Contemporary Mathematics for Business & Consumers
8th Edition
ISBN: 9781305585447
Author: Robert Brechner, Geroge Bergeman
Publisher: Cengage Learning
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Chapter 3, Problem 14AT
Perform the indicated operation for the following. 6.03+45.168
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(7) (12 points) Let F(x, y, z) = (y, x+z cos yz, y cos yz).
Ꮖ
(a) (4 points) Show that V x F = 0.
(b) (4 points) Find a potential f for the vector field F.
(c) (4 points) Let S be a surface in R3 for which the Stokes' Theorem is valid. Use
Stokes' Theorem to calculate the line integral
Jos
F.ds;
as denotes the boundary of S. Explain your answer.
(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).
=
Chapter 3 Solutions
Contemporary Mathematics for Business & Consumers
Ch. 3.I - Read and write the following numbers in word...Ch. 3.I - Round the following numbers to the indicated...Ch. 3.I - Write the following numbers in word form.
Ch. 3.I - Write the following numbers in word form. 2.48Ch. 3.I - Write the following numbers in word form.
3. ...Ch. 3.I - Write the following numbers in word form.
4....Ch. 3.I - Prob. 5RECh. 3.I - Write the following numbers in word form. .000033Ch. 3.I - Write the following numbers in word form. .00938Ch. 3.I - Prob. 8RE
Ch. 3.I - Write the following numbers in word form. .0005712Ch. 3.I - Write the following numbers in word form.
10....Ch. 3.I - Prob. 11RECh. 3.I - Prob. 12RECh. 3.I - Prob. 13RECh. 3.I - Write the following numbers in numerical form....Ch. 3.I - Prob. 15RECh. 3.I - Write the following numbers in numerical form.
16....Ch. 3.I - Prob. 17RECh. 3.I - Round the following numbers to the indicated...Ch. 3.I - Prob. 19RECh. 3.I - Round the following numbers to the indicated...Ch. 3.I - Round the following numbers to the indicated...Ch. 3.I - Round the following numbers to the indicated...Ch. 3.I - Prob. 23RECh. 3.I - Round the following numbers to the indicated...Ch. 3.I - Prob. 25RECh. 3.I - Round the following numbers to the indicated...Ch. 3.I - You are the assistant to the production manager...Ch. 3.II - Perform the indicated operation....Ch. 3.II - Prob. 4TIECh. 3.II - Prob. 5TIECh. 3.II - Prob. 1RECh. 3.II - Perform the indicated operation for the...Ch. 3.II - Prob. 3RECh. 3.II - Prob. 4RECh. 3.II - Prob. 5RECh. 3.II - Prob. 6RECh. 3.II - Prob. 7RECh. 3.II - Prob. 8RECh. 3.II - Prob. 9RECh. 3.II - Prob. 10RECh. 3.II - Prob. 11RECh. 3.II - 12. Subtract fifteen and eighty-eight...Ch. 3.II - Prob. 13RECh. 3.II - 14. In one week of training for the San Francisco...Ch. 3.II - Prob. 15RECh. 3.II - Last week Kate Burke ran a 5-kilometer race in...Ch. 3.II - Prob. 17RECh. 3.II - Faith Sherlock received her monthly pension check...Ch. 3.II - 19. Use the chart “The Pet Story” to answer the...Ch. 3.II - Prob. 20RECh. 3.II - Prob. 21RECh. 3.II - Prob. 22RECh. 3.II - Prob. 23RECh. 3.II - Prob. 24RECh. 3.II - Prob. 25RECh. 3.II - Prob. 26RECh. 3.II - Prob. 27RECh. 3.II - Prob. 28RECh. 3.II - Prob. 29RECh. 3.II - Prob. 30RECh. 3.II - Prob. 31RECh. 3.II - Prob. 32RECh. 3.II - Divide the following numbers. Round to hundredths...Ch. 3.II - Prob. 34RECh. 3.II - Prob. 35RECh. 3.II - Sam Estero received a $50 gift card to iTunes for...Ch. 3.II - Prob. 37RECh. 3.II - 38. Jimmie Masters earns $4,825.50 per month as a...Ch. 3.II - USA Today reported that Ethiopian Airlines had...Ch. 3.II - Prob. 40RECh. 3.II - Prob. 41RECh. 3.II - Edward Nolan has room for 26 bedding plants in his...Ch. 3.II - Prob. 43RECh. 3.II - Prob. 44RECh. 3.II - 45. Tim Meekma owns a PepsiCo vending truck that...Ch. 3.II - According to the Food and Nutrition Service of the...Ch. 3.III - Convert the following decimals to their fractional...Ch. 3.III - Prob. 7TIECh. 3.III - Convert the following decimals to fractions and...Ch. 3.III - Convert the following decimals to fractions and...Ch. 3.III - Convert the following decimals to fractions and...Ch. 3.III - Convert the following decimals to fractions and...Ch. 3.III - Convert the following decimals to fractions and...Ch. 3.III - Convert the following fractions to decimals. Round...Ch. 3.III - Convert the following fractions to decimals. Round...Ch. 3.III - Convert the following fractions to decimals. Round...Ch. 3.III - Convert the following fractions to decimals. Round...Ch. 3.III - Convert the following fractions to decimals. Round...Ch. 3.III - For the following numbers, perform the indicated...Ch. 3.III - For the following numbers, perform the indicated...Ch. 3.III - For the following numbers, perform the indicated...Ch. 3.III - For the following numbers, perform the indicated...Ch. 3.III - a. You are planning a party for your bowling...Ch. 3.III - Catalina Jewelers has 147.25 ounces of 14-carat...Ch. 3.III - a. What is the total cost of fuel for a 4,602 mile...Ch. 3.III - Ever Ready taxicabs charge 1.20 for the first 14...Ch. 3.III - You are the purchasing manager for Five Star...Ch. 3.III - 20. You are the manager of Rally Rent-a-car. A...Ch. 3.III - 21. You are a loan officer at the West Elm Savings...Ch. 3 - 1. As with fractions, ________ are a way of...Ch. 3 - The ________ ________ separates the whole number...Ch. 3 - 3. When rounding decimals, we delete all digits to...Ch. 3 - When rounding monetary amounts, we round to the...Ch. 3 - When adding or subtracting decimals, we begin by...Ch. 3 - 6. When adding or subtracting decimals, we work...Ch. 3 - 7. In the multiplication of decimals, the product...Ch. 3 - 8. When multiplying a decimal by a power of 10, as...Ch. 3 - When dividing decimals, the basic rule is that you...Ch. 3 - 10. When dividing a decimal by a power of 10, as a...Ch. 3 - When converting a decimal to a fraction, we...Ch. 3 - 12. To convert a fraction to a decimal, we divide...Ch. 3 - Write the following numbers in word form. .61Ch. 3 - Write the following numbers in word form. 34.581Ch. 3 - Write the following numbers in word form. $119.85Ch. 3 - Write the following numbers in word form.
4.
Ch. 3 - Write the following numbers in word form.
5.
Ch. 3 - Write the following numbers in numerical form.
6....Ch. 3 - Write the following numbers in numerical form.
7....Ch. 3 - Write the following numbers in numerical form.
8....Ch. 3 - Write the following numbers in numerical form.
9....Ch. 3 - Round the following numbers to the indicated...Ch. 3 - Round the following numbers to the indicated...Ch. 3 - Round the following numbers to the indicated...Ch. 3 - Round the following numbers to the indicated...Ch. 3 - Perform the indicated operation for the...Ch. 3 - Perform the indicated operation for the following....Ch. 3 - Perform the indicated operation for the following....Ch. 3 - Perform the indicated operation for the following....Ch. 3 - Prob. 18ATCh. 3 - Perform the indicated operation for the...Ch. 3 - Perform the indicated operation for the following....Ch. 3 - Perform the indicated operation for the following....Ch. 3 - Perform the indicated operation for the...Ch. 3 - Perform the indicated operation for the following....Ch. 3 - Perform the indicated operation for the...Ch. 3 - Perform the indicated operation for the...Ch. 3 - Convert the following decimals to fractions and...Ch. 3 - Convert the following decimals to fractions and...Ch. 3 - Convert the following fractions to decimals. Round...Ch. 3 - Convert the following fractions to decimals. Round...Ch. 3 - Convert the following fractions to decimals. Round...Ch. 3 - Gary Scott can buy a box of 40 Blu-ray discs for...Ch. 3 - Two Wheeler-Dealer Bike Shop has a 22-inch...Ch. 3 - The chief financial officer of Allied Corporation...Ch. 3 - 34. A spindle of 50 blank DVD discs costs $16.90....Ch. 3 - Liz Thorton has signed up for a one-semester class...Ch. 3 - At Magers Market, a 24-bottle case of spring water...Ch. 3 - 37. Maria Lopez shares an apartment with a friend....Ch. 3 - Ryan Miller wanted to make some money at a flea...Ch. 3 - 39. A cargo ship, The Caribbean Trader, has a...Ch. 3 - As the food manager for a local charity, you are...Ch. 3 - Prob. 41AT
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- (9) (16 points) Let F(x, y, z) = (x² + y − 4)i + 3xyj + (2x2 +z²)k = - = (x²+y4,3xy, 2x2 + 2²). (a) (4 points) Calculate the divergence and curl of F. (b) (6 points) Find the flux of V x F across the surface S given by x² + y²+2² = 16, z ≥ 0. (c) (6 points) Find the flux of F across the boundary of the unit cube E = [0,1] × [0,1] x [0,1].arrow_forward(8) (12 points) (a) (8 points) Let C be the circle x² + y² = 4. Let F(x, y) = (2y + e²)i + (x + sin(y²))j. Evaluate the line integral JF. F.ds. Hint: First calculate V x F. (b) (4 points) Let S be the surface r² + y² + z² = 4, z ≤0. Calculate the flux integral √(V × F) F).dS. Justify your answer.arrow_forwardDetermine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle. a = 13, b = 15, C = 68° Law of Sines Law of Cosines Then solve the triangle. (Round your answers to four decimal places.) C = 15.7449 A = 49.9288 B = 62.0712 × Need Help? Read It Watch Itarrow_forward
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