Reminder Round all the answers to two decimal places unless otherwise indicated.
Cox’s Formula Assume that a long horizontal pipe connects the bottom of a reservoir with a drainage area. Cox’s formula provides a way of determining the velocity
Here
a. Graph the quadratic function
b. Judging on the basis of Cox’s formula, is it possible to have a velocity of
c. Find the velocity of the water in the pipe if the pipe’s diameter is
d. If the water velocity is too high, there will be erosion problems. Assuming that the pipe length is
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Reminder Round all answers to two decimal places unless otherwise indicated. Ship Propellers An ideal diameter d, in feet, of a ships propeller is given by the formula d=ch1/5r3/5. Here h is the horsepower of the engine driving the propeller. r is the maximum number of revolutions per minute of the propeller, and c is a constant. In both parts, give your answer in terms of a percentage. a. If the horsepower is increased by 20 while the number of revolutions per minute remains the same, how is the propeller diameter affected? b. If the horsepower remains the same while the number of revolutions per minute is increased by 20, how is the propeller diameter affected?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Driving Under the Influence: The Widmark formula,30 developed in 1932, is used to model the blood alcohol content B at a time t hours after consuming alcohol B=5.14ArW0.015t Here B is the blood alcohol content, W is the weight in pounds, A is the liquid ounces of alcohol consumed, and r is a factor determined by gender 0.73for men and 0.66 for women. Consider the blood alcohol content of a 180-pound man after consuming six 12-ounce cans of beer. a. The beer consumed is 6 alcohol. How many ounces of alcohol were consumed? b. Write a formula that gives the blood alcohol content for this man t hours after consuming the alcohol. Round the first term to three decimal places. c. In most states, driving with a blood alcohol content of 0.08 or higher may result in arrest and severe penalties. During which time period is it unlawful for this man to drive?arrow_forwardReminder Round all answer to two decimal places unless otherwise indicated. Lean Body Weight in Females This is a continuation of Exercise 20. The text cited in Exercise 20 gives a more complex method of calculating lean body weight for your adult females: L=19.81+0.73W+21.2R0.88A1.39H+2.43F. Here L is lean body weight in pounds, W is weight in pounds, R is wrist diameter in inches, A is abdominal circumference in inches, H is hip circumference in inches, and F is forearm circumference in inches. Assuming the validity of the formulas given here and in Exercise 20, compare the increase in lean body weight of young adult males and of young adult females if their weight increases but all others factors remain the same. Lean Body Weight in Males Your lean body weight L is the amount you would weigh if all the fat in your body were to disappear. One text gives the following estimate of lean body weight L in pounds for young adult males: L=98.42+1.08W4.14A, Where W is total weight in pounds and A is abdominal circumference in inches. 7 a. Consider a group of young adult males who have the same abdominal circumference. If their weight increases but their abdominal circumference remains the same, how does their lean body weight change? b. Consider a group of young adult males who have the same weight. If their abdominal circumference decreases but their weight stays the same, how does their lean body weight change? c. Suppose a young adult male has a lean body weight of 144 pounds. Over a period of time, he gains 15 pounds in total weight, and his abdominal circumference increases by 2 inches. What is his lean body weight now?arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Length of Skid Marks Versus Speed When a car skids to a stop, the length L, in feet, of the skid marks is related to the speed S, in miles per hour, of the car by the power function L=130hS2. Here the constant h is the friction coefficient, which depends on the road surface. For dry concrete pavement, the value of h is about 0.85. a. If a driver going 55milesperhour on dry concrete jams on the brakes and skids to a stop. how long will the skid marks be? b. A policeman investigating an accident on dry concrete pavement finds skid marks 230feet long. The speed limit in the area is 60milesperhour. Is the driver in danger of getting a speeding ticket? c This part of the problem applies to any road surface, so the value of h is not known. Suppose you are driving at 60milesperhour, but, because of approaching darkness, you wish to slow to a speed that will cut your emergency stopping distance in half. What should your new speed be? Hint: You should use the homogeneity property of power functions here. By what factor should you change your speed to ensure that L changes by a factor of 0.5?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Mosteller Formula for Body Surface Area Body surface area is an important piece of medical information because it is a factor in temperature regulation as well as some drug level determinations. The Mosteller formula gives one way of estimating body surface area B in square meters. The formula uses the weight w in kilograms and the height h in centimeters The relation is B=160h1/2w1/2 a. Use the Mosteller formula to estimate the body surface area for a man who is 188 centimeters tall and weighs 86kilograms. b. The weight of an adult increases by 10. How will this change affect his burly surface area? Give your answer as a percentage. Note: You may assume that the adults height will stay the same.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Walking and Running You live east of campus, and you are walking from campus toward your home at a constant speed. When you get there, you rest for 5minutes and then run back west at a rapid speed. After a few minutes, you reach your destination, and then you rest for 10minutes. Measure your location as your distance west of your home, and make graphs of your location and velocity.arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Note Some of the formulas below use the special number e, which was presented in the Prologue. A Roast is taken from the refrigerator where it had been for several days and placed immediately in a preheated oven to cook. The temperature R=R(t) of the roast t minutes after being placed in the oven is given by R=325280e0.005tdegreesFahrenheit a. What is the temperature of the refrigerator? b. Express the temperature of the roast 30 minutes after being put in the oven in functional notation, and then calculate its value. c. By how much did the temperature of the roast increase during the first 10 minutes of cooking? d. By how much did the temperature of the roast increase from the first hour to 10 minutes after the first hour of cooking?arrow_forwardReminder Round all answer to two decimal places unless otherwise indicated. Hair Growth When you are 18 years old you have a hair that is 14 centimeters long, and your hair grows about 12 centimeters each year. Let H(t) be the length, in centimeters, of that hair t years after age 18. a. Find a formula that gives H as a linear function of t. b. How long will it take for the hair to reach a length of 90 centimeters?arrow_forwardReminder Round all answers to decimal places unless otherwise indicated. Hiking You are hiking in a hilly region, and E=E(t) is your elevation at time t. a. Explain the meaning of dEdt in practical terms. b. Where might you be when dEdt is a large positive number? c. You reach a point where dEdt is briefly zero . Where might you be? d. Where might you be when dEdt is a large negative number?arrow_forward
- Reminder Round all answer to two decimal places unless otherwise indicated. Lean Body Weight in Males Your lean body weight L is the amount you would weigh if all the fat in your body were to disappear. One text gives the following estimate of lean body weight L in pounds for young adult males: L=98.42+1.08W4.14A, where W is total weight in pounds and A is abdominal circumference in inches. 7 a. Consider a group of young adult males who have the same abdominal circumference. If their weight increases but their abdominal circumference remains the same, how does their lean body weight change? b. Consider a group of young adult males who have the same weight. If their abdominal circumference decreases but their weight stays the same, how does their lean body weight change? c. Suppose a young adult male has a lean body weight of 144 pounds. Over a period of time, he gains 15 pounds in total weight, and his abdominal circumference increases by 2 inches. What is his lean body weight now?arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Waiting at a Stop SignConsider a side road connecting to a major highway at a stop sign. According to a study by D.R. Drew, the average delay D, in seconds, for a car waiting at the stop sign to enter the highway is given by D=eqt1qtq, where q is the flow rate, or the number of cars per second passing the stop sign on the highway, and T is the critical highway that will allow for safe entry. We assume that the critical headway is T=5seconds. a.What is the average delay time if the flow rate is 500 cars per hour 0.14 car per second? b.The service rate s for a stop sign is the number of cars per second that can leave the stop sign. It is related to the delay by s=D1. Use function composition to represent the service rate as a function of flow rate. Reminder:(a/b)1=b/a. c.What flow rate will permit a stop sign service rate of 5 cars per minute 0.083 car per second?arrow_forwardReminderRound all answers to two decimal places unless otherwise indicated. Water in a TankWater is leaking out of a tank. The amount of water in the tank t minutes after it springs a leak is given by W(t) gallons. a.Explain what dWdt means in practical terms. b.As water leaks out of the tank, is dWdt positive or negative? c.For the first 10 minutes, water is leaking from the tank at a rate of 5 gallons per minute. What do you conclude about the nature of the function W during this period? d.After about 10 minutes, the hole in the tank suddenly gets larger, and water begins to leak out of the tank at 12 gallons per minute. i.Make a graph of W versus t. Be sure to incorporate linearity where it is appropriate. ii.Make a graph of dWdt versus t.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning