A Transition to Advanced Mathematics
8th Edition
ISBN: 9781285463261
Author: Douglas Smith, Maurice Eggen, Richard St. Andre
Publisher: Cengage Learning
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Chapter 5.4, Problem 9E
a.
To determine
To give the example of the given function.
b.
To determine
To give the example of the given function.
c.
To determine
To give the example of the given function.
d.
To determine
To give the example of the given function.
e.
To determine
To give the example of the given function.
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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 5 Solutions
A Transition to Advanced Mathematics
Ch. 5.1 - The Cayley tables for operations o,*,+, and are...Ch. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Give an example of an algebraic structure of order...Ch. 5.1 - Prob. 6ECh. 5.1 - Show that the structure ({1},), with operation ...Ch. 5.1 - (a)In the group G of Exercise 2, find x such that...Ch. 5.1 - Show that (,), with operation # defined by...Ch. 5.1 - Construct the operation table for each of the...
Ch. 5.1 - Prob. 11ECh. 5.1 - (a)Prove that (m,+) is associative and commutative...Ch. 5.1 - Suppose m and m2. Prove that 1 and m1 are distinct...Ch. 5.1 - Let m and a be natural numbers with am. Complete...Ch. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - Consider the set A={a,b,c,d} with operation ogiven...Ch. 5.1 - Repeat Exercise 2 with the operation * given by...Ch. 5.1 - Let m,n and M=A:A is an mn matrix with real number...Ch. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.2 - Show that each of the following algebraic...Ch. 5.2 - Given that G={e,u,v,w} is a group of order 4 with...Ch. 5.2 - Prob. 3ECh. 5.2 - Give an example of an algebraic system (G,o) that...Ch. 5.2 - Construct the operation table for S2. Is S2...Ch. 5.2 - Prob. 6ECh. 5.2 - Let G be a group and aiG for all n. Prove that...Ch. 5.2 - Prove part (d) of Theorem 6.2.3. That is, prove...Ch. 5.2 - Prob. 9ECh. 5.2 - Prob. 10ECh. 5.2 - Prob. 11ECh. 5.2 - Assign a grade of A (correct), C (partially...Ch. 5.3 - Assign a grade of A (correct), C (partially...Ch. 5.3 - Find all subgroups of (8,+). (U11,). (5,+). (U7,)....Ch. 5.3 - In the group S4, find two different subgroups that...Ch. 5.3 - Prove that if G is a group and H is a subgroup of...Ch. 5.3 - Prove that if H and K are subgroups of a group G,...Ch. 5.3 - Let G be a group and H be a subgroup of G. If H is...Ch. 5.3 - Prob. 7ECh. 5.3 - Prob. 8ECh. 5.3 - Prob. 9ECh. 5.3 - List all generators of each cyclic group in...Ch. 5.3 - Prob. 11ECh. 5.3 - Let G be a group, and let H be a subgroup of G....Ch. 5.3 - Let ({0},) be the group of nonzero complex numbers...Ch. 5.3 - Prob. 14ECh. 5.3 - Prob. 15ECh. 5.3 - Let G=a be a cyclic group of order 30. What is the...Ch. 5.4 - Is S3 isomorphic to (6,+)? Explain.Ch. 5.4 - Prob. 2ECh. 5.4 - Use the method of proof of Cayley's Theorem to...Ch. 5.4 - Define f:++ by f(x)=x where + is the set of all...Ch. 5.4 - Assign a grade of A (correct), C (partially...Ch. 5.4 - Prob. 6ECh. 5.4 - Define on by setting (a,b)(c,d)=(acbd,ad+bc)....Ch. 5.4 - Let f the set of all real-valued integrable...Ch. 5.4 - Prob. 9ECh. 5.4 - Find the order of each element of the group S3....Ch. 5.4 - Prob. 11ECh. 5.4 - Let (3,+) and (6,+) be the groups in Exercise 10,...Ch. 5.4 - Prob. 13ECh. 5.4 - Prob. 14ECh. 5.4 - Prob. 15ECh. 5.4 - Prob. 16ECh. 5.4 - Prob. 17ECh. 5.5 - Prob. 1ECh. 5.5 - Prob. 2ECh. 5.5 - Show that any two groups of order 2 are...Ch. 5.5 - Show that the function h: defined by h(x)=3x is...Ch. 5.5 - Let R be the equivalence relation on ({0}) given...Ch. 5.5 - Prob. 6ECh. 5.5 - Prob. 7ECh. 5.5 - Let (R,+,) be an algebraic structure such that...Ch. 5.5 - Assign a grade of A (correct), C (partially...Ch. 5.5 - Let M be the set of all 22 matrices with real...
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