EBK CALCULUS & ITS APPLICATIONS
14th Edition
ISBN: 8220103679527
Author: Asmar
Publisher: YUZU
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Textbook Question
Chapter 10.4, Problem 1E
A Retirement Account refer toExample 1
a. How fast was the amount in the account growing when it reached?
b. How much money was in the account when it was growing at twice the rate of your annual contribution?
c. How long do you have to wait for the money in the account to reach
Example 1: A Retirement Account
You invest in a retirement account that pays
a. Set up an initial-value problem that is satisfied by
b. Find
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Students have asked these similar questions
7.1 (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.
1. 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.
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.]
Chapter 10 Solutions
EBK CALCULUS & ITS APPLICATIONS
Ch. 10.1 - Show that any function of the form y=Aet3/3, where...Ch. 10.1 - If the function f(t) is a solution of the...Ch. 10.1 - Prob. 3CYUCh. 10.1 - Show that the function f(t)=32et212 is a solution...Ch. 10.1 - Show that the function f(t)=t212 is a solution of...Ch. 10.1 - Show that the function f(t)=5e2t satisfies...Ch. 10.1 - Show that the function f(t)=(et+1)1 satisfies...Ch. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Is the constant function f(t)=3 a solution of the...
Ch. 10.1 - Prob. 8ECh. 10.1 - Find a constant solution of y=t2y5t2.Ch. 10.1 - Prob. 10ECh. 10.1 - Prob. 11ECh. 10.1 - Prob. 12ECh. 10.1 - Prob. 13ECh. 10.1 - Prob. 14ECh. 10.1 - Prob. 15ECh. 10.1 - Savings Account Let f(t) be the balance in a...Ch. 10.1 - Spread of News A certain piece of news is being...Ch. 10.1 - Paramecium Growth Let f(t) be the size of...Ch. 10.1 - Rate of Net Investment Let f(t) denote the amount...Ch. 10.1 - Newtons Law of Cooling A cool object is placed in...Ch. 10.1 - Carbon Dioxide Diffusion in Lungs during Breath...Ch. 10.1 - Slope Field The slope field in Fig4(a) suggests...Ch. 10.1 - Prob. 23ECh. 10.1 - On the slope field in Fig5(a), or a copy of it,...Ch. 10.1 - Prob. 25ECh. 10.1 - On the slope field in Fig4(a), or a copy of it,...Ch. 10.1 - Prob. 27ECh. 10.1 - Prob. 28ECh. 10.1 - Prob. 29ECh. 10.1 - Prob. 30ECh. 10.1 - Technology Exercise Consider the differential...Ch. 10.1 - Technology Exercise The function f(t)=50001+49et...Ch. 10.2 - Solve the initial-value problem y=5y,y(0)=2, by...Ch. 10.2 - Solve y=ty,y(1)=4.Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Prob. 8ECh. 10.2 - Prob. 9ECh. 10.2 - Solve the following differential equations:...Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Prob. 12ECh. 10.2 - Prob. 13ECh. 10.2 - Solve the following differential equations:...Ch. 10.2 - Prob. 15ECh. 10.2 - Prob. 16ECh. 10.2 - Prob. 17ECh. 10.2 - Prob. 18ECh. 10.2 - Solve the following differential equations with...Ch. 10.2 - Solve the following differential equations with...Ch. 10.2 - Solve the following differential equations with...Ch. 10.2 - Solve the following differential equations with...Ch. 10.2 - Prob. 23ECh. 10.2 - Solve the following differential equations with...Ch. 10.2 - Prob. 25ECh. 10.2 - Prob. 26ECh. 10.2 - Solve the following differential equations with...Ch. 10.2 - Solve the following differential equations with...Ch. 10.2 - Prob. 29ECh. 10.2 - Prob. 30ECh. 10.2 - Prob. 31ECh. 10.2 - Prob. 32ECh. 10.2 - Probability of AccidentsLet t represent the total...Ch. 10.2 - Amount of Information LearnedIn certain learning...Ch. 10.2 - Prob. 35ECh. 10.2 - Prob. 36ECh. 10.2 - Prob. 37ECh. 10.2 - Rate of DecompositionWhen a certain liquid...Ch. 10.2 - Prob. 39ECh. 10.2 - Prob. 40ECh. 10.3 - Using an integrating factor, solve y+y=1+et.Ch. 10.3 - Find an integrating factor for the differential...Ch. 10.3 - Find an integrating factor for an equation:...Ch. 10.3 - Find an integrating factor for an equation:...Ch. 10.3 - Find an integrating factor for an equation:...Ch. 10.3 - Find an integrating factor for an equation:...Ch. 10.3 - Find an integrating factor for the equation:...Ch. 10.3 - Find an integrating factor for the equation:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the initial value problem: y+2y=1,y(0)=1.Ch. 10.3 - Solve the initial value problem:...Ch. 10.3 - Solve the initial value problem:...Ch. 10.3 - Solve the initial value problem: y=2(10y),y(0)=1.Ch. 10.3 - Solve the initial value problem: y+y=e2t,y(0)=1.Ch. 10.3 - Solve the initial value problem: tyy=1,y(1)=1,t0.Ch. 10.3 - Solve the initial value problem:...Ch. 10.3 - Solve the initial value problem:...Ch. 10.3 - Consider the initial value problem...Ch. 10.4 - Solutions can be found following the section...Ch. 10.4 - A Retirement Account refer toExample 1 a. How fast...Ch. 10.4 - Prob. 2ECh. 10.4 - A Retirement Account A person planning for her...Ch. 10.4 - A Savings Account A person deposits 10,000 in bank...Ch. 10.4 - Prob. 5ECh. 10.4 - Prob. 6ECh. 10.4 - Aperson took out a loan of 100,000 from a bank...Ch. 10.4 - Car Prices in 2012 The National Automobile Dealers...Ch. 10.4 - New Home Prices in 2012 The Federal Housing...Ch. 10.4 - Answer parts (a), (b), and (c) of Exercise 9 if...Ch. 10.4 - Prob. 11ECh. 10.4 - Find the demand function if the elasticity of...Ch. 10.4 - Temperature of a Steel Rod When a red-hot steel...Ch. 10.4 - Prob. 14ECh. 10.4 - Determining the Time of Death A body was found in...Ch. 10.4 - Prob. 16ECh. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - Prob. 19ECh. 10.4 - Radioactive Decay Radium 226 is a radioactive...Ch. 10.4 - In Exercises 2125, solving the differential...Ch. 10.4 - Prob. 22ECh. 10.4 - In Exercises 2125, solving the differential...Ch. 10.4 - Prob. 24ECh. 10.4 - Prob. 25ECh. 10.4 - Technology Exercise Therapeutic Level of a Drug A...Ch. 10.5 - Consider the differential equation y=g(y) where...Ch. 10.5 - Prob. 2CYUCh. 10.5 - Prob. 3CYUCh. 10.5 - Prob. 4CYUCh. 10.5 - Exercise 1-6 review concepts that are important in...Ch. 10.5 - Prob. 2ECh. 10.5 - Prob. 3ECh. 10.5 - Prob. 4ECh. 10.5 - Prob. 5ECh. 10.5 - Prob. 6ECh. 10.5 - One or more initial conditions are given for each...Ch. 10.5 - One or more initial conditions are given for each...Ch. 10.5 - One or more initial conditions are given for each...Ch. 10.5 - One or more initial conditions are given for each...Ch. 10.5 - Prob. 11ECh. 10.5 - Prob. 12ECh. 10.5 - Prob. 13ECh. 10.5 - Prob. 14ECh. 10.5 - Prob. 15ECh. 10.5 - Prob. 16ECh. 10.5 - One or more initial conditions are given for each...Ch. 10.5 - Prob. 18ECh. 10.5 - Prob. 19ECh. 10.5 - Prob. 20ECh. 10.5 -
Ch. 10.5 - Prob. 22ECh. 10.5 - Prob. 23ECh. 10.5 - Prob. 24ECh. 10.5 - Prob. 25ECh. 10.5 -
Ch. 10.5 - Prob. 27ECh. 10.5 - Prob. 28ECh. 10.5 - Prob. 29ECh. 10.5 - Prob. 30ECh. 10.5 - Prob. 31ECh. 10.5 - Prob. 32ECh. 10.5 - Prob. 33ECh. 10.5 - , where , and
Ch. 10.5 - Prob. 35ECh. 10.5 - Prob. 36ECh. 10.5 - Growth of a plant Suppose that, once a sunflower...Ch. 10.5 - Prob. 38ECh. 10.5 - Technology Exercises
Draw the graph of, and use...Ch. 10.5 - Technology Exercises Draw the graph of...Ch. 10.6 - Refer to Example 4, involving the flow of...Ch. 10.6 - In Exercises 1- 4, you are given a logistic...Ch. 10.6 - Prob. 2ECh. 10.6 - In Exercises 1- 4, you are given a logistic...Ch. 10.6 - Prob. 4ECh. 10.6 - Answer part (a) in Example 2, if the pond was...Ch. 10.6 - Prob. 6ECh. 10.6 - Social Diffusion For information being spread by...Ch. 10.6 - Gravity At one point in his study of a falling...Ch. 10.6 - Autocatalytic Reaction In an autocatalytic...Ch. 10.6 - Drying A porous material dries outdoors at a rate...Ch. 10.6 - Movement of Solutes through a Cell Membrane Let c...Ch. 10.6 - Bacteria Growth An experimenter reports that a...Ch. 10.6 - Chemical Reaction Suppose that substance A is...Ch. 10.6 - War Fever L. F. Richardson proposed the following...Ch. 10.6 - Capital Investment Model In economic theory, the...Ch. 10.6 - 16. Evans Price Adjustment Model Consider a...Ch. 10.6 - Fish Population with Harvesting The fish...Ch. 10.6 - Continuous Annuity A continuous annuity is a...Ch. 10.6 - Savings Account with Deposits A company wishes to...Ch. 10.6 - Savings Account A company arranges to make...Ch. 10.6 - Amount of CO2 in a Room The air in a crowded room...Ch. 10.6 - Elimination of a Drug from the Bloodstream A...Ch. 10.6 - Elimination of a Drug A single dose of iodine is...Ch. 10.6 - Litter in a Forest Show that the mathematical...Ch. 10.6 - Population Model In the study of the effect of...Ch. 10.7 - Prob. 1CYUCh. 10.7 - Prob. 2CYUCh. 10.7 - Prob. 1ECh. 10.7 - Prob. 2ECh. 10.7 - Prob. 3ECh. 10.7 - Prob. 4ECh. 10.7 - Prob. 5ECh. 10.7 - Prob. 6ECh. 10.7 - Use Eulers method with n=4 to approximate the...Ch. 10.7 - Let be the solution of , Use Euler’s method with...Ch. 10.7 - Prob. 9ECh. 10.7 - Prob. 10ECh. 10.7 - Suppose that the consumer Products Safety...Ch. 10.7 -
12. Rate of evaporation The Los Angeles plans to...Ch. 10.7 - Prob. 13ECh. 10.7 - The differential equation y=0.5(1y)(4y) has five...Ch. 10.7 - Prob. 15ECh. 10.7 - Prob. 16ECh. 10 - What is a differential equation?Ch. 10 - Prob. 2CCECh. 10 - Prob. 3CCECh. 10 - Prob. 4CCECh. 10 - Prob. 5CCECh. 10 - Prob. 6CCECh. 10 - Prob. 7CCECh. 10 - Prob. 8CCECh. 10 - Prob. 9CCECh. 10 - Prob. 10CCECh. 10 - Prob. 11CCECh. 10 - Prob. 12CCECh. 10 - Describe Eulers method for approximating the...Ch. 10 - Prob. 1RECh. 10 - Prob. 2RECh. 10 - Prob. 3RECh. 10 - Prob. 4RECh. 10 - Prob. 5RECh. 10 - Prob. 6RECh. 10 - Prob. 7RECh. 10 - Solve the differential equation in Exercises 1-10....Ch. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - Prob. 11RECh. 10 - Let P(t) denote the price in dollars of a certain...Ch. 10 - Prob. 13RECh. 10 - Prob. 14RECh. 10 - Prob. 15RECh. 10 - Prob. 16RECh. 10 - Prob. 17RECh. 10 - Prob. 18RECh. 10 - Prob. 19RECh. 10 - Sketch the solutions of the differential equations...Ch. 10 - Sketch the solutions of the differential equations...Ch. 10 - Prob. 22RECh. 10 - Prob. 23RECh. 10 - Prob. 24RECh. 10 - Prob. 25RECh. 10 - Suppose that in a chemical reaction, each gram of...Ch. 10 - Prob. 27RECh. 10 - Prob. 28RECh. 10 - Let f(t) be the solution to y=2e2ty,y(0)=0. Use...Ch. 10 - Prob. 30RECh. 10 - Prob. 31RECh. 10 - Prob. 32RE
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- 5. 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_forward3.14 (B). A beam ABCD, 6 m long, is simply-supported at the right-hand end and at a point B Im from the left-hand end A. It carries a vertical load of 10 KN at A, a second concentrated load of 20 KN at C, 3 m from D, and a uniformly distributed load of 10 kN/m between C and D. Determine: (a) the values of the reactions at B and 0, (6) the position and magnitude of the maximum bending moment. [33 KN, 27 KN, 2.7 m from D, 36.45k Nm.]arrow_forward
- 3.17 (B). A simply supported beam has a span of 6 m and carries a distributed load which varies in a linea manner from 30 kN/m at one support to 90 kN/m at the other support. Locate the point of maximum bendin moment and calculate the value of this maximum. Sketch the S.F. and B.M. diagrams. [U.L.] [3.25 m from l.h. end; 272 KN m 30. 90arrow_forward3.11 (B). A beam, 12 m long, is to be simply supported at 2m from each end and to carry a U.d.l of 30kN/m together with a 30 KN point load at the right-hand end. For ease of transportation the beam is to be jointed in two places, one joint being Situated 5 m from the left-hand end. What load (to the nearest KN) must be applied to the left-hand end to ensure that there is no B.M. at the joint (i.e. the joint is to be a point of contraflexure)? What will then be the best position on the beam for the other joint? Determine the position and magnitude of the maximum B.M. present on the beam. [114 KN, 1.6 m from r.h. reaction; 4.7 m from 1.h. reaction; 43.35 KN m.]arrow_forward2. Using vector algebraic operations, if - Ả = 2ây – mây – C - B = mây tây – 2, C = ây + mây + 20, D = m x + mây tậ Z Find the value(s) of m such that (a) Ả is perpendicular to B (b) B is parallel to Carrow_forward
- 1. Determine whether the following sets are subspaces of $\mathbb{R}^3$ under the operations of addition and scalar multiplication defined on $\mathbb{R}^3$. Justify your answers.(a) $W_1=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1=3 a_2\right.$ and $\left.a_3=\mid a_2\right\}$(b) $W_2=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1=a_3+2\right\}$(c) $W_3=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: 2 a_1-7 a_2+a_3=0\right\}$(d) $W_4=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1-4 a_2-a_3=0\right\}$(e) $W_s=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1+2 a_2-3 a_3=1\right\}$(f) $W_6=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: 5 a_1^2-3 a_2^2+6 a_3^2=0\right\}$arrow_forward3 Evaluate the double integral 10 y√x dy dx. First sketch the area of the integral involved, then carry out the integral in both ways, first over x and next over y, and vice versa.arrow_forwardQuestion 2. i. Suppose that the random variable X takes two possible values 1 and -1, and P(X = 1) = P(X-1)=1/2. Let Y=-X. Are X and Y the same random variable? Do X and Y have the same distribution? Explain your answer. ii. Suppose that the random variable X~N(0, 1), let Y=-X. Are X and Y the same random variable? Do X and Y have the same distribution? Explain your answer.arrow_forward
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