Calculus for Business Economics Life Sciences and Social Sciences Plus NEW
13th Edition
ISBN: 9780321925138
Author: Raymond Barnett
Publisher: PEARSON
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Chapter DPT, Problem 24E
To determine
To simplify: The expression
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Given: AABE ~ ACDE.
Prove: AC bisects BD.
Note: quadrilateral properties are not permitted in this proof.
Step
Statement
Reason
AABE ACDE
Given
2
ZDEC ZAEB
Vertical angles are congruent
try
Type of Statement
A
E
B
D
C
10-2
Let A =
02-4
and b =
4
Denote the columns of A by a₁, a2, a3, and let W = Span {a1, a2, a̸3}.
-4 6
5
- 35
a. Is b in {a1, a2, a3}? How many vectors are in {a₁, a₂, a3}?
b. Is b in W? How many vectors are in W?
c. Show that a2 is in W. [Hint: Row operations are unnecessary.]
a. Is b in {a₁, a2, a3}? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your
choice.
○ A. No, b is not in {a₁, a2, 3} since it cannot be generated by a linear combination of a₁, a2, and a3.
B. No, b is not in (a1, a2, a3}
since b is not equal to a₁, a2, or a3.
C. Yes, b is in (a1, a2, a3} since b = a
(Type a whole number.)
D. Yes, b is in (a1, a2, 3} since, although b is not equal to a₁, a2, or a3, it can be expressed as a linear
combination of them. In particular, b =
+
+
☐ az.
(Simplify your answers.)
(1) (14 points) Let a = (-2, 10, -4) and b = (3, 1, 1).
(a) (4 points) Using the dot product determine the angle between a and b.
(b) (2 points) Determine the cross product vector axb.
(c) (4 points) Calculate the area of the parallelogram spanned by a and b. Justify
your answer.
1
Chapter DPT Solutions
Calculus for Business Economics Life Sciences and Social Sciences Plus NEW
Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...
Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Work all of the problems in this self-test without...Ch. DPT - Give an example of an integer that is not a...Ch. DPT - Prob. 17ECh. DPT - Prob. 18ECh. DPT - Prob. 19ECh. DPT - Prob. 20ECh. DPT - Prob. 21ECh. DPT - In Problems 1724, simplify and write answers using...Ch. DPT - Prob. 23ECh. DPT - Prob. 24ECh. DPT - In Problems 2530, perform the indicated operation...Ch. DPT - In Problems 2530, perform the indicated operation...Ch. DPT - In Problems 2530, perform the indicated operation...Ch. DPT - Prob. 28ECh. DPT - In Problems 2530, perform the indicated operation...Ch. DPT - In Problems 2530, perform the indicated operation...Ch. DPT - Each statement illustrates the use of one of the...Ch. DPT - Round to the nearest integer: (A)173 (B)519Ch. DPT - Multiplying a number x by 4 gives the same result...Ch. DPT - Find the slope of the line that contains the...Ch. DPT - Find the x and y coordinates of the point at which...Ch. DPT - Find the x and y coordinates of the point at which...Ch. DPT - In Problems 37 and 38, factor completely....Ch. DPT - In Problems 37 and 38, factor completely....Ch. DPT - In Problems 3942, write in the form axp + byq...Ch. DPT - Prob. 40ECh. DPT - Prob. 41ECh. DPT - In Problems 3942, write in the form axp + byq...Ch. DPT - Prob. 43ECh. DPT - Prob. 44ECh. DPT - In Problems 4550, solve for x. 45.x2=5xCh. DPT - In Problems 4550, solve for x. 46.3x221=0Ch. DPT - In Problems 4550, solve for x. 47.x2x20=0Ch. DPT - In Problems 4550, solve for x. 48.6x2+7x1=0Ch. DPT - In Problems 4550, solve for x. 49.x2+2x1=0Ch. DPT - In Problems 4550, solve for x. 50.x46x2+5=0
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