MATHEMATICS A PRACTICAL ODYSSEY W/ACCESS
8th Edition
ISBN: 9780357537343
Author: Johnson
Publisher: CENGAGE L
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Chapter 11.CR, Problem 30CR
To determine
The assumptions on which predictions are based.
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For the system consisting of the two planes:plane 1: -x + y + z = 0plane 2: 3x + y + 3z = 0a) Are the planes parallel and/or coincident? Justify your answer. What does this tell you about the solution to the system?b) Solve the system (if possible). Show a complete solution. If there is a line of intersection express it in parametric form.
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Question 2: (10 points) Evaluate the definite integral.
Use the following form of the definition of the integral to evaluate the integral:
Theorem: Iff is integrable on [a, b], then
where Ax = (ba)/n and x₂ = a + i^x.
You might need the following formulas.
IM³
L² (3x²
(3x²+2x-
2x - 1)dx.
n
[f(z)dz lim f(x)Az
a
n→∞
i=1
n(n + 1)
2
n
i=1
n(n+1)(2n+1)
6
Chapter 11 Solutions
MATHEMATICS A PRACTICAL ODYSSEY W/ACCESS
Ch. 11.0A - In Exercises 1-10, a find the dimensions of the...Ch. 11.0A - Prob. 2ECh. 11.0A - Prob. 3ECh. 11.0A - Prob. 4ECh. 11.0A - Prob. 5ECh. 11.0A - Prob. 6ECh. 11.0A - Prob. 7ECh. 11.0A - Prob. 8ECh. 11.0A - Prob. 9ECh. 11.0A - In Exercises 1-10, a find the dimensions of the...
Ch. 11.0A - Prob. 11ECh. 11.0A - Prob. 12ECh. 11.0A - Prob. 13ECh. 11.0A - Prob. 14ECh. 11.0A - Prob. 15ECh. 11.0A - Prob. 16ECh. 11.0A - Prob. 17ECh. 11.0A - Prob. 18ECh. 11.0A - Prob. 19ECh. 11.0A - Prob. 20ECh. 11.0A - Prob. 21ECh. 11.0A - Prob. 22ECh. 11.0A - Prob. 23ECh. 11.0A - Prob. 24ECh. 11.0A - Prob. 25ECh. 11.0A - Prob. 26ECh. 11.0A - Prob. 27ECh. 11.0A - Prob. 28ECh. 11.0A - Prob. 29ECh. 11.0A - Prob. 30ECh. 11.0A - Prob. 31ECh. 11.0A - Prob. 32ECh. 11.0A - Prob. 33ECh. 11.0A - Prob. 34ECh. 11.0A - Prob. 35ECh. 11.0A - Prob. 36ECh. 11.0A - Prob. 37ECh. 11.0A - Prob. 38ECh. 11.0A - Prob. 39ECh. 11.0A - Prob. 40ECh. 11.0A - Prob. 41ECh. 11.0A - Prob. 42ECh. 11.0A - Prob. 43ECh. 11.0A - Prob. 44ECh. 11.0A - Prob. 45ECh. 11.0A - Prob. 46ECh. 11.0A - Prob. 47ECh. 11.0A - Prob. 48ECh. 11.0A - Prob. 49ECh. 11.0A - Prob. 50ECh. 11.0A - Prob. 51ECh. 11.0A - Prob. 52ECh. 11.0A - Prob. 53ECh. 11.0A - Prob. 54ECh. 11.0A - Prob. 55ECh. 11.0A - Prob. 56ECh. 11.0A - Prob. 57ECh. 11.0A - Prob. 58ECh. 11.0A - Prob. 59ECh. 11.0A - Prob. 60ECh. 11.0A - Prob. 61ECh. 11.0A - Prob. 62ECh. 11.0B - Prob. 1ECh. 11.0B - Prob. 2ECh. 11.0B - Prob. 3ECh. 11.0B - Prob. 4ECh. 11.0B - Prob. 5ECh. 11.0B - Prob. 6ECh. 11.0B - Prob. 7ECh. 11.0B - Prob. 8ECh. 11.0B - Prob. 9ECh. 11.0B - Prob. 10ECh. 11.0B - Prob. 11ECh. 11.0B - Prob. 12ECh. 11.0B - Prob. 13ECh. 11.0B - Prob. 14ECh. 11.0B - Prob. 15ECh. 11.0B - Prob. 16ECh. 11.0B - Prob. 17ECh. 11.0B - Prob. 18ECh. 11.0B - Prob. 19ECh. 11.0B - Prob. 20ECh. 11.0B - Prob. 21ECh. 11.0B - Prob. 22ECh. 11.0B - Prob. 23ECh. 11.0B - Prob. 24ECh. 11.0B - Prob. 25ECh. 11.0B - Prob. 26ECh. 11.0B - Prob. 27ECh. 11.0B - Prob. 28ECh. 11.0B - Prob. 29ECh. 11.0B - Prob. 30ECh. 11.0B - Prob. 31ECh. 11.0B - Prob. 32ECh. 11.0B - Prob. 33ECh. 11.0B - Prob. 34ECh. 11.0B - Prob. 35ECh. 11.0B - Prob. 36ECh. 11.0B - Why could you not use a graphing calculator to...Ch. 11.1 - Prob. 1ECh. 11.1 - In Exercises 1-4, a write the given data in...Ch. 11.1 - Prob. 3ECh. 11.1 - In Exercises 1-4, a write the given data in...Ch. 11.1 - Prob. 5ECh. 11.1 - Prob. 6ECh. 11.1 - Use the information in Exercise 3 to predict the...Ch. 11.1 - Prob. 8ECh. 11.1 - Prob. 9ECh. 11.1 - Prob. 10ECh. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.2 - Prob. 1ECh. 11.2 - Prob. 2ECh. 11.2 - Prob. 3ECh. 11.2 - Prob. 4ECh. 11.2 - In Exercises 511, round all percents to the...Ch. 11.2 - Prob. 6ECh. 11.2 - Prob. 7ECh. 11.2 - In Exercises 5-11, round all percent to the...Ch. 11.2 - Prob. 9ECh. 11.2 - Prob. 10ECh. 11.2 - Prob. 11ECh. 11.2 - Prob. 12ECh. 11.2 - Prob. 13ECh. 11.2 - Prob. 14ECh. 11.2 - Prob. 15ECh. 11.2 - Prob. 16ECh. 11.2 - Prob. 17ECh. 11.2 - Prob. 18ECh. 11.2 - Prob. 19ECh. 11.2 - Prob. 20ECh. 11.2 - Prob. 21ECh. 11.2 - Prob. 22ECh. 11.3 - Prob. 1ECh. 11.3 - Prob. 2ECh. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - Prob. 7ECh. 11.3 - Prob. 8ECh. 11.3 - Prob. 9ECh. 11.3 - Monopoly is the most played board game in the...Ch. 11.4 - Prob. 1ECh. 11.4 - Prob. 2ECh. 11.4 - Prob. 3ECh. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - Prob. 13ECh. 11.4 - Prob. 14ECh. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - Prob. 17ECh. 11.4 - Prob. 18ECh. 11.4 - Prob. 19ECh. 11.4 - Prob. 20ECh. 11.4 - Prob. 21ECh. 11.4 - Prob. 22ECh. 11.4 - Prob. 23ECh. 11.4 - Prob. 24ECh. 11.4 - Prob. 25ECh. 11.4 - Prob. 26ECh. 11.4 - Prob. 27ECh. 11.4 - Prob. 28ECh. 11.5 - Prob. 1ECh. 11.5 - Prob. 2ECh. 11.5 - Prob. 3ECh. 11.5 - Prob. 4ECh. 11.5 - Prob. 5ECh. 11.5 - Prob. 6ECh. 11.5 - Prob. 7ECh. 11.5 - Prob. 8ECh. 11.5 - Prob. 10ECh. 11.5 - Prob. 11ECh. 11.5 - Prob. 12ECh. 11.CR - Prob. 1CRCh. 11.CR - Prob. 2CRCh. 11.CR - Prob. 3CRCh. 11.CR - Prob. 4CRCh. 11.CR - Prob. 5CRCh. 11.CR - Prob. 6CRCh. 11.CR - Prob. 7CRCh. 11.CR - Prob. 8CRCh. 11.CR - Prob. 9CRCh. 11.CR - Prob. 10CRCh. 11.CR - Prob. 11CRCh. 11.CR - Prob. 12CRCh. 11.CR - Prob. 13CRCh. 11.CR - Prob. 14CRCh. 11.CR - Prob. 15CRCh. 11.CR - Prob. 16CRCh. 11.CR - Prob. 17CRCh. 11.CR - Prob. 18CRCh. 11.CR - Prob. 19CRCh. 11.CR - Prob. 20CRCh. 11.CR - Prob. 21CRCh. 11.CR - Prob. 22CRCh. 11.CR - Prob. 23CRCh. 11.CR - Prob. 24CRCh. 11.CR - Prob. 25CRCh. 11.CR - Prob. 26CRCh. 11.CR - Prob. 27CRCh. 11.CR - Prob. 28CRCh. 11.CR - Prob. 29CRCh. 11.CR - Prob. 30CRCh. 11.CR - Prob. 31CRCh. 11.CR - Prob. 32CRCh. 11.CR - Prob. 33CR
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- For the system consisting of the three planes:plane 1: -4x + 4y - 2z = -8plane 2: 2x + 2y + 4z = 20plane 3: -2x - 3y + z = -1a) Are any of the planes parallel and/or coincident? Justify your answer.b) Determine if the normals are coplanar. What does this tell you about the system?c) Solve the system if possible. Show a complete solution (do not use matrix operations). Classify the system using the terms: consistent, inconsistent, dependent and/or independent.arrow_forwardFor the system consisting of the three planes:plane 1: -4x + 4y - 2z = -8plane 2: 2x + 2y + 4z = 20plane 3: -2x - 3y + z = -1a) Are any of the planes parallel and/or coincident? Justify your answer.b) Determine if the normals are coplanar. What does this tell you about the system?c) Solve the system if possible. Show a complete solution (do not use matrix operations). Classify the system using the terms: consistent, inconsistent, dependent and/or independent.arrow_forwardOpen your tool box and find geometric methods, symmetries of even and odd functions and the evaluation theorem. Use these to calculate the following definite integrals. Note that you should not use Riemann sums for this problem. (a) (4 pts) (b) (2 pts) 3 S³ 0 3-x+9-dz x3 + sin(x) x4 + cos(x) dx (c) (4 pts) L 1-|x|dxarrow_forward
- A movie studio wishes to determine the relationship between the revenue generated from the streaming of comedies and the revenue generated from the theatrical release of such movies. The studio has the following bivariate data from a sample of fifteen comedies released over the past five years. These data give the revenue x from theatrical release (in millions of dollars) and the revenue y from streaming (in millions of dollars) for each of the fifteen movies. The data are displayed in the Figure 1 scatter plot. Theater revenue, x Streaming revenue, y (in millions of (in millions of dollars) dollars) 13.2 10.3 62.6 10.4 20.8 5.1 36.7 13.3 44.6 7.2 65.9 10.3 49.4 15.7 31.5 4.5 14.6 2.5 26.0 8.8 28.1 11.5 26.1 7.7 28.2 2.8 60.7 16.4 6.7 1.9 Streaming revenue (in millions of dollars) 18+ 16+ 14 12+ xx 10+ 8+ 6+ 2- 0 10 20 30 40 50 60 70 Theater revenue (in millions of dollars) Figure 1 Send data to calculator Send data to Excel The least-squares regression line for these data has a slope…arrow_forward14arrow_forwardf E and F are disjoint events, P(E and F) =arrow_forward
- 15arrow_forward2arrow_forwardAn engineer is designing a pipeline which is supposed to connect two points P and S. The engineer decides to do it in three sections. The first section runs from point P to point Q, and costs $48 per mile to lay, the second section runs from point Q to point R and costs $54 per mile, the third runs from point R to point S and costs $44 per mile. Looking at the diagram below, you see that if you know the lengths marked x and y, then you know the positions of Q and R. Find the values of x and y which minimize the cost of the pipeline. Please show your answers to 4 decimal places. 2 Miles x = 1 Mile R 10 miles miles y = milesarrow_forward
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