Concept explainers
Find the volume of a steel shaft that is 18.64 cm long and has a radius of 1.75 cm. Round your answer to 2 decimal places.

Volume of steel shaft.
Answer to Problem 1A
Volume of steel shaft
Explanation of Solution
Given information:
Length of shaft is 18.64 cm.
Radius of the shaft is 1.75 cm.
Calculation:
The formula for the volume of the shaft is
Where r is the radius of the shaft and h is the length or height of the shaft,
So volume of the shaft is equal to
Want to see more full solutions like this?
Chapter 60 Solutions
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
Additional Math Textbook Solutions
Calculus: Early Transcendentals (2nd Edition)
Precalculus: A Unit Circle Approach (3rd Edition)
Elementary Statistics: Picturing the World (7th Edition)
Basic College Mathematics
Intro Stats, Books a la Carte Edition (5th Edition)
Elementary Statistics Using The Ti-83/84 Plus Calculator, Books A La Carte Edition (5th Edition)
- Q1/(a) Let f be a map from linear space X into linear space Y, show that whether each one of the statements trure or flase or not. 41) If A convex set of X then f(A) is a convex set of w 20 (2) If M is an affine subset of a space X and tEM then M-this an affine set Let R be a field of real numbers and X-M2(R) be a space of 2x2 matrices over R that whether there is a hyperspace of X or not. I love 00arrow_forward21: A: Let f be a function from a normed space X in to a normed space Y. show that of continuous iff for any sequence (x,) in X convergent to xo then the sequence (f(x)) convergent to f(x) in Y. B: Let X be a vector space of dimention n isomorphic to a vector space Y. write with prove the dimension of Y. 32 22: A: Let X be a horned space of finite dimension .show that any two normone X are V equivalent. B: Let M2x3 be a vector space of 2×3. matrices on a field ? write wittraver convex set and hyperplane of M2x3 17 thatarrow_forwardarc. Consider the network of Figure 2, where the capacities of arcs are given in rectangles at each (i) Knowing that (W, W) with W = network. {s, a, b, c} is a minimal s- t cut suggest a maximal flow for thisarrow_forward
- Consider the problem of minimising the Euclidean distance from the point (-4,5) in the plane to the set of points (x, y) that have integer coordinates and satisfy the inequality: x2 y² + ≤1. 4 9 (a) Use an exhaustive search to solve this problem. (b) Use a local search method to solve this problem. First, define the search space and the neighbourhood. Then, attempt to find the minimum starting from the initial point (x, y) = (2,0). The neighbourhood of a point should contain at least two distinct points but must not encompass the entire feasible search space. Will your local search method find the global optimum?arrow_forwardConsider the relation ✓ on R² defined by u ≤ v u₁ + v₂+ 3u1 v² < u₂ + v³ + 3u²v₁ (u³ + v2 + 3u1v = u₂+ v³ + 3u²v₁ and u₂ < v2) u = v for any u, vЄR² with u = = (u1, u2), v = = (V1, V2). or 우우 or 1. Prove that the relation ✓ is translation invariant. Hint: Use the formula of (a + b)³ for a, b = R. 2. Is the relation ✓ scale invariant? Justify your answer. 3. Is the relation ✓ reflexive? Justify your answer. 4. Is the relation ✓ transitive? Justify your answer. 5. Is the relation ✓ antisymmetric? Justify your answer. 6. Is the relation ✓ total? Justify your answer. 7. Is the relation ✓ continuous at zero? Justify your answer.arrow_forwardLet X = [−1, 1] C R and consider the functions ₤1, f2 : X → R to be minimised, where f₁(x) = x + x² and f2(x) = x-x² for all x Є X. Solve the tradeoff model minøx µƒ₁(x)+ƒ2(x), for all values of µ ≥ 0. Show your working.arrow_forward
- Consider the following linear programming problem: min x1 x2 3x3 − x4 s.t. — 2x1 − x2 − x4 ≤ −6 x1 x2 x3 + 2x4 <4 x1, x2, x3, x4 ≥ 0. (i) Write an equivalent formulation of this problem, to which the primal-dual algorithm can be applied. (ii) Write out the dual problem to the problem, which you formulated in (i). (iii) Solve the problem, which you formulated in (i), by the primal-dual algorithm using the dual feasible solution π = (0, -3). Write a full record of each iteration.arrow_forward୮ dx L1+zadz 1+x2arrow_forwardConsider the following Boolean Satisfiability problem: X2 F (X1, X2, X3, X4, x5) = (x1 √ √ ¤;) ^ (ס \/ ˜2\/×3)^(×k \/×4 \/ ×5) ^^\ (×1\/15), Є where i Є {2, 3, 4, 5}, j = {1, 4, 5}, k = {1, 2, 3} and l € {1, 2, 3, 4}. xk Can this problem be solved by using the Divide and Conquer method?arrow_forward
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill





