Applied Calculus
7th Edition
ISBN: 9781337291248
Author: Waner, Stefan.
Publisher: Cengage Learning,
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Textbook Question
Chapter 5.6, Problem 22E
Modeling Linear Demand You have been hired as a marketing consultant by Big Book Publishing, Inc., and you have been approached to determine the best-selling price for the hit calculus text by Whiner and Istanbul entitled Fun with Derivatives. You decide to make life easy and assume that the demand equation for Fun with Derivatives has the linear form
a. Your market studies reveal the following sales figures: When the price is set at $50.00 per book, the sales amount to 10,000 per year; when the price is set at $80.00 per book, the sales drop to 1,000 per year. Use these data to calculate the demand equation.
b. Now estimate the unit price that maximizes annual revenue and predict what Big Book Publishing, Inc.’s annual revenue will be at that price.
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Chapter 5 Solutions
Applied Calculus
Ch. 5.1 - In Exercises 112, locate and classify all extrema...Ch. 5.1 - In Exercises 112, locate and classify all extrema...Ch. 5.1 - In Exercises 112, locate and classify all extrema...Ch. 5.1 - In Exercises 112, locate and classify all extrema...Ch. 5.1 - In Exercises 112, locate and classify all extrema...Ch. 5.1 - Prob. 6ECh. 5.1 - In Exercises 112, locate and classify all extrema...Ch. 5.1 - In Exercises 112, locate and classify all extrema...Ch. 5.1 - In Exercises 112, locate and classify all extrema...Ch. 5.1 - Prob. 10E
Ch. 5.1 - In Exercises 112, locate and classify all extrema...Ch. 5.1 - In Exercises 112, locate and classify all extrema...Ch. 5.1 - In Exercises 13-44, find the exact location of all...Ch. 5.1 - In Exercises 13-44, find the exact location of all...Ch. 5.1 - In Exercises 13-44, find the exact location of all...Ch. 5.1 - Prob. 16ECh. 5.1 - In Exercises 13-44, find the exact location of all...Ch. 5.1 - In Exercises 13-44, find the exact location of all...Ch. 5.1 - In Exercises 13-44, find the exact location of all...Ch. 5.1 - In Exercises 13-44, find the exact location of all...Ch. 5.1 - In Exercises 13-44, find the exact location of all...Ch. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - In Exercises 13-44, find the exact location of all...Ch. 5.1 - In Exercises 13-44, find the exact location of all...Ch. 5.1 - In Exercises 13-44, find the exact location of all...Ch. 5.1 - In Exercises 13-44, find the exact location of all...Ch. 5.1 - In Exercises 13-44, find the exact location of all...Ch. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - Prob. 33ECh. 5.1 - Prob. 34ECh. 5.1 - Prob. 35ECh. 5.1 - Prob. 36ECh. 5.1 - Prob. 37ECh. 5.1 - Prob. 38ECh. 5.1 - In Exercises 13-44, find the exact location of all...Ch. 5.1 - Prob. 40ECh. 5.1 - Prob. 41ECh. 5.1 - Prob. 42ECh. 5.1 - In Exercises 13-44, find the exact location of all...Ch. 5.1 - Prob. 44ECh. 5.1 - Prob. 45ECh. 5.1 - Prob. 46ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - In Exercises 4956 the graph of the derivative of a...Ch. 5.1 - Prob. 50ECh. 5.1 - Prob. 51ECh. 5.1 - Prob. 52ECh. 5.1 - In Exercises 4956 the graph of the derivative of a...Ch. 5.1 - Prob. 54ECh. 5.1 - Prob. 55ECh. 5.1 - In Exercises 4956 the graph of the derivative of a...Ch. 5.1 - Prob. 57ECh. 5.1 - Prob. 58ECh. 5.1 - Draw the graph of a function that has stationary...Ch. 5.1 - Draw the graph of a function that has relative,...Ch. 5.1 - If a stationary point is not a relative maximum,...Ch. 5.1 - If one endpoint is a relative maximum, must the...Ch. 5.1 - We said that if f is continuous on a closed...Ch. 5.1 - Prob. 64ECh. 5.1 - Prob. 65ECh. 5.1 - Prob. 66ECh. 5.2 - In Exercises 1-8, solve the given optimization...Ch. 5.2 - In Exercises 1-8, solve the given optimization...Ch. 5.2 - In Exercises 1-8, solve the given optimization...Ch. 5.2 - In Exercises 1-8, solve the given optimization...Ch. 5.2 - In Exercises 1-8, solve the given optimization...Ch. 5.2 - In Exercises 1-8, solve the given optimization...Ch. 5.2 - In Exercises 1-8, solve the given optimization...Ch. 5.2 - In Exercises 1-8, solve the given optimization...Ch. 5.2 - For a rectangle with perimeter 20 to have the...Ch. 5.2 - For a rectangle with area 100 to have the smallest...Ch. 5.2 - Advertising Costs The cost, in thousands of...Ch. 5.2 - Advertising Costs The cost, in billions of...Ch. 5.2 - Average Cost: iPhones Assume that it costs Apple...Ch. 5.2 - Prob. 14ECh. 5.2 - Pollution Control The cost of controlling...Ch. 5.2 - Prob. 16ECh. 5.2 - Pollution Control (Compare Exercise 15.) The cost...Ch. 5.2 - Pollution Control (Compare Exercise 16.) Repeat...Ch. 5.2 - Fences I would like to create a rectangular...Ch. 5.2 - Fences I would like to create a rectangular orchid...Ch. 5.2 - Prob. 21ECh. 5.2 - Prob. 22ECh. 5.2 - Fences (Compare Exercise 19.) For tax reasons I...Ch. 5.2 - Fences (Compare Exercise 20.) For reasons too...Ch. 5.2 - Revenue Hercules Films is deciding on the price of...Ch. 5.2 - Profit Hercules Films is also deciding on the...Ch. 5.2 - Revenue: Smartphones Worldwide annual sales of...Ch. 5.2 - Projected Revenue: Smartphones Worldwide annual...Ch. 5.2 - Revenue: Monorail Service The demand for monorail...Ch. 5.2 - Revenue: Mars Monorail The demand for monorail...Ch. 5.2 - Revenue Assume that the demand for tuna in a small...Ch. 5.2 - Revenue In the 1930s the economist Henry Schultz...Ch. 5.2 - Revenue During the 1950s the wholesale price for...Ch. 5.2 - Revenue Your underground used-book business is...Ch. 5.2 - Profit: Smartphones (Compare Exercise 27.)...Ch. 5.2 - Projected Profit: Smartphones (Compare Exercise...Ch. 5.2 - Profit The demand equation for your companys...Ch. 5.2 - Profit Because of sales by a competing company,...Ch. 5.2 - Paint Cans A company manufactures cylindrical...Ch. 5.2 - Metal Drums A company manufactures cylindrical...Ch. 5.2 - Tin Cans A company manufactures cylindrical tin...Ch. 5.2 - Metal Drums A company manufactures cylindrical...Ch. 5.2 - Box Design Chocolate Box Company is going to make...Ch. 5.2 - Box Design Vanilla Box Company is going to make...Ch. 5.2 - Box Design A packaging company is going to make...Ch. 5.2 - Prob. 46ECh. 5.2 - Luggage Dimensions American Airlines requires that...Ch. 5.2 - Carry-on Dimensions American Airlines requires...Ch. 5.2 - Luggage Dimensions Fly-by-Night Airlines has a...Ch. 5.2 - Luggage Dimensions Fair Weather Airlines has a...Ch. 5.2 - Package Dimensions The U.S. Postal Service (USPS)...Ch. 5.2 - Prob. 52ECh. 5.2 - Prob. 53ECh. 5.2 - Cellphone Revenues (Refer to Exercise 53.) If we...Ch. 5.2 - Research and Development Spending on research and...Ch. 5.2 - Prob. 56ECh. 5.2 - Asset Appreciation As the financial consultant to...Ch. 5.2 - Plantation Management The value of a fir tree in...Ch. 5.2 - Prob. 59ECh. 5.2 - Prob. 60ECh. 5.2 - Average Profit The FeatureRich Software Company...Ch. 5.2 - Prob. 62ECh. 5.2 - Resource Allocation Your company manufactures...Ch. 5.2 - Prob. 64ECh. 5.2 - Resource Allocation Your automobile assembly plant...Ch. 5.2 - Prob. 66ECh. 5.2 - Prob. 67ECh. 5.2 - Prob. 68ECh. 5.2 - Prob. 69ECh. 5.2 - Prob. 70ECh. 5.2 - Prob. 71ECh. 5.2 - Prob. 72ECh. 5.2 - Prob. 73ECh. 5.2 - Harvesting Forests The following equation models...Ch. 5.2 - Agriculture The fruit yield per tree in an orchard...Ch. 5.2 - Agriculture Two years ago, your orange orchard...Ch. 5.2 - Prob. 77ECh. 5.2 - Prob. 78ECh. 5.2 - Prob. 79ECh. 5.2 - Prob. 80ECh. 5.2 - Prob. 81ECh. 5.2 - Explain why finding the production level that...Ch. 5.2 - Prob. 83ECh. 5.2 - Prob. 84ECh. 5.2 - Prob. 85ECh. 5.2 - Prob. 86ECh. 5.3 - In Exercises 1-10, calculate d2ydx2. [HINT: See...Ch. 5.3 - Prob. 2ECh. 5.3 - In Exercises 1-10, calculate d2ydx2. [HINT: See...Ch. 5.3 - In Exercises 1-10, calculate d2ydx2. [HINT: See...Ch. 5.3 - In Exercises 1-10, calculate d2ydx2. [HINT: See...Ch. 5.3 - In Exercises 1-10, calculate d2ydx2. [HINT: See...Ch. 5.3 - In Exercises 1-10, calculate d2ydx2. [HINT: See...Ch. 5.3 - In Exercises 1-10, calculate d2ydx2. [HINT: See...Ch. 5.3 - In Exercises 1-10, calculate d2ydx2. [HINT: See...Ch. 5.3 - In Exercises 1-10, calculate d2ydx2. [HINT: See...Ch. 5.3 - In Exercises 1116 the position s of a point (in...Ch. 5.3 - In Exercises 1116 the position s of a point (in...Ch. 5.3 - In Exercises 1116 the position s of a point (in...Ch. 5.3 - In Exercises 1116 the position s of a point (in...Ch. 5.3 - In Exercises 1116 the position s of a point (in...Ch. 5.3 - In Exercises 1116 the position s of a point (in...Ch. 5.3 - In Exercises 1724 the graph of a function is...Ch. 5.3 - In Exercises 1724 the graph of a function is...Ch. 5.3 - In Exercises 1724 the graph of a function is...Ch. 5.3 - In Exercises 1724 the graph of a function is...Ch. 5.3 - In Exercises 1724 the graph of a function is...Ch. 5.3 - In Exercises 1724 the graph of a function is...Ch. 5.3 - In Exercises 1724 the graph of a function is...Ch. 5.3 - In Exercises 1724 the graph of a function is...Ch. 5.3 - In Exercises 2528 the graph of the derivative,...Ch. 5.3 - In Exercises 2528 the graph of the derivative,...Ch. 5.3 - In Exercises 2528 the graph of the derivative,...Ch. 5.3 - In Exercises 2528 the graph of the derivative,...Ch. 5.3 - In Exercises 2932 the graph of the second...Ch. 5.3 - In Exercises 2932 the graph of the second...Ch. 5.3 - In Exercises 2932 the graph of the second...Ch. 5.3 - Prob. 32ECh. 5.3 - In Exercises 3344, find the x-coordinates of all...Ch. 5.3 - In Exercises 3344, find the x-coordinates of all...Ch. 5.3 - In Exercises 3344, find the x-coordinates of all...Ch. 5.3 - Prob. 36ECh. 5.3 - Prob. 37ECh. 5.3 - In Exercises 3344, find the x-coordinates of all...Ch. 5.3 - Prob. 39ECh. 5.3 - Prob. 40ECh. 5.3 - Prob. 41ECh. 5.3 - Prob. 42ECh. 5.3 - Prob. 43ECh. 5.3 - Prob. 44ECh. 5.3 - Prob. 45ECh. 5.3 - Prob. 46ECh. 5.3 - Prob. 47ECh. 5.3 - Prob. 48ECh. 5.3 - Prob. 49ECh. 5.3 - Prob. 50ECh. 5.3 - Prob. 51ECh. 5.3 - Prob. 52ECh. 5.3 - Prob. 53ECh. 5.3 - Prob. 54ECh. 5.3 - Acceleration on Mars If a stone is dropped from a...Ch. 5.3 - Acceleration on the Moon If a stone is thrown up...Ch. 5.3 - Motion in a Straight Line The position of a...Ch. 5.3 - Motion in a Straight Line The position of a...Ch. 5.3 - Bottled Water Sales Annual sales of bottled water...Ch. 5.3 - Bottled Water Sales Annual U.S. per capita sales...Ch. 5.3 - Prob. 61ECh. 5.3 - Embryo Development The daily oxygen consumption of...Ch. 5.3 - Inflation The following graph shows the...Ch. 5.3 - Inflation The following graph shows the...Ch. 5.3 - Inflation The following graph shows the...Ch. 5.3 - Inflation The following graph shows the...Ch. 5.3 - Scientific Research: 19832003 The percentage of...Ch. 5.3 - Scientific Research: 19832003 The percentage of...Ch. 5.3 - Prob. 69ECh. 5.3 - Prob. 70ECh. 5.3 - Prob. 71ECh. 5.3 - Prob. 72ECh. 5.3 - Epidemics The following graph shows the total...Ch. 5.3 - Prob. 74ECh. 5.3 - Prob. 75ECh. 5.3 - Prob. 76ECh. 5.3 - Prob. 77ECh. 5.3 - Prob. 78ECh. 5.3 - Prob. 79ECh. 5.3 - Prob. 80ECh. 5.3 - Prob. 81ECh. 5.3 - Oil Imports from Mexico Repeat Exercises 81 using...Ch. 5.3 - Prob. 83ECh. 5.3 - Prob. 84ECh. 5.3 - Prob. 85ECh. 5.3 - Prob. 86ECh. 5.3 - Prob. 87ECh. 5.3 - Prob. 88ECh. 5.3 - Prob. 89ECh. 5.3 - Prob. 90ECh. 5.3 - Complete the following: If the graph of a function...Ch. 5.3 - Prob. 92ECh. 5.3 - Prob. 93ECh. 5.3 - The graph of daily sales of Luddingtons Wellington...Ch. 5.3 - Prob. 95ECh. 5.3 - Company Cs profits satisfy P(0)=1 million, P;(0)=1...Ch. 5.3 - Prob. 97ECh. 5.3 - Prob. 98ECh. 5.4 - In Exercises 126, sketch the graph of the given...Ch. 5.4 - Prob. 2ECh. 5.4 - Prob. 3ECh. 5.4 - Prob. 4ECh. 5.4 - Prob. 5ECh. 5.4 - In Exercises 126, sketch the graph of the given...Ch. 5.4 - In Exercises 126, sketch the graph of the given...Ch. 5.4 - Prob. 8ECh. 5.4 - Prob. 9ECh. 5.4 - Prob. 10ECh. 5.4 - Prob. 11ECh. 5.4 - Prob. 12ECh. 5.4 - Prob. 13ECh. 5.4 - In Exercises 126, sketch the graph of the given...Ch. 5.4 - Prob. 15ECh. 5.4 - Prob. 16ECh. 5.4 - Prob. 17ECh. 5.4 - Prob. 18ECh. 5.4 - In Exercises 126, sketch the graph of the given...Ch. 5.4 - Prob. 20ECh. 5.4 - Prob. 21ECh. 5.4 - Prob. 22ECh. 5.4 - Prob. 23ECh. 5.4 - Prob. 24ECh. 5.4 - Prob. 25ECh. 5.4 - Prob. 26ECh. 5.4 - Prob. 27ECh. 5.4 - Prob. 28ECh. 5.4 - Prob. 29ECh. 5.4 - Prob. 30ECh. 5.4 - Home Prices The following graph shows a rough...Ch. 5.4 - Prob. 32ECh. 5.4 - Prob. 33ECh. 5.4 - Prob. 34ECh. 5.4 - Consumer Price Index The following graph shows the...Ch. 5.4 - Consumer Price Index The following graph shows the...Ch. 5.4 - Prob. 37ECh. 5.4 - Prob. 38ECh. 5.4 - Prob. 39ECh. 5.4 - Average Cost: PlayStation 4s Assume that it costs...Ch. 5.4 - Prob. 41ECh. 5.4 - Subprime Mortgage Debt during the Housing Bubble...Ch. 5.4 - Prob. 43ECh. 5.4 - Prob. 44ECh. 5.4 - Prob. 45ECh. 5.4 - Prob. 46ECh. 5.4 - Prob. 47ECh. 5.4 - Prob. 48ECh. 5.4 - Prob. 49ECh. 5.4 - Prob. 50ECh. 5.5 - Rewrite the statements and questions in Exercises...Ch. 5.5 - Rewrite the statements and questions in Exercises...Ch. 5.5 - Prob. 3ECh. 5.5 - Rewrite the statements and questions in Exercises...Ch. 5.5 - Prob. 5ECh. 5.5 - Prob. 6ECh. 5.5 - Rewrite the statements and questions in Exercises...Ch. 5.5 - Rewrite the statements and questions in Exercises...Ch. 5.5 - Prob. 9ECh. 5.5 - Puddles The radius of a circular puddle is growing...Ch. 5.5 - Balloons A spherical party balloon is being...Ch. 5.5 - Prob. 12ECh. 5.5 - Prob. 13ECh. 5.5 - Prob. 14ECh. 5.5 - Sliding Ladders The base of a 50-foot ladder is...Ch. 5.5 - Prob. 16ECh. 5.5 - Prob. 17ECh. 5.5 - Descending Elevator You are situated 300 feet from...Ch. 5.5 - Average Cost The average cost function for the...Ch. 5.5 - Average Cost Repeat Exercise 19, using the revised...Ch. 5.5 - Demand Demand for your tie-dyed T-shirts is given...Ch. 5.5 - Supply The number of retro portable CD players you...Ch. 5.5 - Revenue You can now sell 50 cups of lemonade per...Ch. 5.5 - Revenue You can now sell 40 cars per month at...Ch. 5.5 - Oil Revenues Daily oil production by Pemex,...Ch. 5.5 - Oil Expenditures Daily oil imports to the United...Ch. 5.5 - Resource Allocation Your company manufactures...Ch. 5.5 - Resource Allocation Your company is the largest...Ch. 5.5 - Production The automobile assembly plant you...Ch. 5.5 - Prob. 30ECh. 5.5 - Prob. 31ECh. 5.5 - Demand The demand equation for rubies at Royal...Ch. 5.5 - Ships Sailing Apart The H.M.S. Dreadnaught is 40...Ch. 5.5 - Near Miss My aunt and I were approaching the same...Ch. 5.5 - Baseball A baseball diamond is a square with side...Ch. 5.5 - Baseball Refer to Exercise 35. Another player is...Ch. 5.5 - Prob. 37ECh. 5.5 - Prob. 38ECh. 5.5 - Prob. 39ECh. 5.5 - Prob. 40ECh. 5.5 - Prob. 41ECh. 5.5 - Grades A production formula for a students...Ch. 5.5 - Cones A right circular conical vessel is being...Ch. 5.5 - More Cones A circular conical vessel is being...Ch. 5.5 - Prob. 45ECh. 5.5 - Prob. 46ECh. 5.5 - Computers vs. Income In the 1990s the demand for...Ch. 5.5 - Computers vs. Income Refer back to the model in...Ch. 5.5 - Prob. 49ECh. 5.5 - Prob. 50ECh. 5.5 - Prob. 51ECh. 5.5 - Prob. 52ECh. 5.5 - Prob. 53ECh. 5.5 - Prob. 54ECh. 5.5 - Prob. 55ECh. 5.5 - Prob. 56ECh. 5.5 - Prob. 57ECh. 5.5 - Prob. 58ECh. 5.5 - Prob. 59ECh. 5.5 - Prob. 60ECh. 5.5 - Prob. 61ECh. 5.5 - Prob. 62ECh. 5.6 - Demand for Oranges The weekly sales of Honolulu...Ch. 5.6 - Prob. 2ECh. 5.6 - Prob. 3ECh. 5.6 - Prob. 4ECh. 5.6 - College Tuition An old study of about 1,800 U.S....Ch. 5.6 - Monorail Services The demand for monorail service...Ch. 5.6 - Tissues The consumer demand equation for tissues...Ch. 5.6 - Bodybuilding The consumer demand curve for...Ch. 5.6 - T-Shirts The Physics Club sells E=mc2 T-shirts at...Ch. 5.6 - Comics The demand curve for original Iguanawoman...Ch. 5.6 - E-Readers The demand for Amazons Kindle e-reader...Ch. 5.6 - Prob. 12ECh. 5.6 - Corn In the 1930s the economist Henry Schultz...Ch. 5.6 - Demand for Fried Chicken A fried chicken franchise...Ch. 5.6 - Paint-By-Number The estimated monthly sales of...Ch. 5.6 - Paint-By-Number Repeat Exercise 15 using the...Ch. 5.6 - Linear Demand Functions A general linear demand...Ch. 5.6 - Exponential Demand Functions A general exponential...Ch. 5.6 - Hyperbolic Demand Functions A general hyperbolic...Ch. 5.6 - Quadratic Demand Functions A general quadratic...Ch. 5.6 - Modeling Linear Demand You have been hired as a...Ch. 5.6 - Modeling Linear Demand You have been hired as a...Ch. 5.6 - Modeling Exponential Demand As the new owner of a...Ch. 5.6 - Prob. 24ECh. 5.6 - Prob. 25ECh. 5.6 - Prob. 26ECh. 5.6 - Income Elasticity of Demand: Broadband in 2010 The...Ch. 5.6 - Income Elasticity of Demand: Broadband in 2007 The...Ch. 5.6 - Prob. 29ECh. 5.6 - Prob. 30ECh. 5.6 - Prob. 31ECh. 5.6 - Price Elasticity of Supply Given a supply equation...Ch. 5.6 - Income Elasticity of Demand (based on a question...Ch. 5.6 - Prob. 34ECh. 5.6 - Complete the following: When demand is inelastic,...Ch. 5.6 - Prob. 36ECh. 5.6 - Prob. 37ECh. 5.6 - Given that the demand q is a differentiable...Ch. 5.6 - Prob. 39ECh. 5.6 - Prob. 40ECh. 5 - In Exercises 18, find all the relative and...Ch. 5 - Prob. 2RECh. 5 - Prob. 3RECh. 5 - Prob. 4RECh. 5 - Prob. 5RECh. 5 - Prob. 6RECh. 5 - Prob. 7RECh. 5 - Prob. 8RECh. 5 - Prob. 9RECh. 5 - Prob. 10RECh. 5 - Prob. 11RECh. 5 - Prob. 12RECh. 5 - Prob. 13RECh. 5 - Prob. 14RECh. 5 - Prob. 15RECh. 5 - Prob. 16RECh. 5 - Prob. 17RECh. 5 - Prob. 18RECh. 5 - Prob. 19RECh. 5 - Prob. 20RECh. 5 - Prob. 21RECh. 5 - Prob. 22RECh. 5 - Revenue Demand for the latest best-seller at...Ch. 5 - Revenue Demand for The Secret Loves of John O, a...Ch. 5 - Prob. 25RECh. 5 - Prob. 26RECh. 5 - Office Space Although still a sophomore at...Ch. 5 - Recreation Space As a result of complaints by the...Ch. 5 - Box Design The sales department at...Ch. 5 - Prob. 30RECh. 5 - Prob. 31RECh. 5 - Prob. 32RECh. 5 - Prob. 33RECh. 5 - Company Logos OHaganBooks.coms website has an ani-...Ch. 5 - Prob. 35RECh. 5 - Prob. 36RECh. 5 - Prob. 37RECh. 5 - Prob. 38RE
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- 1 R2 X2 2) slots per pole per phase = 3/31 B = 180 - 60 msl Kd Kol, Sin (no) Isin (6) 2 sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed; 120*50 Looo rem G S = 1000-950 solos 1000 Copper losses: 5kw Rotor input: 5 loo kw 0.05 1 اذا میرید شرح الكتب فقط look 7) rotor DC ined sove in pea PU+96er Q2// Find the volume of the solid bounded above by the cynnuer 2=6-x², on the sides by the cylinder x² + y² = 9, and below by the xy-plane. Q041 Convert 2 2x-2 Lake Gex 35 w2x-xབོ ,4-ཙཱཔ-y √4-x²-yz 21xy²dzdydx to(a) cylindrical coordinates, (b) Spherical coordinates. 201 25arrow_forwardshow full work pleasearrow_forward3. Describe the steps you would take to find the absolute max of the following function using Calculus f(x) = : , [-1,2]. Then use a graphing calculator to x-1 x²-x+1 approximate the absolute max in the closed interval.arrow_forward
- (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.arrow_forward(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). =arrow_forward(6) (8 points) Change the order of integration and evaluate (z +4ry)drdy . So S√ ² 0arrow_forward
- (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+?arrow_forward(1) (8 points) Let c(t) = (et, et sint, et cost). Reparametrize c as a unit speed curve starting from the point (1,0,1).arrow_forward(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
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