 15 mm 2. 14.1 m × 4 3. 9.6 m ÷ 5
Solve. Remember to insert units when writing your answers. For following Exercises complete the charts.1.2.
Solve. Remember to insert units when writing your answers. For following Exercises complete the charts.1.2. 3.
1. While exploring in the Marianas Trench, a submarine probe was lowered to a point 1 mile 1400 feet below the ocean's surface. Later it was lowered an additional 1 mile 4000 feet below this point.
1. The sediment on the bottom of the Towamencin Creek is normally 14 cm thick, but a recent flood washed away 22 mm of sediment. How thick is it now?2. The highway commission is installing concrete
The large Coca-Cola sign in the Tokyo Ginza shopping district is in the shape of a rectangle whose length is 31 yards and whose width is 49 feet. Find the area of the sign in square feet.
True or false? See the second Concept Check in this section. 1. A decigram is larger than a milligram. 2. To change 8 pounds to ounces, multiply by 16. Why is this the correct procedure?
Add the polynomials 1. (9y - 16)+(-43y +16) 2. (8a2 + 5a - 9)+)5a2 - 11a + 6) 3. (5x2 - 6)+(-3x2 + 17x - 2) 4. (-12.7z3 - 14z)+(8.9z3 + 12z +2)
Find the value of each polynomial when x = 2. 1. -5x -7 2. 5x2 + 4x -100 3. 7x3 /14 - x + 5
Find the value of each polynomial when x = 5. 1. -5x -6 2. x3 3. 4x2 -5x +10
The distance in feet traveled by a free-falling object in t seconds is given by the polynomial 16t2. Use this polynomial for following Exercises. It takes 8 seconds for a hard hat to fall from the
Office Supplies, Inc. manufactures office products. The company determines that the total cost for manufacturing x file cabinets is given by the polynomial 3000 + 20x. Use this polynomial for
Devils Tower National Monument in Wyoming became America's first national monument in 1906. This rock formation has a height of 867 feet and is a popular climbing site. It was also used as the alien
An object is dropped from the deck of the Royal Gorge Bridge, which stretches across Royal Gorge at a height of 1053 feet above the Arkansas River. The height of the object above the river at t
The continuously growing number of cellular subscribers means that the number of cell phone antennas needs to be constantly increased to carry the additional cellular traffic. The number of cell
Find the perimeter of each figure.
Given the lengths in the figure below, we find the unknown length by subtracting. Use the information to find the unknown lengths in below Exercises.1.
Find the area of each figure.1.2.
Write each number as a product of prime numbers 1. 48 2. 36 3. 300
Find the area of each figure.
Find the area of the shaded figure. To do so, subtract the area of the smaller square from the area of the larger geometric figure.
Find the greatest common factor of each list of terms. 1. x3 , x, x5 2. b6,b6, b4 3. a5b3, a5b2, a5b 4. 9z6, 4z5, 2z3 5. 6y7, 9y6, 15y5
Find the greatest common factor of each list of numbers. 1. 36 and 20 2. 96 and 45 3. 18,24, and 60 4. 30,50, and 200
1. Find 45% of 265. 2. Write 65% as a fraction in simplified form. 3. write 3/4 as a percent.
1. a. Write an expression for the area of the largest rectangle in two different ways.
1. For the expression (xy + z)x, let x = 2 and z = -7. Then multiply and simplify. 2. Explain two ways in which 12y - 722 and your answer to Exercise 42 are related. Use the words multiply and factor
True or false? See the second Concept Check in this section. 1. A decigram is larger than a milligram. 2. To change 8 pounds to ounces, multiply by 16. Why is this the correct procedure? Discuss.
True or false? See the second Concept Check in this section. 1. A decigram is larger than a milligram. 2. To change 8 pounds to ounces, multiply by 16. Why is this the correct procedure? Discuss in
Convert as indicated. 1. 9.5 pounds to ounces 2. 8.3 tons to pounds 3. 4 3/4 pounds to ounces 4. 9 1/8 pounds to ounces 5. 51 ounces to the nearest tenth of a pound
Convert as indicated. 1. 5 pounds to ounces 2. 7 tons to pounds 3. 28,000 pounds to tons 4. 90 ounces to pounds 5. 11,000 pounds to tons
Convert as indicated. 1. 2 1/4 lb to ounces 2. 7 lb 6 oz to ounces 3. 100 oz = ____ lb ____ oz
Perform each indicated operation. 1. 6 lb 10 oz + 10 lb 8 oz 2. 1 ton 1140 lb + 5 tons 1200 lb 3. 4 tons 850 lb - 1 ton 260 lb
Perform each indicated operation. 1. 45 lb 6 oz - 26 lb 10 oz 2. 2 lb 5 oz × 5 3. 5 tons 400 lb ÷ 4
Convert as indicated. 1. 820 g to kilograms 2. 9 g to milligrams 3. 18 kg to grams 4. 112 mg to grams
Convert as indicated.1. 4.9 g to kilograms2. 16.23 g to milligrams3. 3.16 kg to grams4. 4.26 cg to dekagrams
Perform each indicated operation. Remember to insert units when writing your answers. 1. 41.6g + 9.8g 2. 2.1g +153 mg 3. 6.13g -418 mg
Perform each indicated operation. Remember to insert units when writing your answers. 1. 4 kg - 2410 g 2. 4.8 kg × 9.3 3. 8.25 g ÷ 6
Remember to insert units when writing your answers. For following Exercises, complete the chart.1.2.
Remember to insert units when writing your answers. For following Exercises complete the chart.1.2.
1. Guy Green normally weighs 73 kg, but he lost 2800 grams after being sick with the flu. Find Guy's new weight.2. A small can of Planters sunflower seeds weighs 177 g. If each can contains 6
1. Dru Mizel maintains the records of the amount of coal delivered to his department in the steel mill. In January, 3 tons 1500 lb were delivered. In February, 2 tons 1200 lb were delivered. Find the
1. A large bottle of Hire's Root Beer weighs 1900 grams. If a carton contains 6 large bottles of root beer, find the weight in kilograms of 5 cartons2. One box of Swiss Miss Cocoa Mix weighs 0.385
1. The supermarket prepares hamburger in 85-gram market packages. When Leo Gonzalas gets home, he divides the package in half before refrigerating the meat. How much will each package weigh? 2. The
Determine whether the measurement in each statement is reasonable. 1. A full-grown cat weighs approximately 15 g. 2. A staple weighs 15 mg. 3. A car weighs 2000 mg.
Convert each measurement as indicated 1. 20 cups to gallons 2. 7 quarts to cups 3. 6 1/2 gallons to quarts 4. 4 gal 1 qt to quarts 5. 1/2 pint to quarts
Convert each measurement as indicated 1. 16 quarts to gallons 2. 9 pints top quarts 3. 11 cups to pints 4. 18 pints to gallons 5. 3 pints to fluid ounces
Convert each measurement as indicated. 1. 70 qt = ______gal______qt 2. 29 pt =_______gal______qt_______pt 3. 3 1/4 quarts to cups
Perform each indicated operation. 1. 2 gal 2 qt + 9 gal 3 qt 2. 2 c 3 fl oz + 2 c 6 fl oz 3. 2 pt - 1 pt 1 c
Perform each indicated operation. 1. 3 qt 1 c - 1 c 4 fl oz
Let x represent the time (in seconds), and let y represent the distance (in feet) between you and a tree. Draw a possible graph that demonstrate how x and y are related when you are walking toward
Let x represent the time (in seconds), and let y represent the distance (in feet) between you and a tree. Sketch a possible graph that shows how x and y are related when you are walking toward the
Determine the solutions x1 and x2 of each quadratic equation. Use the values of x1 and x2 to fill in the boxes.
The solutions of a quadratic equation are(a) Prove that the sum of the solutions is s = - b/a. (b) Prove that the product of the solutions is P = c/a?
(a) The principal cube root of 125, 3(125, is 5. Evaluate the expression x3 for each value of x.(i)(ii) (b) The principal cube root of 27, 3(27, is 3. Evaluate the expression x3 for each value of
The multiplicative inverse of a complex number z is a complex number zm such that z ( zm = 1. Find the multiplicative inverse of each complex number? (a) z = 1 + i (b) z = 3 − i (c) z = −2 + 8i
Prove that the product of a complex number a + bi and its complex conjugate is a real number?
A fractal is a geometric figure that consists of a pattern that is repeated infinitely on a smaller and smaller scale. The most famous fractal is the Mandelbrot Set, named after the Polish-born
(a) Find each sum. 1 + 2 + 3 + 4 + 5 = ? 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = ? 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = ? (b) Use the formula below for the sum of the first n natural numbers to verify
The area of an ellipse is equal to A = ab (see figure). For the ellipse below, a + b = 20.(a) Show that A = a(20 ˆ’ a). (b) Complete the table. (c) Find two values of a such that A =
Use the graph of y = x4 − x3 − 6x2 + 4x + 8 To solve the inequality x4 − x3 − 6x2 + 4x + 8 > 0?
A building code requires that a building be able to withstand a specific amount of wind pressure. The pressure P (in pounds per square foot) from wind blowing at s miles per hour is given by P =
For a bathtub with a rectangular base, Toricelli's Law implies that the height h of water in the tub t seconds after it begins draining is given byWhere l and w are the tub's length and width, d is
(a) Consider the sum of squares x2 + 9. If the sum can be factored, then there are integers m and n such that x2 + 9 = (x + m)(x + n). Write two equations relating the sum and the product of m and n
Use the equation 4(x = 2x + k to find three different values of k such that the equation has two solutions, one solution, and no solution. Describe the process you used to find the values?
A Pythagorean Triple is a group of three integers, such as 3, 4, and 5, that could be the lengths of the sides of a right triangle. (a) Find two other Pythagorean Triples. (b) Notice that 3 ( 4 ( 5 =
Construct a table of values that consists of several solution points of the equation. Use the resulting solution points to sketch the graph of the equation. 1. y = −4x + 1 2. y = x2 + 2x
Solve the inequality. Then graph the solution set. 1. 3(x + 2) + 7 < 2x − 5 2. 2(x + 7) − 4 ( 5(x − 3) 3. 4(5 − 2x) ( ½ (8 − x) 4. 1/2 (3 − x) > 1/3 (2 − 3x)
1. The revenue for selling x units of a product is R = 125.33x. The cost of producing x units is C = 92x + 1200. To obtain a profit, the revenue must be greater than the cost. For what values of x
Solve the inequality. Then graph the solution set. 1. x2 − 6x − 27 < 0 2. x2 − 2x ( 3 3. 5x3 − 45x < 0 4. 2x3 − 5x2 − 3x ( 0
1. An investment of P dollars at interest rate r (in decimal form) compounded annually increases to an amount A = P(1 + r)2 in 2 years. An investment of $5000 increases to an amount greater than
Determine whether the statement is true or false. Justify your answer. 1. (−18 (−2 = ((−18)(−2) 2. The equation 325x2 − 717x + 398 = 0 has no solution?
1. Explain why it is essential to check your solutions to radical, absolute value, and rational equations?2. Describe the error below
Find the center and radius of the circle with the given equation. Then sketch the circle. 1. x2 + y2 = 9 2. x2 + y2 = 4 3. (x + 2)2 + y2 = 16 4. x2 + (y − 8)2 = 81
Write the standard form of the equation of the circle for which the endpoints of a diameter are (0, 0) and (4, −6)?
Write the standard form of the equation of the circle for which the endpoints of a diameter are (−2, −3) and (4, −10)?
The sales S (in millions of dollars) for Jazz Pharmaceuticals for the years 2006 through 2014 can be approximated by the model S = 27.215t2 − 409.06t + 1563.6, 6 ( t ( 14 Where t represents the
The force F (in pounds) required to stretch a spring x inches from its natural length (see figure) isF = 54x, 0 ( x ( 20.(a) Use the model to complete the table (b) Sketch a graph of the model. (c)
Determine whether the equation is an identity, a conditional equation, or a contradiction. 1. 2(x − 2) = 2x - 4 2. 2(x + 3) = 2x − 2 3. 3(x − 2) + 2x = 2(x + 3) 4. 5(x − 1) − 2x = 3x − 5
Solve the equation and check your solution. (If not possible, explain why.) 1. 8x − 5 = 3x + 20 2. 7x + 3 = 3x − 17 3. 2(x + 5) − 7 = x + 9 4. 7(x − 4) = 1 − (x + 9)
Find the x- and y-intercepts of the graph of the equation algebraically. 1. y = 3x - 1 2. y = −5x + 6 3. y = 2(x − 4) 4. y = 4(7x + 1)
1. The surface area S of the cylinder shown in the figure is approximated by the equation S = 2(3.14)(3)2 + 2(3.14)(3)h. The surface area is 244.92 square inches. Find the height h of the cylinder.2.
In 2014, LinkedIn's total revenue was 45.2% more than it was in 2013. The total revenue for the two years was $3.75 billion. Find the revenue for each year?
The sale price of a digital camera after a 20% discount is $340. Find the original price?

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