Finite Mathematics and Calculus with Applications (10th Edition)
10th Edition
ISBN: 9780321979407
Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey
Publisher: PEARSON
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Chapter 7, Problem 94RE
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Question 1. (10 points)
A researcher is studying tumours in mice. The growth rate for the volume of the tumour V(t) in cm³ is given by
dV
=
1.45V(2 In(V+1)).
dt
(a) (4 pts) Find all the equilibria and determine their stability using the stability condition.
(b) (2 pts) Draw the phase plot f(V) versus V where f(V) = V'. You may find it helpful to use Desmos or Wolfram Alpha to plot the graph of
f(V) versus V (both are free to use online), or you can plot it by hand if you like. On the plot identify each equilibrium as stable or unstable.
(c) (4 pts) Draw direction arrows for the case where the tumour starts at size 3cm³ and for the case where the tumour starts at size 9cm³. Explain
in biological terms what happens to the size of each of these tumours at time progresses.
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.
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 7 Solutions
Finite Mathematics and Calculus with Applications (10th Edition)
Ch. 7.1 - Prob. 1YTCh. 7.1 - Prob. 2YTCh. 7.1 - Find the number of subsets for the set {x|x is a...Ch. 7.1 - Prob. 4YTCh. 7.1 - Prob. 5YTCh. 7.1 - Prob. 1ECh. 7.1 - Prob. 2ECh. 7.1 - Prob. 3ECh. 7.1 - Prob. 4ECh. 7.1 - Prob. 5E
Ch. 7.1 - Prob. 6ECh. 7.1 - Prob. 7ECh. 7.1 - Prob. 8ECh. 7.1 - In Exercises 110, write true or false for each...Ch. 7.1 - Prob. 10ECh. 7.1 - Prob. 11ECh. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - Prob. 16ECh. 7.1 - Prob. 17ECh. 7.1 - Prob. 18ECh. 7.1 - Prob. 19ECh. 7.1 - Prob. 20ECh. 7.1 - Prob. 21ECh. 7.1 - Prob. 22ECh. 7.1 - Prob. 23ECh. 7.1 - Prob. 24ECh. 7.1 - Prob. 25ECh. 7.1 - Prob. 26ECh. 7.1 - Prob. 27ECh. 7.1 - Prob. 28ECh. 7.1 - Prob. 29ECh. 7.1 - Insert or to make each statement true. 30. {3,...Ch. 7.1 - Insert or to make each statement true. 31. {1,...Ch. 7.1 - Insert or to make each statement true. 32. {0,...Ch. 7.1 - Prob. 33ECh. 7.1 - Prob. 34ECh. 7.1 - Prob. 35ECh. 7.1 - Prob. 36ECh. 7.1 - Prob. 37ECh. 7.1 - Prob. 38ECh. 7.1 - Prob. 39ECh. 7.1 - Prob. 40ECh. 7.1 - Prob. 41ECh. 7.1 - Prob. 42ECh. 7.1 - Prob. 43ECh. 7.1 - Prob. 44ECh. 7.1 - Prob. 45ECh. 7.1 - Prob. 46ECh. 7.1 - Prob. 47ECh. 7.1 - Prob. 48ECh. 7.1 - Prob. 49ECh. 7.1 - Prob. 50ECh. 7.1 - Prob. 51ECh. 7.1 - Prob. 52ECh. 7.1 - Prob. 53ECh. 7.1 - Prob. 54ECh. 7.1 - Prob. 55ECh. 7.1 - Prob. 56ECh. 7.1 - Prob. 57ECh. 7.1 - Prob. 58ECh. 7.1 - Prob. 59ECh. 7.1 - Prob. 60ECh. 7.1 - Prob. 61ECh. 7.1 - Prob. 62ECh. 7.1 - Prob. 63ECh. 7.1 - Prob. 64ECh. 7.1 - Prob. 65ECh. 7.1 - Prob. 66ECh. 7.1 - Prob. 67ECh. 7.1 - Prob. 68ECh. 7.1 - Prob. 69ECh. 7.1 - General Interest 70. Musicians A concert featured...Ch. 7.1 - Prob. 71ECh. 7.1 - Prob. 72ECh. 7.1 - Prob. 73ECh. 7.1 - Prob. 74ECh. 7.1 - Prob. 75ECh. 7.1 - Prob. 76ECh. 7.1 - Prob. 77ECh. 7.1 - Prob. 78ECh. 7.1 - Prob. 79ECh. 7.2 - Prob. 1YTCh. 7.2 - Prob. 2YTCh. 7.2 - One hundred students were asked which fast food...Ch. 7.2 - A group of students are sitting in the lounge. All...Ch. 7.2 - Prob. 1WECh. 7.2 - Prob. 2WECh. 7.2 - Prob. 1ECh. 7.2 - Prob. 2ECh. 7.2 - Prob. 3ECh. 7.2 - Prob. 4ECh. 7.2 - Prob. 5ECh. 7.2 - Prob. 6ECh. 7.2 - Prob. 7ECh. 7.2 - Prob. 8ECh. 7.2 - Prob. 9ECh. 7.2 - Prob. 10ECh. 7.2 - Prob. 11ECh. 7.2 - Prob. 12ECh. 7.2 - Prob. 13ECh. 7.2 - Prob. 14ECh. 7.2 - Prob. 15ECh. 7.2 - Prob. 16ECh. 7.2 - Prob. 17ECh. 7.2 - Prob. 18ECh. 7.2 - Prob. 19ECh. 7.2 - Prob. 20ECh. 7.2 - Prob. 21ECh. 7.2 - Prob. 22ECh. 7.2 - Prob. 23ECh. 7.2 - Prob. 24ECh. 7.2 - Draw a Venn diagram and use the given information...Ch. 7.2 - Prob. 26ECh. 7.2 - Prob. 27ECh. 7.2 - Prob. 28ECh. 7.2 - Prob. 29ECh. 7.2 - Prob. 30ECh. 7.2 - Prob. 31ECh. 7.2 - Prob. 32ECh. 7.2 - Prob. 33ECh. 7.2 - Prob. 34ECh. 7.2 - Prob. 35ECh. 7.2 - Prob. 36ECh. 7.2 - Prob. 37ECh. 7.2 - Business and Economics Use Venn diagrams to answer...Ch. 7.2 - Harvesting Fruit Toward the middle of the...Ch. 7.2 - Prob. 42ECh. 7.2 - Prob. 43ECh. 7.2 - Investment Survey Most mathematics professors love...Ch. 7.2 - Prob. 45ECh. 7.2 - Prob. 46ECh. 7.2 - Prob. 47ECh. 7.2 - Prob. 48ECh. 7.2 - Prob. 49ECh. 7.2 - Lyme Disease Scientists have found a way to...Ch. 7.2 - Social Sciences 51. Military The number of female...Ch. 7.2 - Prob. 52ECh. 7.2 - Prob. 53ECh. 7.2 - Prob. 54ECh. 7.2 - Prob. 55ECh. 7.2 - Prob. 56ECh. 7.2 - Prob. 57ECh. 7.2 - Prob. 58ECh. 7.2 - Prob. 59ECh. 7.2 - Prob. 60ECh. 7.2 - Prob. 61ECh. 7.2 - Prob. 62ECh. 7.2 - Poultry Analysis A chicken farmer surveyed his...Ch. 7.3 - Prob. 1YTCh. 7.3 - Prob. 2YTCh. 7.3 - Prob. 3YTCh. 7.3 - Prob. 4YTCh. 7.3 - Prob. 5YTCh. 7.3 - Prob. 1ECh. 7.3 - Prob. 2ECh. 7.3 - Prob. 3ECh. 7.3 - Write sample spaces for the experiments in...Ch. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - Prob. 7ECh. 7.3 - Prob. 8ECh. 7.3 - Prob. 9ECh. 7.3 - Prob. 10ECh. 7.3 - Define an event.Ch. 7.3 - Prob. 12ECh. 7.3 - Prob. 13ECh. 7.3 - For the experiments in Exercises 1318, write out...Ch. 7.3 - For the experiments in Exercises 1318, write out...Ch. 7.3 - For the experiments in Exercises 1318, write out...Ch. 7.3 - For the experiments in Exercises 1318, write out...Ch. 7.3 - Prob. 18ECh. 7.3 - Prob. 19ECh. 7.3 - Prob. 20ECh. 7.3 - Prob. 21ECh. 7.3 - Prob. 22ECh. 7.3 - Prob. 23ECh. 7.3 - Prob. 24ECh. 7.3 - Prob. 25ECh. 7.3 - Prob. 26ECh. 7.3 - Prob. 27ECh. 7.3 - Prob. 28ECh. 7.3 - Prob. 29ECh. 7.3 - Prob. 30ECh. 7.3 - Prob. 31ECh. 7.3 - Prob. 32ECh. 7.3 - Prob. 33ECh. 7.3 - Prob. 34ECh. 7.3 - Prob. 35ECh. 7.3 - Prob. 36ECh. 7.3 - Prob. 37ECh. 7.3 - Prob. 38ECh. 7.3 - Prob. 39ECh. 7.3 - Prob. 40ECh. 7.3 - Prob. 41ECh. 7.3 - Prob. 42ECh. 7.3 - Prob. 43ECh. 7.3 - Prob. 44ECh. 7.3 - Prob. 45ECh. 7.3 - Prob. 46ECh. 7.3 - Prob. 47ECh. 7.3 - Prob. 48ECh. 7.3 - Prob. 49ECh. 7.3 - Prob. 50ECh. 7.3 - Prob. 51ECh. 7.3 - Prob. 52ECh. 7.3 - Prob. 53ECh. 7.3 - Prob. 54ECh. 7.3 - Prob. 55ECh. 7.3 - Prob. 56ECh. 7.3 - Prob. 57ECh. 7.3 - Prob. 58ECh. 7.3 - Prob. 59ECh. 7.3 - Prob. 60ECh. 7.3 - Civil War Estimates of the Confederate Armys...Ch. 7.3 - Prob. 62ECh. 7.3 - Prob. 63ECh. 7.4 - In Example 1, find the probability of an ace or a...Ch. 7.4 - Prob. 2YTCh. 7.4 - Prob. 3YTCh. 7.4 - If the probability of snow tomorrow is 3/10, find...Ch. 7.4 - Prob. 5YTCh. 7.4 - If the odds against a particular horse winning a...Ch. 7.4 - Prob. 1WECh. 7.4 - Prob. 2WECh. 7.4 - Prob. 1ECh. 7.4 - Prob. 2ECh. 7.4 - Prob. 3ECh. 7.4 - Prob. 4ECh. 7.4 - Prob. 5ECh. 7.4 - Decide whether the events in Exercises 38 are...Ch. 7.4 - Prob. 7ECh. 7.4 - Prob. 8ECh. 7.4 - Prob. 9ECh. 7.4 - Prob. 10ECh. 7.4 - Prob. 11ECh. 7.4 - Prob. 12ECh. 7.4 - Two dice are rolled. Find the probabilities of the...Ch. 7.4 - Prob. 14ECh. 7.4 - Prob. 15ECh. 7.4 - Prob. 16ECh. 7.4 - Prob. 17ECh. 7.4 - Kristina Karganova invites 13 relatives to a...Ch. 7.4 - Prob. 19ECh. 7.4 - The numbers 1, 2, 3, 4, and 5 are written on slips...Ch. 7.4 - Prob. 21ECh. 7.4 - Prob. 22ECh. 7.4 - Prob. 23ECh. 7.4 - Prob. 24ECh. 7.4 - Prob. 25ECh. 7.4 - Prob. 27ECh. 7.4 - Prob. 28ECh. 7.4 - Prob. 29ECh. 7.4 - Prob. 30ECh. 7.4 - Prob. 31ECh. 7.4 - Prob. 32ECh. 7.4 - What is a probability distribution?Ch. 7.4 - What conditions must hold for a probability...Ch. 7.4 - An experiment is conducted for which the sample...Ch. 7.4 - An experiment is conducted for which the sample...Ch. 7.4 - An experiment is conducted for which the sample...Ch. 7.4 - Prob. 38ECh. 7.4 - An experiment is conducted for which the sample...Ch. 7.4 - An experiment is conducted for which the sample...Ch. 7.4 - Prob. 46ECh. 7.4 - Prob. 47ECh. 7.4 - Prob. 48ECh. 7.4 - Prob. 49ECh. 7.4 - Prob. 50ECh. 7.4 - Prob. 51ECh. 7.4 - Prob. 52ECh. 7.4 - Prob. 53ECh. 7.4 - Prob. 54ECh. 7.4 - Prob. 55ECh. 7.4 - Prob. 56ECh. 7.4 - Doctor Visit The probability that a visit to a...Ch. 7.4 - Prob. 58ECh. 7.4 - Prob. 59ECh. 7.4 - Prob. 60ECh. 7.4 - Prob. 61ECh. 7.4 - Prob. 62ECh. 7.4 - Prob. 63ECh. 7.4 - Prob. 64ECh. 7.4 - Prob. 65ECh. 7.4 - Prob. 66ECh. 7.4 - Prob. 67ECh. 7.4 - Prob. 68ECh. 7.4 - Prob. 69ECh. 7.4 - Prob. 70ECh. 7.4 - Prob. 71ECh. 7.5 - In Example 1, find P(A|B). EXAMPLE 1 Stocks Use...Ch. 7.5 - Prob. 2YTCh. 7.5 - Prob. 3YTCh. 7.5 - At a local college, 4/5 of the students live on...Ch. 7.5 - Prob. 5YTCh. 7.5 - Prob. 6YTCh. 7.5 - Prob. 7YTCh. 7.5 - Prob. 8YTCh. 7.5 - Prob. 1WECh. 7.5 - Prob. 2WECh. 7.5 - Prob. 1ECh. 7.5 - Prob. 2ECh. 7.5 - Prob. 3ECh. 7.5 - Prob. 4ECh. 7.5 - Prob. 5ECh. 7.5 - Prob. 6ECh. 7.5 - Prob. 7ECh. 7.5 - Prob. 8ECh. 7.5 - Prob. 9ECh. 7.5 - Prob. 10ECh. 7.5 - Prob. 11ECh. 7.5 - Prob. 12ECh. 7.5 - Prob. 13ECh. 7.5 - Prob. 14ECh. 7.5 - Prob. 15ECh. 7.5 - Prob. 16ECh. 7.5 - Prob. 17ECh. 7.5 - Prob. 18ECh. 7.5 - Decide whether the following pairs of events are...Ch. 7.5 - Prob. 20ECh. 7.5 - Prob. 21ECh. 7.5 - Decide whether the following pairs of events are...Ch. 7.5 - In the previous section, we described an...Ch. 7.5 - In the previous section, we described an...Ch. 7.5 - Prob. 25ECh. 7.5 - Prob. 26ECh. 7.5 - Another friend asks you to explain how to tell...Ch. 7.5 - Prob. 28ECh. 7.5 - Let A and B be independent events with P(A)=14 and...Ch. 7.5 - Prob. 30ECh. 7.5 - Prob. 32ECh. 7.5 - Prob. 33ECh. 7.5 - Prob. 34ECh. 7.5 - Prob. 35ECh. 7.5 - Prob. 36ECh. 7.5 - Prob. 37ECh. 7.5 - Prob. 38ECh. 7.5 - Prob. 39ECh. 7.5 - Prob. 40ECh. 7.5 - Prob. 41ECh. 7.5 - Backup Computers Corporations where a computer is...Ch. 7.5 - Prob. 43ECh. 7.5 - Prob. 44ECh. 7.5 - Prob. 45ECh. 7.5 - Prob. 46ECh. 7.5 - Prob. 47ECh. 7.5 - Prob. 48ECh. 7.5 - Genetics Assuming that boy and girl babies are...Ch. 7.5 - Prob. 50ECh. 7.5 - Genetics Assuming that boy and girl babies are...Ch. 7.5 - Prob. 52ECh. 7.5 - Prob. 53ECh. 7.5 - Prob. 54ECh. 7.5 - Prob. 55ECh. 7.5 - Prob. 56ECh. 7.5 - Prob. 57ECh. 7.5 - Prob. 58ECh. 7.5 - Prob. 59ECh. 7.5 - Prob. 60ECh. 7.5 - Prob. 61ECh. 7.5 - Prob. 62ECh. 7.5 - Prob. 63ECh. 7.5 - Prob. 64ECh. 7.5 - Prob. 65ECh. 7.5 - Prob. 66ECh. 7.5 - Prob. 67ECh. 7.5 - Prob. 68ECh. 7.5 - Prob. 69ECh. 7.5 - Prob. 70ECh. 7.5 - Prob. 71ECh. 7.5 - Prob. 72ECh. 7.5 - Prob. 73ECh. 7.5 - Prob. 74ECh. 7.5 - Prob. 75ECh. 7.5 - Prob. 76ECh. 7.5 - Prob. 77ECh. 7.5 - Prob. 78ECh. 7.5 - Prob. 79ECh. 7.5 - Prob. 80ECh. 7.5 - Prob. 81ECh. 7.5 - Prob. 82ECh. 7.5 - Prob. 83ECh. 7.5 - Prob. 84ECh. 7.5 - Prob. 85ECh. 7.5 - Prob. 86ECh. 7.5 - Basketball A basketball player is fouled and now...Ch. 7.5 - Basketball The same player from Exercise 87 is now...Ch. 7.5 - Prob. 89ECh. 7.5 - Prob. 90ECh. 7.6 - The probability that a student will pass a math...Ch. 7.6 - Prob. 2YTCh. 7.6 - Prob. 1WECh. 7.6 - Prob. 2WECh. 7.6 - Prob. 1ECh. 7.6 - Prob. 2ECh. 7.6 - Prob. 3ECh. 7.6 - Prob. 4ECh. 7.6 - Prob. 5ECh. 7.6 - Prob. 6ECh. 7.6 - Prob. 7ECh. 7.6 - Suppose you have three jars with the following...Ch. 7.6 - Prob. 9ECh. 7.6 - Prob. 10ECh. 7.6 - Prob. 11ECh. 7.6 - Job Qualifications Of all the people applying for...Ch. 7.6 - Prob. 13ECh. 7.6 - Prob. 14ECh. 7.6 - Prob. 15ECh. 7.6 - Prob. 16ECh. 7.6 - Prob. 17ECh. 7.6 - Prob. 18ECh. 7.6 - Prob. 19ECh. 7.6 - Prob. 20ECh. 7.6 - Prob. 21ECh. 7.6 - Prob. 22ECh. 7.6 - Colorectal Cancer Researchers found that only one...Ch. 7.6 - Hepatitis Blood Test The probability that a person...Ch. 7.6 - Sensitivity and Specificity The sensitivity of a...Ch. 7.6 - Prob. 26ECh. 7.6 - Smokers A health study tracked a group of persons...Ch. 7.6 - Prob. 28ECh. 7.6 - Prob. 29ECh. 7.6 - Prob. 30ECh. 7.6 - Prob. 31ECh. 7.6 - Murder During the murder trial of O. J. Simpson,...Ch. 7.6 - Prob. 33ECh. 7.6 - Prob. 34ECh. 7.6 - Prob. 35ECh. 7.6 - Prob. 36ECh. 7.6 - Prob. 37ECh. 7.6 - Prob. 38ECh. 7.6 - Prob. 39ECh. 7.6 - Three Prisoners The famous problem of three...Ch. 7 - Prob. 1RECh. 7 - Prob. 2RECh. 7 - Prob. 3RECh. 7 - Prob. 4RECh. 7 - Prob. 5RECh. 7 - Prob. 6RECh. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Prob. 10RECh. 7 - Prob. 11RECh. 7 - Prob. 12RECh. 7 - Prob. 13RECh. 7 - Prob. 14RECh. 7 - Write true or false for each statement. 15. 2 {0,...Ch. 7 - Prob. 16RECh. 7 - Prob. 17RECh. 7 - Prob. 18RECh. 7 - Prob. 19RECh. 7 - Prob. 20RECh. 7 - Prob. 21RECh. 7 - Prob. 22RECh. 7 - Prob. 23RECh. 7 - Prob. 24RECh. 7 - Prob. 25RECh. 7 - Prob. 26RECh. 7 - Prob. 27RECh. 7 - Prob. 28RECh. 7 - Prob. 29RECh. 7 - Prob. 30RECh. 7 - Prob. 31RECh. 7 - Prob. 32RECh. 7 - Prob. 33RECh. 7 - In Exercises 3338, let U = {all employees of the...Ch. 7 - Prob. 35RECh. 7 - Prob. 36RECh. 7 - Prob. 37RECh. 7 - Prob. 38RECh. 7 - Prob. 39RECh. 7 - Prob. 40RECh. 7 - Prob. 41RECh. 7 - Prob. 42RECh. 7 - Prob. 43RECh. 7 - Prob. 44RECh. 7 - Prob. 45RECh. 7 - Prob. 46RECh. 7 - Prob. 47RECh. 7 - Prob. 48RECh. 7 - Prob. 49RECh. 7 - Prob. 50RECh. 7 - Prob. 51RECh. 7 - Prob. 52RECh. 7 - Prob. 53RECh. 7 - Prob. 54RECh. 7 - Prob. 55RECh. 7 - Prob. 56RECh. 7 - Prob. 57RECh. 7 - Prob. 58RECh. 7 - Prob. 59RECh. 7 - Prob. 60RECh. 7 - Prob. 61RECh. 7 - Prob. 62RECh. 7 - Prob. 63RECh. 7 - Prob. 64RECh. 7 - Prob. 65RECh. 7 - Find the odds in favor of a card drawn from an...Ch. 7 - Prob. 67RECh. 7 - Prob. 68RECh. 7 - Prob. 69RECh. 7 - Prob. 70RECh. 7 - Prob. 71RECh. 7 - Prob. 72RECh. 7 - Prob. 73RECh. 7 - Prob. 74RECh. 7 - Prob. 75RECh. 7 - Prob. 76RECh. 7 - Prob. 77RECh. 7 - An urn contains 10 balls: 4 red and 6 blue. A...Ch. 7 - Prob. 79RECh. 7 - Prob. 80RECh. 7 - Prob. 81RECh. 7 - Prob. 82RECh. 7 - Prob. 83RECh. 7 - Prob. 84RECh. 7 - Prob. 85RECh. 7 - Prob. 86RECh. 7 - Prob. 87RECh. 7 - Prob. 88RECh. 7 - Prob. 89RECh. 7 - Prob. 90RECh. 7 - Prob. 91RECh. 7 - Prob. 92RECh. 7 - Prob. 93RECh. 7 - Prob. 94RECh. 7 - Prob. 95RECh. 7 - Prob. 96RECh. 7 - Prob. 97RECh. 7 - Prob. 98RECh. 7 - Prob. 99RECh. 7 - Prob. 100RECh. 7 - Prob. 101RECh. 7 - Prob. 102RECh. 7 - Prob. 103RECh. 7 - Prob. 104RECh. 7 - Defective Items A manufacturer buys items from...Ch. 7 - Prob. 106RECh. 7 - Prob. 107RECh. 7 - Auto Insurance An auto insurance company has...Ch. 7 - Prob. 109RECh. 7 - Insurance An insurance company estimates that 40%...Ch. 7 - Prob. 111RECh. 7 - Prob. 112RECh. 7 - Prob. 113RECh. 7 - Elections In the 2012 presidential election, over...Ch. 7 - Prob. 115RECh. 7 - Prob. 116RECh. 7 - Prob. 117RECh. 7 - Prob. 118RECh. 7 - Earthquake It has been reported that government...Ch. 7 - Prob. 120RECh. 7 - Prob. 121RECh. 7 - Prob. 122RECh. 7 - Prob. 123RECh. 7 - Prob. 124RECh. 7 - Prob. 125RE
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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
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