EBK MATHEMATICS FOR MACHINE TECHNOLOGY
8th Edition
ISBN: 9781337798396
Author: SMITH
Publisher: CENGAGE LEARNING - CONSIGNMENT
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Chapter 16, Problem 8A
To determine
The fraction or decimal equivalents of given number.
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2. Show that
8
xa
S
-dx
(b² + 12) dr = 2 cos(π2)
пра-1
a, b real and
-1 0
Your solution should clearly explain the closed contour you are using, and state clearly any
vanishing properties of integrals over contours that are being used. You are free to quote
from the lectures, the appropriate results on such vanishing properties, without deriving
these properties. Any residue calculations involved should be explained clearly.
1. Calculate the integral
500
x sin x
(a² +x2)20
dx
by using the residue theorem. You may assume that a is real and a > 0. Your solution should
clearly explain the closed contour you are using, and state clearly any vanishing properties
of integrals over contours that are being used.
Steel Production Planning:
Let S represent the amount of steel produced (in tons). Steel Production is related to the amount of labor used(L) and the amount of capital used ( C ) by the following function:S = 20L⁰˙³⁰C⁰˙⁷⁰In this formula L represents the units of Labor input and C the units of Capital input. Each unit of Labor costs $50, and each unit of Capital costs $100.
a:Formulate an optimization problem that will determine how much labor and capital are needed to produce 50,000 tons of steel at minimum cost.
Q#3B: Solve the optimization problem you formulated in part (a). (Hint: When using Excel Solver, start with an initial L>0 and C>0.)…
Chapter 16 Solutions
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
Ch. 16 - A sphere has a volume, V, of 12.249 cu in. Use the...Ch. 16 - Prob. 2ACh. 16 - Prob. 3ACh. 16 - Write 0.275 as a common fraction.Ch. 16 - Evaluate 734(916+212) .Ch. 16 - The feed on a lathe is set for 132inch. How many...Ch. 16 - Prob. 7ACh. 16 - Prob. 8ACh. 16 - Prob. 9ACh. 16 - Prob. 10A
Ch. 16 - Prob. 11ACh. 16 - Prob. 12ACh. 16 - Prob. 13ACh. 16 - Find the fraction or decimal equivalents of these...Ch. 16 - Prob. 15ACh. 16 - Prob. 16ACh. 16 - Prob. 17ACh. 16 - Prob. 18ACh. 16 - Prob. 19ACh. 16 - Prob. 20ACh. 16 - Prob. 21ACh. 16 - Prob. 22ACh. 16 - Prob. 23ACh. 16 - Prob. 24ACh. 16 - Prob. 25ACh. 16 - Prob. 26ACh. 16 - Prob. 27ACh. 16 - Prob. 28ACh. 16 - Prob. 29ACh. 16 - Solve these examples of combined operations. Round...Ch. 16 - Prob. 31ACh. 16 - Prob. 32ACh. 16 - A bronze bushing with a diameter of 22.225...Ch. 16 - A stamped sheet steel plate is shown in Figure...Ch. 16 - Prob. 35ACh. 16 - A slot is machined in a circular plate with a...Ch. 16 - A 60° slot has been machined in a fixture. The...
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- Find the area bounded by f(x) = sin x, g(x) = cos x in the first quadrant.arrow_forward1. Matrix Operations Given: A = [ 33 ]A-[3-321] -3 B = [342]B-[3-41-2] (a) A² A2 Multiply A× A: -3 = (3 x 32x-3) (3 x 22 x 1) | = |[19–63 |-9-3 -6+21] = A² = 33 33 1-3×3+1x-3) (-3×2+1x1) [12]A2=[3-321][3-321]=[(3×3+2x-3)(-3×3+1x-3)(3×2+2×1)(-3×2+1×1)]=[9-6-9-36+2-6+1 ]=[3-128-5] (b) | A ||A| Determinant of A | A | (3 × 1) (2 x-3)=3+ 6 = 9|A|=(3×1)-(2x-3)=3+6=9 (c) Adjoint of A Swap diagonal elements and change sign of off-diagonals: A = [33], so adj (A) = |¯²]A=[3-321], so adj(A)=[13–23] -3 (d) B-¹B-1 First find | B ||B|: |B | (3x-2)- (1 × -4) = -6 + 4 = −2|B|=(3x-2)-(1x-4)=-6+4=-2 Then the adjoint of B: adj (B) = [² 3 adj(B)=[-24-13] Now, B-1 1 = |B| · adj (B) = 1 [²¯¯³¹³] = [2₂ B 0.5 |B-1=|B|1-adj(B)=-21[-24-13]=[1-20.5-1.5] 2. (a) Matrix Method: Solve (2x + 3y = 6 (2x-3y=14 {2x+3y=62x-3y=14 Matrix form: 22 33-22 = [223-3][xy]=[614] Find inverse of coefficient matrix: Determinant: | M | (2x-3) - (3 x 2) = -6 -6 = -12|M|=(2x-3)-(3×2)=-6-6=-12 Adjoint: adj(M) = [3]adj(M)-[-3-2-32] So…arrow_forwardQuestions An insurance company's cumulative incurred claims for the last 5 accident years are given in the following table: Development Year Accident Year 0 2018 1 2 3 4 245 267 274 289 292 2019 255 276 288 294 2020 265 283 292 2021 263 278 2022 271 It can be assumed that claims are fully run off after 4 years. The premiums received for each year are: Accident Year Premium 2018 306 2019 312 2020 318 2021 326 2022 330 You do not need to make any allowance for inflation. 1. (a) Calculate the reserve at the end of 2022 using the basic chain ladder method. (b) Calculate the reserve at the end of 2022 using the Bornhuetter-Ferguson method. 2. Comment on the differences in the reserves produced by the methods in Part 1.arrow_forward
- The numbered disks shown are placed in a box and one disk is selected at random. Find the probability of selecting a 4, given that a green disk is selected. Find the probability of selecting a 4, given that a green disk is selected. (Type an integer or a simplified fraction.) green blue green green green blue green bluearrow_forwardThe table shows the distribution, by age, of a random sample of 3160 moviegoers ages 12-74. If one moviegoer is randomly selected from this population, find the probability, expressed as a simplified fraction, that the moviegoer is not in the 65-74 age range. The probability is (Type an integer or a simplified fraction.) Age Distribution of Moviegoers Ages Number 12-24 1090 25-44 860 45-64 890 65-74 320arrow_forwardUse the spinner shown. It is equally probable that the pointer will land on any one of the six regions. If the pointer lands on a borderline, spin again. If the pointer is spun twice, find the probability that it will land on yellow and then yellow. Find the probability that the spinner will land on yellow and then yellow. The probability is (Type an integer or a simplified fraction.) Green Red Gray Red Blue Yellow Q ☑arrow_forward
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