Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 77, Problem 9A
To determine
To compute the angle
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5. 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)90
Consider 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.
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]
Chapter 77 Solutions
Mathematics for Machine Technology
Ch. 77 - Prob. 1ACh. 77 - Prob. 2ACh. 77 - Prob. 3ACh. 77 - Prob. 4ACh. 77 - Determine the arc dimension x in inches to 3...Ch. 77 - Prob. 6ACh. 77 - Prob. 7ACh. 77 - Prob. 8ACh. 77 - Prob. 9ACh. 77 - Prob. 10A
Ch. 77 - In each of Exercises 11 through 14, three Views of...Ch. 77 - Prob. 12ACh. 77 - Prob. 13ACh. 77 - In each of Exercises 11 through 14, three Views of...Ch. 77 - Prob. 15ACh. 77 - Prob. 16ACh. 77 - Prob. 17ACh. 77 - Prob. 18ACh. 77 - Prob. 19ACh. 77 - Prob. 20ACh. 77 - Prob. 21ACh. 77 - Prob. 22ACh. 77 - Prob. 23ACh. 77 - Prob. 24ACh. 77 - Prob. 25ACh. 77 - Prob. 26ACh. 77 - Prob. 27ACh. 77 - Prob. 28ACh. 77 - Prob. 29ACh. 77 - Prob. 30A
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