Concept explainers
Use the four-step procedure for solving variation problems given on page 445 to solve Exercises 21–36.
31. Body-mass index, or BMI, takes both weight and height into account when assessing whether an individual is underweight or overweight. BMI varies directly as one’s weight, in pounds, and inversely as the square of one’s height, in inches. In adults, normal values for the BMI are between 20 and 25, inclusive. Values below 20 indicate that an individual is underweight and values above 30 indicate that an individual is obese. A person who weighs 180 pounds and is 5 feet, or 60 inches, tall has a BMI of 35.15. What is the BMI, to the nearest tenth, for a 170-pound person who is 5 feet 10 inches tall? Is this person overweight?
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Chapter 3 Solutions
COLLEGE ALGEBRA ESSENTIALS-MYMATHLAB
- Solve the variation problems in Exercises 68–73. 68. A company's profit varies directly as the number of products it sells. The company makes a profit of $1175 on the sale of 25 products. What is the company's profit when it sells 105 products? 69. The distance that a body falls from rest varies directly as the square of the time of the fall. If skydivers fall 144 feet in 3 seconds, how far will they fall in 10 seconds? 70. The pitch of a musical tone varies inversely as its wavelength. A tone has a pitch of 660 vibrations per second and a wavelength of 1.6 feet. What is the pitch of a tone that has a wavelength of 2.4 feet? 71. The loudness of a stereo speaker, measured in decibels, varies inversely as the square of your distance from the speaker. When you are 8 feet from the speaker, the loudness is 28 decibels. What is the loudness when you are 4 feet from the speaker? 72. The time required to assemble computers varies directly as the number of computers assembled and inversely as…arrow_forwardIs all variation necessarily numerical?arrow_forward(3.7) #2arrow_forward
- In Exercises 1–6, solve for x.arrow_forwardIn Exercises 69–70, traffic speed S along a certain road (in kilometers per hour) varies as a function of traffic density q (number of cars per kilometer of road). Use the following data to answer the questions: q (density) 60 S (speed) 90 100 70 80 72.5 67.5 63.5 60 56 69. Estimate S'(80).arrow_forwardthe length of time taken to run 100m a continous data?arrow_forward
- problen 1.4arrow_forwardThe value of (8.1)/ .arrow_forwardAn alternative to the body mass index (BMI) for estimating the health risks of obesity is A Body Shape Index (ABSI), given by the formula shown below, where w and h are the waist and height, respectively, in meters, and b is the BMI. The national Heart, Lung, and Blood Institute uses the BMI to determine whether a person is "overweight" (25 ≤ BMI <30) or "obese" (BMI ≥ 30). Complete parts (a) through (d). ABSI = W 2 1 32 bh a. Suppose a man is 1.83 m tall with a waist of 0.885 m and a BMI of 22.9. Find the ABSI for such a person. How does this compare with the average ABSI for a 52-year-old man of 0.0831? The ABSI for this person is 0.081, which is (Round to three decimal places as needed.) less than the average ABSI for a 52-year-old man. b. For the person described in part a, find the rate that the ABSI is going up with respect to his waist. To find the rate that the ABSI is going up with respect to his waist, take the partial derivative of ABSI with respect to w. The value of ABSI…arrow_forward
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