Advanced Placement Calculus 2016 Graphical Numerical Algebraic Fifth Edition Test Prep Workbook Update
5th Edition
ISBN: 9780328909148
Author: Prentice Hall
Publisher: Prentice Hall
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- A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.arrow_forwardA soda can is made from 40 square inches of aluminum. Let x denote the radius of the top of the can, and let h denote the height, both in inches. a. Express the total surface area S of the can, using x and h. Note: The total surface area is the area of the top plus the area of the bottom plus the area of the cylinder. b. Using the fact that the total area is 40 square inches, express h in terms of x. c. Express the volume V of the can in terms of x.arrow_forwardThe volume V of a cube is V=s3 , where s is the length of one side. Determine the volume of a cube with a side that measures 3.45 feet. Round your answer to 1 decimal place.arrow_forward
- Tsunami Waves and BreakwatersThis is a continuation of Exercise 16. Breakwaters affect wave height by reducing energy. See Figure 5.30. If a tsunami wave of height H in a channel of width W encounters a breakwater that narrows the channel to a width w, then the height h of the wave beyond the breakwater is given by h=HR0.5, where R is the width ratio R=w/W. a. Suppose a wave of height 8 feet in a channel of width 5000feet encounters a breakwater that narrows the channel to 3000feet. What is the height of the wave beyond the breakwater? b. If a channel width is cut in half by a breakwater, what is the effect on wave height? 16. Height of Tsunami WavesWhen waves generated by tsunamis approach shore, the height of the waves generally increases. Understanding the factors that contribute to this increase can aid in controlling potential damage to areas at risk. Greens law tells how water depth affects the height of a tsunami wave. If a tsunami wave has height H at an ocean depth D, and the wave travels to a location with water depth d, then the new height h of the wave is given by h=HR0.25, where R is the water depth ratio given by R=D/d. a. Calculate the height of a tsunami wave in water 25feet deep if its height is 3feet at its point of origin in water 15,000feet deep. b. If water depth decreases by half, the depth ratio R is doubled. How is the height of the tsunami wave affected?arrow_forwardHow are the absolute maximum and minimum similar to and different from the local extrema?arrow_forwardAssume that an object tossed vertically upward reaches a height of h feet after t seconds, where h=100t16t2. What is that maximum height?arrow_forward
- The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?arrow_forwardThe carbon content of machine steel for gages usually ranges from 0.15% to 0.25%. Round the answers for a and b to 2 decimal places. a. What is the minimum weight of carbon in 250 kilograms of machine steel? b. What is the maximum weight of carbon in 250 kilograms of machine steel?arrow_forwardA zinc casting is in the shape of a frustum of a right circular cone. The larger base area is 280 inches in diameter and the smaller base area is 2.30 inches in diameter. The height is 3.50 inches. Round the answers for a and b to 1 decimal point. a. Compute the volume of the casting. b. Determine the weight of the casting. Zinc weighs 0.256 pound per cubic inch.arrow_forward
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