Calculus & Its Applications
12th Edition
ISBN: 9780137590810
Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar, William Edward Tavernetti
Publisher: PEARSON
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Chapter 5.1, Problem 56E
Time to Finish Consider the exponential decay function
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Qize
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Solve the equation using Newton
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27 de febrero de 2025
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3.9 (A/B). A beam ABCDE, with A on the left, is 7 m long and is simply supported at
Band E. The lengths of the various portions are AB 1-5m, BC = 1-5m, CD = 1 m and DE
: 3 m. There is a uniformly distributed load of 15kN/m between B and a point 2m
to the right of B and concentrated loads of 20 KN act at 4 and 0 with one of 50
KN at C. (a) Draw the S.F. diagrams and hence determine the position from A at
which the S.F. is zero. (b) Determine the value of the B.M. at this point. (c) Sketch
the B.M. diagram approximately to scale, quoting the principal values. [3.32 m, 69.8
KNm, 0, 30, 69.1, 68.1, 0 kNm.]
Chapter 5 Solutions
Calculus & Its Applications
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Ch. 5.1 - In Exercises 110, determine the growth constant k,...Ch. 5.1 - In Exercises 110, determine the growth constant k,...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - In Exercises 1118, solve the given differential...Ch. 5.1 - Population and Exponential Growth Let P(t) be the...Ch. 5.1 - Growth of a Colony of Fruit Flies A colony of...Ch. 5.1 - GrowthConstant for a Bacteria Culture Abacteria...Ch. 5.1 - Growth of a Bacteria Culture The initial size of a...Ch. 5.1 - Using the Differential Equation Let P(t) be the...Ch. 5.1 - Growth of Bacteria Approximately 10,000 bacteria...Ch. 5.1 - Growth of cells After t hours, there are P(t)...Ch. 5.1 - 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Radioactive Decay Forty grams of a certain...Ch. 5.1 - Radioactive Decay A sample of radioactive material...Ch. 5.1 - Rate of Decay A sample of radioactive material has...Ch. 5.1 - Carbon Dating In 1947, a cave with beautiful...Ch. 5.1 - King Arthur's Round Table According to legend, in...Ch. 5.1 - Prob. 49ECh. 5.1 - Population of the PacificNorthwest In 1938,...Ch. 5.1 - Time of the Fourth Ice Age Many scientists believe...Ch. 5.1 - Time Constant Let T be the time constant of the...Ch. 5.1 - Prob. 53ECh. 5.1 - Time Constant and Half-life Consider as...Ch. 5.1 - An Initial Value Problem Suppose that the function...Ch. 5.1 - Time to Finish Consider the exponential decay...Ch. 5.2 - One thousand dollars is to be invested in a bank...Ch. 5.2 - A building was bought for 150,000 and sold 10...Ch. 5.2 - Savings Account Let A(t)=5000e0.04t be the balance...Ch. 5.2 - Savings Account Let A(t) be the balance in a...Ch. 5.2 - Savings Account Four thousand dollars is deposited...Ch. 5.2 - Savings Account Ten thousand dollars is deposited...Ch. 5.2 - 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Prob. 26ECh. 5.2 - Prob. 27ECh. 5.2 - Prob. 28ECh. 5.2 - Prob. 29ECh. 5.2 - Prob. 30ECh. 5.2 - Prob. 31ECh. 5.3 - The current toll for the use of a certain toll...Ch. 5.3 - The current toll for the use of a certain toll...Ch. 5.3 - The current toll for the use of a certain toll...Ch. 5.3 - Find the logarithmic derivative and then determine...Ch. 5.3 - Prob. 2ECh. 5.3 - Find the logarithmic derivative and then determine...Ch. 5.3 - Find the logarithmic derivative and then determine...Ch. 5.3 - Find the logarithmic derivative and then determine...Ch. 5.3 - Prob. 6ECh. 5.3 - Find the logarithmic derivative and then determine...Ch. 5.3 - Prob. 8ECh. 5.3 - Percentage Rate of Growth The annual sales S(in...Ch. 5.3 - Prob. 10ECh. 5.3 - Price of Ground Beef The wholesale price in...Ch. 5.3 - Price of Pork The wholesale price in dollars of...Ch. 5.3 - For each demand function, find E(p) and determine...Ch. 5.3 - Prob. 14ECh. 5.3 - For each demand function, find E(p) and determine...Ch. 5.3 - For each demand function, find E(p) and determine...Ch. 5.3 - For each demand function, find E(p) and determine...Ch. 5.3 - Prob. 18ECh. 5.3 - Elasticity of Demand Currently 1800 people ride a...Ch. 5.3 - Prob. 20ECh. 5.3 - Elasticity of Demand A movie theater has a seating...Ch. 5.3 - Prob. 22ECh. 5.3 - Elasticity of Demand A country that is the major...Ch. 5.3 - Prob. 24ECh. 5.3 - Prob. 25ECh. 5.3 - Prob. 26ECh. 5.3 - Prob. 27ECh. 5.3 - Prob. 28ECh. 5.3 - Prob. 29ECh. 5.4 - A sociological study was made to examine the...Ch. 5.4 - Prob. 2CYUCh. 5.4 - Prob. 1ECh. 5.4 - Prob. 2ECh. 5.4 - Prob. 3ECh. 5.4 - Prob. 4ECh. 5.4 - Prob. 5ECh. 5.4 - Prob. 6ECh. 5.4 - Prob. 7ECh. 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 - Prob. 14ECh. 5.4 - Prob. 15ECh. 5.4 - Prob. 16ECh. 5.4 - Prob. 17ECh. 5.4 - Prob. 18ECh. 5.4 - Prob. 19ECh. 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 - Prob. 31ECh. 5.4 - Prob. 32ECh. 5.4 - Prob. 33ECh. 5.4 - Prob. 34ECh. 5.4 - Prob. 35ECh. 5.4 - Prob. 36ECh. 5.4 - Prob. 37ECh. 5.4 - Prob. 38ECh. 5.4 - Prob. 39ECh. 5.4 - Prob. 40ECh. 5.4 - Prob. 41ECh. 5.4 - Prob. 42ECh. 5 - What differential equation is key to solving...Ch. 5 - Prob. 2FCCECh. 5 - Prob. 3FCCECh. 5 - Explain how radiocarbon dating works.Ch. 5 - Prob. 5FCCECh. 5 - Prob. 6FCCECh. 5 - Define the elasticity of demand, E(p), for a...Ch. 5 - Describe an application of the differential...Ch. 5 - Prob. 9FCCECh. 5 - Atmospheric Pressure The atmospheric pressure...Ch. 5 - Population Model The herring gull population in...Ch. 5 - Present Value Find the present value of 10,000...Ch. 5 - Compound Interest One thousand dollars is...Ch. 5 - Half-Life The half-life of the radioactive element...Ch. 5 - Carbon Dating A piece of charcoal found at...Ch. 5 - Population Model From January 1, 2010, to January...Ch. 5 - Compound Interest A stock portfolio increased in...Ch. 5 - Comparing Investments An investor initially...Ch. 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. 22RE
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- 4. Verify that V X (aẢ) = (Va) XẢ + aV X Ả where Ả = xyz(x + y + 2) A and a = 3xy + 4zx by carrying out the detailed differentiations.arrow_forward3. For each of the arrow or quiver graphs shown below, determine analytically V°C and V X Č. From these analytical solutions, identify the extrema (+/-) and plot these points on the arrow graph. (a) C = −✰CosxSiny + ŷSinxCosy -π<ׂу<π Ty (b) C = −xSin2y + ŷCos2y x, y<π -π< (c) C = −xCosx + ŷSiny -π< x, y < πarrow_forward7.10 (B/C). A circular flat plate of diameter 305 mm and thickness 6.35 mm is clamped at the edges and subjected to a Uniform lateral pressure of 345 kN/m². Evaluate: (a) the central deflection, (b) the position and magnitude of the maximum radial stress. C6.1 x 10 m; 149.2 MN/m².] 100 200arrow_forward
- 3.15 (B). A beam ABCD is simply supported at B and C with ABCD=2m; BC 4 m. It carries a point load of 60 KN at the free end A, a Uniformly distributed load of 60 KN/m between B and C and an anticlockwise moment of 80 KN m in the plane of the beam applied at the free end D. Sketch and dimension the S.F. and B.M. diagrams, and determine the position and magnitude of the maximum bending moment. CEL.E.] CS.F. 60, 170, 70KN, B.M. 120, +120.1, +80 kNm, 120.1 kNm at 2.83 m to right of 8.7arrow_forward7.1 (A/B). A Uniform I-section beam has flanges 150 mm wide by 8 mm thick and a web 180 mm wide and 8 mm thick. At a certain section there is a shearing force of 120 KN. Draw a diagram to illustrate the distribution of shear stress across the section as a result of bending. What is the maximum shear stress? [86.7 MN/m².arrow_forward1. Let Ả = −2x + 3y+42, B = - - 7x +lý +22, and C = −1x + 2y + 42. Find (a) Ả X B (b) ẢX B°C c) →→ Ả B X C d) ẢB°C e) ẢX B XC.arrow_forward
- 3.13 (B). A beam ABC, 6 m long, is simply-supported at the left-hand end A and at B I'm from the right-hand end C. The beam is of weight 100 N/metre run. (a) Determine the reactions at A and B. (b) Construct to scales of 20 mm = 1 m and 20 mm = 100 N, the shearing-force diagram for the beam, indicating thereon the principal values. (c) Determine the magnitude and position of the maximum bending moment. (You may, if you so wish, deduce the answers from the shearing force diagram without constructing a full or partial bending-moment diagram.) [C.G.] C240 N, 360 N, 288 Nm, 2.4 m from A.]arrow_forward5. Using parentheses make sense of the expression V · VXVV · Å where Ả = Ã(x, y, z). Is the result a vector or a scaler?arrow_forward3.10 (A/B). A beam ABCDE is simply supported at A and D. It carries the following loading: a distributed load of 30 kN/m between A and B, a concentrated load of 20 KN at B, a concentrated load of 20 KN at C, a concentrated load of 10 KN at E; a distributed load of 60 kN/m between 0 and E. Span AB = 1.5 BC = CD = DE 1 m. Calculate the value of the reactions at A and D and hence draw the S.F. and B.M. diagrams. What are the magnitude and position of the maximum B.M. on the beam? [41.1, 113.9 KN, 28.15 kNm; 1.37 m from A.J m,arrow_forward
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