College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)
5th Edition
ISBN: 9780134179025
Author: Ronald J. Harshbarger, Lisa S. Yocco
Publisher: PEARSON
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Textbook Question
Chapter 3.2, Problem 1E
In Exercises 1–10, use factoring to solve the equations.
1. x2 – 3x – 10 = 0
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(3) (16 points) Consider
z = uv,
u = x+y,
v=x-y.
(a) (4 points) Express z in the form z = fog where g: R² R² and f: R² →
R.
(b) (4 points) Use the chain rule to calculate Vz = (2, 2). Show all intermediate
steps otherwise no credit.
(c) (4 points) Let S be the surface parametrized by
T(x, y) = (x, y, ƒ (g(x, y))
(x, y) = R².
Give a parametric description of the tangent plane to S at the point p = T(x, y).
(d) (4 points) Calculate the second Taylor polynomial Q(x, y) (i.e. the quadratic
approximation) of F = (fog) at a point (a, b). Verify that
Q(x,y) F(a+x,b+y).
=
(6) (8 points) Change the order of integration and evaluate
(z +4ry)drdy .
So S√ ²
0
(10) (16 points) Let R>0. Consider the truncated sphere S given as
x² + y² + (z = √15R)² = R², z ≥0.
where F(x, y, z) = −yi + xj .
(a) (8 points) Consider the vector field
V (x, y, z) = (▼ × F)(x, y, z)
Think of S as a hot-air balloon where the vector field V is the velocity vector
field measuring the hot gasses escaping through the porous surface S. The flux
of V across S gives the volume flow rate of the gasses through S. Calculate
this flux.
Hint: Parametrize the boundary OS. Then use Stokes' Theorem.
(b) (8 points) Calculate the surface area of the balloon. To calculate the surface
area, do the following:
Translate the balloon surface S by the vector (-15)k. The translated
surface, call it S+ is part of the sphere x² + y²+z² = R².
Why do S and S+ have the same area?
⚫ Calculate the area of S+. What is the natural spherical parametrization
of S+?
Chapter 3 Solutions
College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)
Ch. 3.1 - In Exercises 16, (a) determine whether the...Ch. 3.1 - In Exercises 16, (a) determine whether the...Ch. 3.1 - In Exercises 16, (a) determine whether the...Ch. 3.1 - In Exercises 16, (a) determine whether the...Ch. 3.1 - In Exercises 16, (a) determine whether the...Ch. 3.1 - In Exercises 16, (a) determine whether the...Ch. 3.1 - Prob. 7ECh. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - In Exercises 714, (a) graph each quadratic...
Ch. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - In Exercises 714, (a) graph each quadratic...Ch. 3.1 - In Exercises 714, (a) graph each quadratic...Ch. 3.1 - Prob. 15ECh. 3.1 - Write the equation of the quadratic function whose...Ch. 3.1 - The two graphs shown have equations of the forni y...Ch. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - Prob. 20ECh. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - In Exercises 2130, (a) give the coordinates of the...Ch. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - In Exercises 2130, (a) give the coordinates of the...Ch. 3.1 - In Exercises 2130, (a) give the coordinates of the...Ch. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - Prob. 31ECh. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - Prob. 39ECh. 3.1 - Prob. 40ECh. 3.1 - Prob. 41ECh. 3.1 - Prob. 42ECh. 3.1 - Use the graph of each function in Exercises 4146...Ch. 3.1 - Prob. 44ECh. 3.1 - Use the graph of each function in Exercises 4146...Ch. 3.1 - Use the graph of each function in Exercises 4146...Ch. 3.1 - Profit The daily profit for a product is given by...Ch. 3.1 - Profit The daily profit for a product is given by...Ch. 3.1 - Worldwide Mobile Phone Shipments For selected...Ch. 3.1 - Prob. 50ECh. 3.1 - Tourism Spending The equation y = 1.69x2 0.92x +...Ch. 3.1 - Prob. 52ECh. 3.1 - Flight of a Ball If a ball is thrown upward at...Ch. 3.1 - Prob. 54ECh. 3.1 - Crude Oil The U.S. Crude Oil production, in...Ch. 3.1 - Prob. 56ECh. 3.1 - Profit The profit for a certain brand of MP3...Ch. 3.1 - Prob. 58ECh. 3.1 - Prob. 59ECh. 3.1 - Prob. 60ECh. 3.1 - Prob. 61ECh. 3.1 - Prob. 63ECh. 3.1 - Prob. 64ECh. 3.1 - Prob. 65ECh. 3.1 - Prob. 66ECh. 3.1 - Wind and Pollution The amount of particulate...Ch. 3.1 - Drug Sensitivity The sensitivity S to a drug is...Ch. 3.1 - Falling Object A tennis ball is thrown downward...Ch. 3.1 - Break-Even The profit for a product is given by P...Ch. 3.1 - Flight of a Ball A softball is hit with upward...Ch. 3.1 - Flight of a Ball A baseball is hit with upward...Ch. 3.1 - Apartment Rental The owner of an apartment...Ch. 3.1 - Rink Rental The owner of a skating rink rents the...Ch. 3.1 - World Population A low-projection scenario for...Ch. 3.2 - In Exercises 110, use factoring to solve the...Ch. 3.2 - In Exercises 110, use factoring to solve the...Ch. 3.2 - In Exercises 110, use factoring to solve the...Ch. 3.2 - In Exercises 110, use factoring to solve the...Ch. 3.2 - In Exercises 110, use factoring to solve the...Ch. 3.2 - In Exercises 110, use factoring to solve the...Ch. 3.2 - In Exercises 110, use factoring to solve the...Ch. 3.2 - In Exercises 110, use factoring to solve the...Ch. 3.2 - In Exercises 110, use factoring to solve the...Ch. 3.2 - In Exercises 110, use factoring to solve the...Ch. 3.2 - In Exercises 116, find the x-intercepts...Ch. 3.2 - In Exercises 116, find the x-intercepts...Ch. 3.2 - In Exercises 116, find the x-intercepts...Ch. 3.2 - In Exercises 116, find the x-intercepts...Ch. 3.2 - In Exercises 116, find the x-intercepts...Ch. 3.2 - In Exercises 116, find the x-intercepts...Ch. 3.2 - Use a graphing utility to find or to approximate...Ch. 3.2 - Prob. 18ECh. 3.2 - Use a graphing utility to find or to approximate...Ch. 3.2 - Prob. 20ECh. 3.2 - Prob. 21ECh. 3.2 - Prob. 22ECh. 3.2 - Prob. 23ECh. 3.2 - Prob. 24ECh. 3.2 - Prob. 25ECh. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - In Exercises 2934, use the square root method to...Ch. 3.2 - Prob. 30ECh. 3.2 - Prob. 31ECh. 3.2 - Prob. 32ECh. 3.2 - Prob. 33ECh. 3.2 - Prob. 34ECh. 3.2 - Prob. 35ECh. 3.2 - Prob. 36ECh. 3.2 - Prob. 37ECh. 3.2 - Prob. 38ECh. 3.2 - Prob. 39ECh. 3.2 - Prob. 40ECh. 3.2 - Prob. 41ECh. 3.2 - Prob. 42ECh. 3.2 - Prob. 43ECh. 3.2 - Prob. 44ECh. 3.2 - Prob. 45ECh. 3.2 - Prob. 46ECh. 3.2 - Prob. 47ECh. 3.2 - Prob. 48ECh. 3.2 - Prob. 49ECh. 3.2 - Prob. 50ECh. 3.2 - Prob. 51ECh. 3.2 - In Exercises 4954, find the exact solutions to...Ch. 3.2 - Prob. 53ECh. 3.2 - Prob. 54ECh. 3.2 - Prob. 55ECh. 3.2 - Prob. 56ECh. 3.2 - In Exercises 5558, you are given the graphs of...Ch. 3.2 - Prob. 58ECh. 3.2 - Prob. 59ECh. 3.2 - Prob. 60ECh. 3.2 - Prob. 61ECh. 3.2 - Prob. 62ECh. 3.2 - In Exercises 6374, solve analytically and then...Ch. 3.2 - Prob. 64ECh. 3.2 - Prob. 65ECh. 3.2 - In Exercises 6374, solve analytically and then...Ch. 3.2 - In Exercises 6374, solve analytically and then...Ch. 3.2 - Prob. 68ECh. 3.2 - Prob. 69ECh. 3.2 - Prob. 70ECh. 3.2 - Prob. 71ECh. 3.2 - In Exercises 6374, solve analytically and then...Ch. 3.2 - Prob. 73ECh. 3.2 - In Exercises 6374, solve analytically and then...Ch. 3.2 - Prob. 75ECh. 3.2 - Prob. 76ECh. 3.2 - Prob. 77ECh. 3.2 - Prob. 78ECh. 3.2 - Prob. 79ECh. 3.2 - Prob. 80ECh. 3.2 - Prob. 81ECh. 3.2 - International Travel to the United States The...Ch. 3.2 - Gold Prices The price of an ounce of gold in U.S....Ch. 3.2 - Non-White Population The number of millions of...Ch. 3.2 - Retail Sales November and December retail sales,...Ch. 3.2 - Prob. 86ECh. 3.2 - World Population One projection of the world...Ch. 3.3 - In Exercises 110, sketch the graph of each...Ch. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - Prob. 9ECh. 3.3 - Prob. 10ECh. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - a.Graph f(x)={4x3ifx3x2ifx3 b.Find f(2) and f(4)....Ch. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 17ECh. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - Prob. 24ECh. 3.3 - Prob. 25ECh. 3.3 - Prob. 26ECh. 3.3 - Prob. 27ECh. 3.3 - Prob. 28ECh. 3.3 - Prob. 29ECh. 3.3 - Prob. 30ECh. 3.3 - Prob. 31ECh. 3.3 - Prob. 32ECh. 3.3 - Compare the graph in Exercise 30 with the graph in...Ch. 3.3 - Prob. 34ECh. 3.3 - Prob. 35ECh. 3.3 - Prob. 36ECh. 3.3 - Prob. 37ECh. 3.3 - Prob. 38ECh. 3.3 - Prob. 39ECh. 3.3 - Prob. 40ECh. 3.3 - Prob. 41ECh. 3.3 - Prob. 42ECh. 3.3 - Electric Charges For the nonextreme weather...Ch. 3.3 - Prob. 44ECh. 3.3 - First-Class Postage The first-class postage...Ch. 3.3 - Income Tax The U.S. federal income tax owed by a...Ch. 3.3 - Banks The number of banks in the United States for...Ch. 3.3 - Wind Chill The formula that gives the wind chill...Ch. 3.3 - Female Physicians Representation of females in...Ch. 3.3 - Prob. 50ECh. 3.3 - Prob. 51ECh. 3.3 - U.S. Population The U.S. population can be modeled...Ch. 3.3 - Prob. 53ECh. 3.3 - Prob. 54ECh. 3.3 - Prob. 55ECh. 3.3 - Prob. 56ECh. 3.3 - Purchasing Power The purchasing power of a 1983...Ch. 3.3 - Trust in the Government The percent of people who...Ch. 3.3 - Prob. 59ECh. 3.3 - Concentration of Body Substances The concentration...Ch. 3.3 - Investing If money is invested for 3 years with...Ch. 3.3 - Investing If money is invested for 4 years with...Ch. 3.3 - Investing The present value that will give a...Ch. 3.3 - Investing The present value that will give a...Ch. 3.4 - In Exercises 16, write the equation of the...Ch. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 3.4 - Prob. 5ECh. 3.4 - Prob. 6ECh. 3.4 - A ball is thrown upward from the top of a...Ch. 3.4 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Prob. 13ECh. 3.4 - Prob. 14ECh. 3.4 - Find the quadratic function that is the best fit...Ch. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - Prob. 22ECh. 3.4 - Prob. 23ECh. 3.4 - Prob. 24ECh. 3.4 - Smart Phones Bill payment using smart phones is...Ch. 3.4 - Obesity Obesity (BMI 30) increases the risk of...Ch. 3.4 - Wind Chill The table gives the wind chill...Ch. 3.4 - Prob. 28ECh. 3.4 - Prob. 29ECh. 3.4 - Prob. 30ECh. 3.4 - Alzheimers Disease Partially because of American...Ch. 3.4 - Prob. 32ECh. 3.4 - Prob. 33ECh. 3.4 - World Population One projection of the world...Ch. 3.4 - Prob. 35ECh. 3.4 - Prob. 36ECh. 3.4 - Prob. 37ECh. 3.4 - Prob. 38ECh. 3.4 - Prob. 39ECh. 3.4 - Prob. 40ECh. 3.4 - Energy Use The following table shows the energy...Ch. 3.4 - Average Annual Wage The following table shows the...Ch. 3.4 - Insurance Rates The following table gives the...Ch. 3.4 - Banks The table gives the number of banks in the...Ch. 3.4 - U.S. Gross Domestic Product The table gives the...Ch. 3.4 - Auto Noise The noise level of a Volvo S60...Ch. 3.4 - Crude Oil The following table gives the U.S. crude...Ch. 3.4 - Box-Office Revenues The data in the table in the...Ch. 3 - In Exercises 16, use the rules of exponents to...Ch. 3 - In Exercises 16, use the rules of exponents to...Ch. 3 - In Exercises 16, use the rules of exponents to...Ch. 3 - In Exercises 16, use the rules of exponents to...Ch. 3 - In Exercises 16, use the rules of exponents to...Ch. 3 - In Exercises 16, use the rules of exponents to...Ch. 3 - Prob. 7TECh. 3 - Prob. 8TECh. 3 - Prob. 9TECh. 3 - Prob. 10TECh. 3 - Prob. 11TECh. 3 - Prob. 12TECh. 3 - Prob. 13TECh. 3 - Prob. 14TECh. 3 - Prob. 15TECh. 3 - Prob. 16TECh. 3 - Prob. 17TECh. 3 - Prob. 18TECh. 3 - Prob. 19TECh. 3 - Prob. 20TECh. 3 - Prob. 21TECh. 3 - Prob. 22TECh. 3 - Prob. 23TECh. 3 - Prob. 24TECh. 3 - Prob. 25TECh. 3 - Prob. 26TECh. 3 - Prob. 27TECh. 3 - Prob. 28TECh. 3 - Prob. 29TECh. 3 - Prob. 30TECh. 3 - In Exercises 2342, factor each of the polynomials...Ch. 3 - Prob. 32TECh. 3 - Prob. 33TECh. 3 - Prob. 34TECh. 3 - Prob. 35TECh. 3 - Prob. 36TECh. 3 - Prob. 37TECh. 3 - Prob. 38TECh. 3 - Prob. 39TECh. 3 - Prob. 40TECh. 3 - Prob. 41TECh. 3 - Prob. 42TECh. 3 - Prob. 43TECh. 3 - Prob. 44TECh. 3 - Prob. 45TECh. 3 - Prob. 46TECh. 3 - Prob. 47TECh. 3 - Prob. 1RECh. 3 - Prob. 2RECh. 3 - Prob. 3RECh. 3 - Prob. 4RECh. 3 - Prob. 5RECh. 3 - Prob. 6RECh. 3 - Prob. 7RECh. 3 - Prob. 8RECh. 3 - Prob. 9RECh. 3 - Prob. 10RECh. 3 - Prob. 11RECh. 3 - Prob. 12RECh. 3 - Prob. 13RECh. 3 - Prob. 14RECh. 3 - Prob. 15RECh. 3 - Prob. 16RECh. 3 - Prob. 17RECh. 3 - Prob. 18RECh. 3 - Prob. 19RECh. 3 - Prob. 20RECh. 3 - Prob. 21RECh. 3 - Prob. 22RECh. 3 - Prob. 23RECh. 3 - Prob. 24RECh. 3 - Prob. 25RECh. 3 - Prob. 26RECh. 3 - Prob. 27RECh. 3 - Prob. 28RECh. 3 - Prob. 29RECh. 3 - Prob. 30RECh. 3 - Determine whether the function y=3x2 is increasing...Ch. 3 - Prob. 32RECh. 3 - Prob. 33RECh. 3 - Prob. 34RECh. 3 - Find the equation of a quadratic function whose...Ch. 3 - Find the equation of a quadratic function whose...Ch. 3 - Prob. 37RECh. 3 - Prob. 38RECh. 3 - Suppose that q varies directly as the 3/2 power of...Ch. 3 - Prob. 40RECh. 3 - Prob. 41RECh. 3 - Prob. 42RECh. 3 - Prob. 43RECh. 3 - Height of a Ball If a ball is thrown into the air...Ch. 3 - Visas The number of skilled workers visas issued...Ch. 3 - Prob. 46RECh. 3 - Prob. 47RECh. 3 - Prob. 48RECh. 3 - Millionaire's Tax Rate The effective tax rate for...Ch. 3 - Prob. 50RECh. 3 - ATV Deaths The number of ATV-related deaths for...Ch. 3 - Home Range The home range of an animal is the...Ch. 3 - Internet Usage Around 40% of the worlds population...Ch. 3 - Personal Income The income received by people from...Ch. 3 - Prob. 55RECh. 3 - Prob. 56RECh. 3 - National Health Expenditures Health spending is...Ch. 3 - Prob. 58RECh. 3 - Prob. 59RECh. 3 - Prob. 60RE
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