Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 3, Problem 3A
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You are provided with data that includes all 50 states of the United States. Your task is to draw a sample of: o 20 States using Random Sampling (2 points: 1 for random number generation; 1 for random sample) o 10 States using Systematic Sampling (4 points: 1 for random numbers generation; 1 for random sample different from the previous answer; 1 for correct K value calculation table; 1 for correct sample drawn by using systematic sampling) (For systematic sampling, do not use the original data directly. Instead, first randomize the data, and then use the randomized dataset to draw your sample. Furthermore, do not use the random list previously generated, instead, generate a new random sample for this part. For more details, please see the snapshot provided at the end.) Upload a Microsoft Excel file with two separate sheets. One sheet provides random sampling while the other provides systematic sampling. Excel snapshots that can help you in organizing columns are provided on the next…
The University of the West Indies
Open Campus
ECON2016 Mathematical Methods of Economics II
Final Assessment
Instructions: Answer ALL the questions. Show all working
1. Solve the following Differential Equations
a) dy = x²-1; y(-1) = 1
dx y²+1
dy
b) d x + 2y = 3;
dx
c) dy-4y = 4y²
dt
d) 6dzy
dx²
dy
-5+ y = 0; y(0) = 4 y'(0) = 0
dx
[6]
[5]
[5]
[6]
Problems
Determine I, and Iy for the cross-sections
6.11 See the steel tables in the Appendix Table A3.
|x=
=
"
-2x8 STEEL
PLATE CENTERED
-W14x82
Chapter 3 Solutions
Mathematics for Machine Technology
Ch. 3 - Determine the least common denominator of 23,58,...Ch. 3 - Express 14,56, and 712as equivalent fractions...Ch. 3 - Express 298 as a mixed number.Ch. 3 - Express the mixed number 516as an improper...Ch. 3 - Add 512+34+16 .Ch. 3 - Add 238+134+513 .Ch. 3 - Prob. 7ACh. 3 - Prob. 8ACh. 3 - Determine dimensions A, B, C, D, E, and F of the...Ch. 3 - Determine dimensions A, B, C, D, E, F, and G of...
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- Problems Construct shear and moment diagrams using the equilib- rium method. Indicate the magnitudes of Vmax and Mmax. 7.4 8=2K/FT. W=2K/FT. 10' 10'arrow_forwardProblems Determine I, and Iy for the cross-sections 6.8 89 2" 1011 2" ส 10 |x= ly=arrow_forwardProblems Construct shear and moment diagrams using the equilib- rium method. Indicate the magnitudes of Vmax and Mmax. 7.3 107 B 5' 201arrow_forward
- Can you help me with this problem using linear recurrance: Find an explicit formula for the recurrence relation an = 2can−1 + 3c2an−2 where c not equal to 0 with initial conditions a0=4c and a1 = 0arrow_forwardCan you help me solved this problem using generalized combination:How many combinations are there to pick r objects from 2n objects numbered from 1to 2n when repetitions are allowed and at least one object of odd type does not appear?arrow_forwardNarrow_forward
- Please help me organize the proof of the following theorem:arrow_forwardHow come that I marked ?arrow_forwardIn Exercises 1-14, state whether each statement is true or false. If false, give a reason. 1. The set of stores located in the state of Wyoming is a well- defined set. 2. The set of the three best songs is a well-defined set. 3. maple = {oak, elm, maple, sycamore} 4{} cơ 5. {3, 6, 9, 12,...} and {2, 4, 6, 8, ...} are disjoint sets. 6. {Mercury, Venus, Earth, Mars} is an example of a set in roster form. 7. {candle, picture, lamp} = {picture, chair, lamp } 8. {apple, orange, banana, pear} is equivalent to {tomato, corn, spinach, radish}.arrow_forward
- Exercises Evaluate the following limits. 1. lim cot x/ln x +01x 2. lim x² In x +014 3. lim x* x0+ 4. lim (cos√√x)1/x +014 5. lim x2/(1-cos x) x10 6. lim e*/* 818 7. lim (secx - tan x) x-x/2- 8. lim [1+(3/x)]* x→∞0arrow_forwardIn Exercises 1 through 3, let xo = O and calculate P7(x) and R7(x). 1. f(x)=sin x, x in R. 2. f(x) = cos x, x in R. 3. f(x) = In(1+x), x≥0. 4. In Exercises 1, 2, and 3, for |x| 1, calculate a value of n such that P(x) approximates f(x) to within 10-6. 5. Let (an)neN be a sequence of positive real numbers such that L = lim (an+1/an) exists in R. If L < 1, show that an → 0. [Hint: Let 1111 Larrow_forwardiation 7. Let f be continuous on [a, b] and differentiable on (a, b). If lim f'(x) xia exists in R, show that f is differentiable at a and f'(a) = lim f'(x). A similar result holds for b. x-a 8. In reference to Corollary 5.4, give an example of a uniformly continuous function on [0, 1] that is differentiable on (0, 1] but whose derivative is not bounded there. 9. Recall that a fixed point of a function f is a point c such that f(c) = c. (a) Show that if f is differentiable on R and f'(x)| x if x 1 and hence In(1+x) 0. 12. For 0 л/2. (Thus, as x л/2 from the left, cos x is never large enough for x+cosx to be greater than л/2 and cot x is never small enough for x + cot x to be less than x/2.)arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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