Mathematical Methods in the Physical Sciences
3rd Edition
ISBN: 9780471198260
Author: Mary L. Boas
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 9.6, Problem 2P
In Problems 1 and 2, given the length
The plane area between the curve and a straight line joining the points is a maximum.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
23. [0/3 Points]
DETAILS
MY NOTES
SCALCET8 12.2.042.
(a) Find the unit vectors that are parallel to the tangent line to the curve y = 8 sin(x) at the point (π/6, 4). (Enter your answer as a comm
½(1+4√√31 ), − ½ (1+4√√3j
(b) Find the unit vectors that are perpendicular to the tangent line.
(4√31 − 1), (4√√31 –j)
— ½-½
(c) Sketch the curve y = 8 sin(x) and the vectors in parts (a) and (b), all starting at (π/6, 4).
y
10
5
-5
Need Help? Read It
5
-5
10
y
-5
5
X
-5
о
5
x
-5
y
10
-5
y
10
5
-5
5
x
5
X
Find the cross product a x b.
a = i + 4j - 3k, b = -i + 5k
Verify that it is orthogonal to both a and b.
(a x b) a =
(a x b) b =
Need Help?
Read It
Watch It
Find the cross product a x b.
a = (t, 1, 1/t),
b = (t², t², 1)
Verify that it is orthogonal to both a and b.
(a x b) a =
(a x b) b =
Need Help?
Read It
Watch It
Chapter 9 Solutions
Mathematical Methods in the Physical Sciences
Ch. 9.1 - The speed of light in a medium of index of...Ch. 9.1 - The speed of light in a medium of index of...Ch. 9.1 - The speed of light in a medium of index of...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...
Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.2 - Write and solve the Euler equations to make the...Ch. 9.3 - Change the independent variable to simplify the...Ch. 9.3 - Change the independent variable to simplify the...Ch. 9.3 - Change the independent variable to simplify the...Ch. 9.3 - Change the independent variable to simplify the...Ch. 9.3 - Write and solve the Euler equations to make the...Ch. 9.3 - Write and solve the Euler equations to make the...Ch. 9.3 - Write and solve the Euler equations to make the...Ch. 9.3 - Write and solve the Euler equations to make the...Ch. 9.3 - Write and solve the Euler equations to make the...Ch. 9.3 - Write and solve the Euler equations to make the...Ch. 9.3 - Use Fermats principle to find the path followed by...Ch. 9.3 - Use Fermats principle to find the path followed by...Ch. 9.3 - Use Fermats principle to find the path followed by...Ch. 9.3 - Use Fermats principle to find the path followed by...Ch. 9.3 - Find the geodesics on a plane using polar...Ch. 9.3 - Prob. 16PCh. 9.3 - Find the geodesics on the cone x2+y2=z2. Hint: Use...Ch. 9.3 - Find the geodesics on a sphere. Hints: Use...Ch. 9.4 - Verify equations (4.2).Ch. 9.4 - Show, in Figure 4.4, that for a point like...Ch. 9.4 - In the brachistochrone problem, show that if the...Ch. 9.4 - Consider a rapid transit system consisting of...Ch. 9.4 - In Problems 5 to 7, use Fermats principle to find...Ch. 9.4 - In Problems 5 to 7, use Fermats principle to find...Ch. 9.4 - In Problems 5 to 7, use Fermats principle to find...Ch. 9.5 - (a) Consider the case of two dependent variables....Ch. 9.5 - Set up Lagranges equations in cylindrical...Ch. 9.5 - Do Problem 2 in spherical coordinates.Ch. 9.5 - Use Lagranges equations to find the equation of...Ch. 9.5 - Find the equation of motion of a particle moving...Ch. 9.5 - A particle moves on the surface of a sphere of...Ch. 9.5 - Prove that a particle constrained to stay on a...Ch. 9.5 - Two particles each of mass m are connected by an...Ch. 9.5 - A mass m moves without friction on the surface of...Ch. 9.5 - Do Example 3 above, using cylindrical coordinates...Ch. 9.5 - A yo-yo (as shown) falls under gravity. Assume...Ch. 9.5 - Find the Lagrangian and Lagranges equations for a...Ch. 9.5 - A particle moves without friction under gravity on...Ch. 9.5 - 2A hoop of mass M and radius a rolls without...Ch. 9.5 - Generalize Problem 14 to any mass M of circular...Ch. 9.5 - Find the Lagrangian and the Lagrange equation for...Ch. 9.5 - A simple pendulum (Problem 4) is suspended from a...Ch. 9.5 - A hoop of mass m in a vertical plane rests on a...Ch. 9.5 - For the following problems, use the Lagrangian to...Ch. 9.5 - For the following problems, use the Lagrangian to...Ch. 9.5 - For the following problems, use the Lagrangian to...Ch. 9.5 - For the following problems, use the Lagrangian to...Ch. 9.5 - For the following problems, use the Lagrangian to...Ch. 9.5 - For the following problems, use the Lagrangian to...Ch. 9.5 - For the following problems, use the Lagrangian to...Ch. 9.6 - In Problems 1 and 2, given the length l of a curve...Ch. 9.6 - In Problems 1 and 2, given the length l of a curve...Ch. 9.6 - Given 10 cc of lead, find how to form it into a...Ch. 9.6 - Prob. 4PCh. 9.6 - A curve y=y(x), joining two points x1 and x2 on...Ch. 9.6 - In Problem 5, given the volume, find the shape of...Ch. 9.6 - Integrate (6.2), simplify the result and integrate...Ch. 9.8 - (a) In Section 3, we showed how to obtain a first...Ch. 9.8 - Find a first integral of the Euler equation to...Ch. 9.8 - Find a first integral of the Euler equation to...Ch. 9.8 - Find a first integral of the Euler equation to...Ch. 9.8 - Write and solve the Euler equations to make...Ch. 9.8 - Write and solve the Euler equations to make...Ch. 9.8 - Write and solve the Euler equations to make...Ch. 9.8 - Find the geodesics on the cylinder r=1+cos.Ch. 9.8 - Prob. 9MPCh. 9.8 - Find the geodesics on the parabolic cylinder y=x2.Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - In Problems 11 to 18, use Fermats principle to...Ch. 9.8 - Find Lagranges equations in polar coordinates for...Ch. 9.8 - Repeat Problem 19 if V=K/r.Ch. 9.8 - Write Lagranges equations in cylindrical...Ch. 9.8 - In spherical coordinates, find the Lagrange...Ch. 9.8 - A particle slides without friction around a...Ch. 9.8 - Write and simplify the Euler equation to make...Ch. 9.8 - Prob. 25MPCh. 9.8 - A wire carrying a uniform distribution of positive...Ch. 9.8 - Find a first integral of the Euler equation for...Ch. 9.8 - Write the Lagrange equation for a particle moving...
Additional Math Textbook Solutions
Find more solutions based on key concepts
CHECK POINT 1 In a survey on musical tastes, respondents were asked: Do you listed to classical music? Do you l...
Thinking Mathematically (6th Edition)
Continuity at a point Determine whether the following functions are continuous at a. Use the continuity checkli...
Calculus: Early Transcendentals (2nd Edition)
Whether the requirements for a hypothesis test are satisfied or not.
Elementary Statistics
NOTE: Write your answers using interval notation when appropriate.
CHECKING ANALYTIC SKILLS Fill in each blank ...
Graphical Approach To College Algebra
Testing Hypotheses. In Exercises 13-24, assume that a simple random sample has been selected and test the given...
Elementary Statistics Using The Ti-83/84 Plus Calculator, Books A La Carte Edition (5th Edition)
Suppose you toss one coin three times in a row and get heads, tails, heads (HTH). If you are interested in the ...
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Find the cross product a x b. a = (4, 5, 0), b = (1, 0, 7) Verify that it is orthogonal to both a and b. (a x b) a = (a x b). b = Need Help? Read Itarrow_forwardSketch the graph of a function f(y) such that the one-parameter family of differential equations dy = f(y) + a satisfies the below properties: i) For all a <-3, the DE has exactly two equilibria. ii) For all a ≥ 3, the equation has no equilibria. iii) For a = 0, the equation has exactly four equilibria Consider the population model given by dP = 2P - P dt 50 for a species of deer in a forest. It is decided that hunting will be allowed, but it is unclear how many hunting licenses should be issued. The average licensed hunter will kill 3 deer per year. (a) What is the largest number of licenses that can be issued for the deer population to survive? (b) What will happen to the deer population if this many licenses are issued? (c) Draw a bifurcation diagram for the parameter which represents the number of issued hunting licenses.arrow_forwardConsider the function below. (If an answer does not exist, enter DNE.) h(x) = 5x³-3x³ (a) Find the interval of increase. (Enter your answer using interval notation.) (-00,0) U (1,00) Find the interval of decrease. (Enter your answer using interval notation.) (0,1) (b) Find the local minimum value(s). (Enter your answers as a comma-separated list.) -1.6 Find the local maximum value(s). (Enter your answers as a comma-separated list.) 1.6 (c) Find the inflection points. (x, y) = (smallest x-value) (x, y) (x, y) = = (largest x-value) Find the interval where the graph is concave upward. (Enter your answer using interval notation.) Find the interval where the graph is concave downward. (Enter your answer using interval notation.)arrow_forward
- Given the following line segment of length a units, draw a picture that illustrates how you a would use only a straight-edge and a compass to construct a segment of length exactly 5 units. Also, provide a written explanation of your process. You may use, without justification, the fact that if you are given a line L and a point P that is not on L, a line L' can be constructed that passes through point P and is parallel to line L. aarrow_forwardSuppose you are given only the following segment of length 1. Thoroughly describe your process for constructing a segment of length √5 using only a straight-edge and compass, and this segment of length 1.arrow_forwardConsider ∆ABC shown below. Using only a Straight edge and Compas, construct a triangle ∆A′B′C′, where A′,B′, and C′ are points in the plane distinct from A,B, and C, and such that ∆ABC is congruent to ∆A′B′C′. Please thoroughly explain your process and provide justification for how you know these triangles are congruentarrow_forward
- Suppose you are given that the following angle measures 38°. Please show and explain how you could use this angle as well as a SE&C to construct an angle that measures 57°.arrow_forwardSuppose you are given two lines that are not parallel, and are each intersected at separate points by a third line (a transversal). Please explain what contradiction would arise if you assume that alternate interior angles at the transversal are congruent.arrow_forwardName: Instructions: BAVAROKO JUNIOR HIGH SCHOOL QUALITY & EQUALITY GRADE 9 NINE MATHEMATICS ASSIGNMENT #2 TERM 2, Wk 9, 2025 Class: Date 9/6/25 Due-date: 16/06/25 Worth: 125marks Read the assignment questions carefully before answering it. Clearly show all working out neatly on the space provided using a pen. A poorly presented assignment with insufficient working out will result in a low mark. All final Answer must be boxed. Two (2) marks will be deducted for late submission of assignment. Cheating is NOT allowed. QUESTION 1 3 marks Find the value of arc QT. QUESTION 3 Solve for x. a) 55" 95 79° 3x+23 S 75" QUESTION 2 Find the value of arc LK. x K 65 J74" M b) 3 marks 159 8x+34/ 53" 9 marks (3 marks each)arrow_forward
- 3. Use the Gram-Schmidt process to find an orthonormal basis for the subspace of R4 spanned by the vectors u₁ = (1,0,0,0), u2 = (1,1,0,0), uз = (0, 1, 1, 1). U3arrow_forward1. Suppose u = (1,0, -1), v = (0, 1, −1), and w = (1,2,-3). (a) Find || 2u3v+w||. (b) Find the angle between u and v. (c) Find ||u||||v|| — u · v. (d) Find the orthogonal projection of u onto v. Show all your work.arrow_forward2. Suppose x and y are nonzero vectors in an inner product space. Show that x and y are orthogonal if and only if ||x+y|| = ||x − y||. -arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Trigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Cengage Learning
Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY