Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 52, Problem 10A
Solve the following exercises:
In
a. Find ∠A.
b. Find ∠F.
c. Find ∠B.
d. Find ∠E.
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Chapter 52 Solutions
Mathematics for Machine Technology
Ch. 52 - Determine the size of 1.Ch. 52 - If ABCD,BCDE , and 1=2725 , what are the sizes of...Ch. 52 - What is the supplement of a 1051344 angle?Ch. 52 - Determine the center diameter of a pinion gear...Ch. 52 - Solve 578=234x.Ch. 52 - Determine the value of 406.442-1/3. Round the...Ch. 52 - Determine which of the following pairs of...Ch. 52 - Solve the following exercises: In ABC and...Ch. 52 - Solve the following exercises: In figure,...Ch. 52 - Solve the following exercises: In ABC and...
Ch. 52 - Solve the following exercises: Use the figure to...Ch. 52 - Solve the following exercises: In HPM,PMJK. a....Ch. 52 - Solve the following exercises: Refer to the figure...Ch. 52 - Solve the following exercises: Refer to the figure...Ch. 52 - Solve the following exercises: In this figure,...Ch. 52 - Solve the following exercises: a. Find x. b. Find...Ch. 52 - Solve the following exercises: a. Find x. b. Find...Ch. 52 - All dimensions are in inches. a. Find 1. b. Find ...Ch. 52 - All dimensions are in millimeters. a. Find x. b....Ch. 52 - All dimensions are in inches. a. Find 1. b. Find...Ch. 52 - Refer to this figure. Using the given values, find...Ch. 52 - Using the figure and these given values, find the...Ch. 52 - Using the figure and these given values, find the...Ch. 52 - Three holes are drilled in the plate shown. All...Ch. 52 - All dimensions are in inches. Round the answers to...Ch. 52 - All dimensions are in inches. Round the answers to...Ch. 52 - Solve the following exercises: A template is...Ch. 52 - Refer to polygon ABCD. a. If 2 = 87.0, find 1. b....Ch. 52 - Use the angle values given. a. If 1 = 114, find 2....Ch. 52 - Use the angle values given to find 2. a. If 1 =...
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- Q3. Find all solutions of x² - 29y² = ±1 with x, y ɛ Z.arrow_forwardProblem 11 (Gram-Schmidt). Try the Gram-Schmidt procedure for the vectors, 1 0 2 with respect to the standard dot product on R4. What happens? Can you explain why you are unable to complete the algorithm? Problem 12 (Orthogonal Matrices Preserve Orthogonality). Suppose x, y = Rn" are orthogonal to each other with respect to some inner product (.,.) and that A is an orthogonal matrix and B is some invertible matrix. 1. Prove that Ax and Ay are also orthogonal to each other and that ||x|| = ||Ax|| and ||y|| : = ||Ay||. 2. Is it true that Bx and By are also orthogonal to each other and that ||x|| = ||Bx|| and ||y|| = = ||By||? Provide a proof or a counter-example. Problem 13 (Orthogonal Complement). Let W be the subspace of R5 spanned by, 1 2 2 4 u = 3 , v= 7 2 2 Find a basis of the orthogonal complement W- of W. Verify in this particular example that WW₁ = {0} and that dim(W) + dim(W¹) = 5.arrow_forwardProblem 5 (Rank-Nullity Theorem). Let T : P3 → M2×2 be defined as, T(p(x)) P(0) p'(1)] = 1. Prove that T is a linear transformation. 2. Find ker(T). Is T injective? 3. Find im(T). Is T surjective? 4. Verify the Rank-Nullity Theorem for T. Problem 6 (Change of Basis). Let B₁ = polynomials in P3. - - {1, x, x², x³} and B₁ = {1, x, x(x − 1), x(x − 1)(x − 2)} be two sets of 1. Is B2 a basis for P3? Justify your answer. 2. Find SB₁→B₂ and SB2→B₁. Which one is "easier" to find? - Problem 7 (Change of Basis). Let B₁ = {eª, sin² (x), cos² (x)} and B₁ = {e*, sin(2x)}. Recall that sin(20) = 2 sin(0) cos(0). Suppose V = span (B₁) and W = span(B2). Let T: VW be a linear transformation defined as T(f(x)) = f'(x). 1 1. Prove that B₁ is a basis. 2. Let g(x) = 5 - 3e. Show that g = V and find T(g(x)). 3. Find [TB₁B2 4. Is T injective? 5. Is T surjective?arrow_forward
- Problem 14 (Orthogonal Matrices). Prove each of the following. 1. P is orthogonal PT is orthogonal. 2. If P is orthogonal, then P-1 is orthogonal. 3. If P, Q are orthogonal, then PQ is orthogonal. Problem 15 (Orthogonal Complement). Consider P2 with the inner product, (f,g) = f(x)g(x)dx. Put W = span(2x+1). Find a basis of W. (1)arrow_forwardProblem 8 (Diagonalization). Let T : P₂ → P₂ be defined as, T(p(x)) = xp'(x). 1. Find the eigenvalues and eigenvectors of T. 2. Show that T is diagonalizable and write P2 as the sum of the eigenspaces of T. Problem 9 (Basis). Determine all the values of the scalar k for which the following four matrices form a basis for M2×2: A₁ = , A2 = k -3 0 , A3 = [ 1 0 -k 2 0 k " A₁ = . -1 -2 Problem 10 (Orthogonality). In this question, we will again see how orthogonality makes computations sim- pler. 1. Let u1,..., un be an (ONB) of a finite-dimensional inner product space V. Let v = c₁u₁ + ... + Сnun and w = d¹µ₁ + ... + dnUn be any two elements of V. Prove that (v, w) = c₁d₁ + ... + Cndn. 2. Write down the corresponding inner product formula for an orthogonal basis.arrow_forwardLet 01(x) = * 0(t) dt, for x > 1, where 0 is Chebyshev's function. Let A1(n) = log n if n is prime, and A₁(n) = 0 otherwise. Prove that 01(x) = (x − n) A1(n), narrow_forwardLet 01 (x) = [* 0(t) dt, for x > 1, where 0 is Chebyshev's function. Let = lim 01(x)/x². 1+00 By considering (t) dt, prove that T-ET 01(x) 01(x Ex) Ex-(x), where = (> 0) is small. - Assuming that 0(x)/x →1 as x → ∞, deduce that (1-1) ≤ 1. By similarly considering (t) dt, prove that (1+½)1 ≥1. 2 Deduce that 01(x) 1½². 2arrow_forwardConsider a rectangular membrane with fixed boundaries of dimensions 5 (horizontal) by 3 (vertical). The deflection u(x, y, t) satisfies the equation utt = 6(uxx + Uyy). (a) Find a formula for the deflection u(x, y, t), if the initial velocity g(x, y) is zero and the initial displacement f(x, y) is f(x, y) = u(x, y, 0) = 2 sin(5πx) sin(лy) - 4 sin(2x) sin(3лy) Do not show the separation of variables. Start with the formula for u(x, y, t). You need to show all details of integration or superposition (if it applies) for credit. (b) Find a numerical approximation for u(5/2, 3/2, 2).arrow_forward(a) Find the general solution to the following differential equation. Express your answer in terms of Bessel functions of the first and second kinds. Do not write any series expansions of these Bessel functions. Please explain how you arrived at your answer. x²y" + xy' + (2x² - 5)y = 0 (b) Solve the heat flow problem. Please start with the formula for u(x, t); Do not show separation of variables. Simplify your answer as much as possible. ди Ət = J²u 2 მე2 u(0,t) = u(5,t) = 0 x, 0 < x <1 u(x, 0): = 1, 1 ≤ x < 4 0, 4≤x≤5arrow_forwardis g(x) = x^4 + x -2 contraction on [0;2]?arrow_forwardConsider the steady state temperature problem over the disk of radius 3 centered at the origin. ▼²u(r, 0) = 0 subject to the following boundary condition: u(3,0) = f(0) = 4 sin³ (0) + 4 cos³ (0) (a) Find u(r, 0). Please go straight to the final formula for u(r, 0); do not show the separation of variables process. You need to show all details of integration or superposition (if it applies) for credit. (b) Approximate numerically u(3/2,π/4).arrow_forward(a) If X is a normal N(2,64) distribution, find k such that P(k ≤ X ≤12) = 0.2957 (b) The random variable T follows a t-distribution with 14 degrees of freedom. Find k such that P(-0.54arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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