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Concept explainers
The solution of the following problems requires more than one formula and the rearrangement of formulas.
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A carbide milling cutter is used for machining a 560.00-millimeter length of stainless steel. The cutting time is 11.95 minutes, the cutting speed is 60.000 meters per minute, and the feed is0.250 millimeter per revolution. What is the diameter of the carbide milling cutter? Round the answer to 1 decimal place.
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Chapter 47 Solutions
Mathematics For Machine Technology
- Suppose p > 3 is a prime. Show that (p − 3)!= − P+1 (mod p). Hint: Use Wilson's theorem.arrow_forwardSuppose a = p²¹...p be the canonical factorization. Then the sum of all the factors of a, denoted by σ(a) is given by o(a) = II + k₂+1 P -1 Pi - 1 (you don't need to prove this). (a) Let a = 2³ × 7². Find σ(a), which the sum of all the factors a.arrow_forwardEvaluate the Legendre symbol (999|823). (Note that 823 is prime.)arrow_forward
- If p = 7 (mod 8), where p is prime, show that p divides 2(p-1)/2 — 1. Deduce that 275 - 1 and 2155 -1 are composite.arrow_forwardSolve the simultaneous linear congruences 3x = 2 (mod 5), 3x = 4 (mod 7), 3x = 6 (mod 11).arrow_forwardcondition: Throughout this question, n is a positive integer satisfying the following (n) = 2³ × 17 × q, gcd(n,6) = 1, q = 2(mod3) is an odd prime. (a) Show that 17†n. - (b) Show that 17|(p − 1) for some prime factor p of n.arrow_forward
- I bought sparrows at 3 for a penny, turtle doves at 2 for a penny, and doves at 2 pence each. If I spent 30 pence buying 30 birds and bought at least one of each kind of bird, how many birds of each kind did I buy?arrow_forward- Prove that if (n − 1)! + 1 is divisible by n (> 1), then n must be prime.arrow_forwardFrom the differential equation y′ = x + sin(y):a) A solution curve passes through the point (1, π/2). What is its slope at that point?b) Justify why for x > 1 the solutions are increasing.c) Show that the concavity of each solution has the function 1 + x cos(y) + 1/2 sin(2y).Justify each of the steps.d) A solution curve passes through the point (0, 0). Show that the curve has a minimumrelative at (0, 0).arrow_forward
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellElementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage Learning
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