Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 15, Problem 10A
To determine
The fraction or decimal equivalents of given number.
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Unit 1: Logic
1. Let P be the statement "x > 5” and let Q be the statement “y +3≤ x," and let R
be the statement “y Є Z.”
(a) Translate the following statements to English.
(b) Negate the statements symbolically
(c) Write the negated statements in English. The negations should not include any
implications.
• (QV¬R) AP
• (P⇒¬Q) VR
• (PVQ)¬R
2. Let R, S, and T be arbitrary statements. Write out truth tables for the following
statements. Determine whether they are a tautology or a contradiction or neither,
with justification.
⚫ (RAS) V (¬R ⇒ S)
(R¬S) V (RAS)
• (TA (SV¬R)) ^ [T⇒ (R^¬S)]
10. Suppose the statement -R
(SV-T) is false, and that S is true. What are the
truth values of R and T? Justify your answer.
5. Rewrite the statements below as an implication (that is, in "if... then..." structure).
n is an even integer, or n = 2k - 1 for some k Є Z.
x²> 0 or x = 0.
6. Rewrite each statement below as a disjunction (an or statement).
If I work in the summer, then I can take a vacation.
• If x2
y.
Chapter 15 Solutions
Mathematics for Machine Technology
Ch. 15 - A sphere has a volume, V, of 12.249 cu in. Use the...Ch. 15 - Prob. 2ACh. 15 - Prob. 3ACh. 15 - Write 0.275 as a common fraction.Ch. 15 - Evaluate 734(916+212) .Ch. 15 - The feed on a lathe is set for 132inch. How many...Ch. 15 - Prob. 7ACh. 15 - Prob. 8ACh. 15 - Prob. 9ACh. 15 - Prob. 10A
Ch. 15 - Prob. 11ACh. 15 - Prob. 12ACh. 15 - Prob. 13ACh. 15 - Find the fraction or decimal equivalents of these...Ch. 15 - Prob. 15ACh. 15 - Prob. 16ACh. 15 - Prob. 17ACh. 15 - Prob. 18ACh. 15 - Prob. 19ACh. 15 - Prob. 20ACh. 15 - Prob. 21ACh. 15 - Prob. 22ACh. 15 - Prob. 23ACh. 15 - Prob. 24ACh. 15 - Prob. 25ACh. 15 - Prob. 26ACh. 15 - Prob. 27ACh. 15 - Prob. 28ACh. 15 - Prob. 29ACh. 15 - Solve these examples of combined operations. Round...Ch. 15 - Prob. 31ACh. 15 - Prob. 32ACh. 15 - A bronze bushing with a diameter of 22.225...Ch. 15 - Prob. 34ACh. 15 - Prob. 35ACh. 15 - A slot is machined in a circular plate with a...Ch. 15 - A 60° slot has been machined in a fixture. The...
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- 4. Negate the following sentences. Then (where appropriate) indicate whether the orig- inal statement is true, or the negation is true. ⚫ If I take linear algebra, then I will do my homework or go to class. • (x > 2 or x < −2) ⇒ |x| ≥ 2 • P⇒ (QVR) ⇒(¬PV QV R) Vn EN Em E Q (nm = 1) • Ex E N Vy & Z (x. y = 1)arrow_forward8. Give three statements that are logically equivalent to x ≥ 0⇒ (x² = 0V −x < 0). You may use any equivalences that you like.arrow_forward3. Let P, Q, and R be arbitrary statements, and let x E R. Determine whether the statements below are equivalent using whatever method you like. • • -[-P → (QVR)] and ¬(¬P V Q) A¬R (PA¬Q) ⇒(¬PVS) and (SVP) VQ • x = 4 and √√√x=2 x = 4 and x2. = 16arrow_forward
- 7. Write the inverse, converse, and contrapositive. Which are true? Which are false? If x is an even integer, then x² + 3x + 5 is an odd integer. If y 5n+1 for some natural number If a <0, then 2a < 0. n, then 5 y.arrow_forward5. The volume V of a given mass of monoatomic gas changes with temperat re T according to the relation V = KT2/3. The work done when temperature changes by 90 K will be xR. The value of x is (a) 60 (b)20 (c)30 S (d)90arrow_forwardConsider a matrix 3 -2 1 A = 0 5 4 -6 2 -1 Define matrix B as transpose of the inverse of matrix A. Find the determinant of matrix A + B.arrow_forward
- 5) State any theorems that you use in determining your solution. a) Suppose you are given a model with two explanatory variables such that: Yi = a +ẞ1x1 + ẞ2x2i + Ui, i = 1, 2, ... n Using partial differentiation derive expressions for the intercept and slope coefficients for the model above. [25 marks] b) A production function is specified as: Yi = α + B₁x1i + ẞ2x2i + Ui, i = 1, 2, ... n, u₁~N(0,σ²) where: y = log(output), x₁ = log(labor input), x2 = log(capital input) The results are as follows: x₁ = 10, x2 = 5, ỹ = 12, S11 = 12, S12= 8, S22 = 12, S₁y = 10, = 8, Syy = 10, S2y n = 23 (individual firms) i) Compute values for the intercept, the slope coefficients and σ². [20 marks] ii) Show that SE (B₁) = 0.102. [15 marks] iii) Test the hypotheses: ẞ1 = 1 and B2 = 0, separately at the 5% significance level. You may take without calculation that SE (a) = 0.78 and SE (B2) = 0.102 [20 marks] iv) Find a 95% confidence interval for the estimate ẞ2. [20 marks]arrow_forwardPage < 2 of 2 - ZOOM + The set of all 3 x 3 upper triangular matrices 6) Determine whether each of the following sets, together with the standard operations, is a vector space. If it is, then simply write 'Vector space'. You do not have to prove all ten vector space axioms. If it is not, then identify one of the ten vector space axioms with its number in the attached sheet that fails and also show that how it fails. a) The set of all polynomials of degree four or less. b) The set of all 2 x 2 singular matrices. c) The set {(x, y) : x ≥ 0, y is a real number}. d) C[0,1], the set of all continuous functions defined on the interval [0,1]. 7) Given u = (-2,1,1) and v = (4,2,0) are two vectors in R³-space. Find u xv and show that it is orthogonal to both u and v. 8) a) Find the equation of the least squares regression line for the data points below. (-2,0), (0,2), (2,2) b) Graph the points and the line that you found from a) on the same Cartesian coordinate plane.arrow_forwardPage < 1 of 2 - ZOOM + 1) a) Find a matrix P such that PT AP orthogonally diagonalizes the following matrix A. = [{² 1] A = b) Verify that PT AP gives the correct diagonal form. 2 01 -2 3 2) Given the following matrices A = -1 0 1] an and B = 0 1 -3 2 find the following matrices: a) (AB) b) (BA)T 3) Find the inverse of the following matrix A using Gauss-Jordan elimination or adjoint of the matrix and check the correctness of your answer (Hint: AA¯¹ = I). [1 1 1 A = 3 5 4 L3 6 5 4) Solve the following system of linear equations using any one of Cramer's Rule, Gaussian Elimination, Gauss-Jordan Elimination or Inverse Matrix methods and check the correctness of your answer. 4x-y-z=1 2x + 2y + 3z = 10 5x-2y-2z = -1 5) a) Describe the zero vector and the additive inverse of a vector in the vector space, M3,3. b) Determine if the following set S is a subspace of M3,3 with the standard operations. Show all appropriate supporting work.arrow_forward
- Please help solve the following whilst showing all working out. Is part of exam revision questions but no solution is givenarrow_forwardplease help me with this question with working out thanksarrow_forwardPage < 1 of 2 - ZOOM + 1) a) Find a matrix P such that PT AP orthogonally diagonalizes the following matrix A. = [{² 1] A = b) Verify that PT AP gives the correct diagonal form. 2 01 -2 3 2) Given the following matrices A = -1 0 1] an and B = 0 1 -3 2 find the following matrices: a) (AB) b) (BA)T 3) Find the inverse of the following matrix A using Gauss-Jordan elimination or adjoint of the matrix and check the correctness of your answer (Hint: AA¯¹ = I). [1 1 1 A = 3 5 4 L3 6 5 4) Solve the following system of linear equations using any one of Cramer's Rule, Gaussian Elimination, Gauss-Jordan Elimination or Inverse Matrix methods and check the correctness of your answer. 4x-y-z=1 2x + 2y + 3z = 10 5x-2y-2z = -1 5) a) Describe the zero vector and the additive inverse of a vector in the vector space, M3,3. b) Determine if the following set S is a subspace of M3,3 with the standard operations. Show all appropriate supporting work.arrow_forward
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