Pearson eText for Precalculus: A Unit Circle Approach -- Instant Access (Pearson+)
3rd Edition
ISBN: 9780137442591
Author: J. S. Ratti, Marcus McWaters
Publisher: PEARSON+
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Chapter A.1, Problem 142E
To determine
(a)
To verify:
To verify that doubling the length of the diameter of a circular skating rink increases the area of the rink by a factor of
To determine
(b)
To verify:
To verify that tripling the length of the diameter of a circular skating rink increases the area of the rink by a factor of
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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 A.1 Solutions
Pearson eText for Precalculus: A Unit Circle Approach -- Instant Access (Pearson+)
Ch. A.1 - In Exercises 1-4, write each of the following...Ch. A.1 - In Exercises 1-4, write each of the following...Ch. A.1 - In Exercises 1-4, write each of the following...Ch. A.1 - Prob. 4ECh. A.1 - Prob. 5ECh. A.1 - Prob. 6ECh. A.1 - Prob. 7ECh. A.1 - Prob. 8ECh. A.1 - In Exercises 5-10, classify each of the following...Ch. A.1 - Prob. 10E
Ch. A.1 - Prob. 11ECh. A.1 - Prob. 12ECh. A.1 - Prob. 13ECh. A.1 - Prob. 14ECh. A.1 - Prob. 15ECh. A.1 - Prob. 16ECh. A.1 - Prob. 17ECh. A.1 - Prob. 18ECh. A.1 - Prob. 19ECh. A.1 - Prob. 20ECh. A.1 - Prob. 21ECh. A.1 - Prob. 22ECh. A.1 - Prob. 23ECh. A.1 - Prob. 24ECh. A.1 -
In Exercises 25-38, rewrite each expression...Ch. A.1 - Prob. 26ECh. A.1 - Prob. 27ECh. A.1 - Prob. 28ECh. A.1 - Prob. 29ECh. A.1 - Prob. 30ECh. A.1 - Prob. 31ECh. A.1 - Prob. 32ECh. A.1 - Prob. 33ECh. A.1 - Prob. 34ECh. A.1 - Prob. 35ECh. A.1 - Prob. 36ECh. A.1 - Prob. 37ECh. A.1 - Prob. 38ECh. A.1 - Prob. 39ECh. A.1 - Prob. 40ECh. A.1 - Prob. 41ECh. A.1 - Prob. 42ECh. A.1 - Prob. 43ECh. A.1 - Prob. 44ECh. A.1 - Prob. 45ECh. A.1 - Prob. 46ECh. A.1 - Prob. 47ECh. A.1 - Prob. 48ECh. A.1 - Prob. 49ECh. A.1 - Prob. 50ECh. A.1 - Prob. 51ECh. A.1 - Prob. 52ECh. A.1 - Prob. 53ECh. A.1 - Prob. 54ECh. A.1 - Prob. 55ECh. A.1 - Prob. 56ECh. A.1 - Prob. 57ECh. A.1 - Prob. 58ECh. A.1 - Prob. 59ECh. A.1 - Prob. 60ECh. A.1 - Prob. 61ECh. A.1 - Prob. 62ECh. A.1 - Prob. 63ECh. A.1 - Prob. 64ECh. A.1 - Prob. 65ECh. A.1 - Prob. 66ECh. A.1 - Prob. 67ECh. A.1 -
In Exercises 59-68, evaluate each expression for...Ch. A.1 - Prob. 69ECh. A.1 - Prob. 70ECh. A.1 - Prob. 71ECh. A.1 - Prob. 72ECh. A.1 - Prob. 73ECh. A.1 - Prob. 74ECh. A.1 - Prob. 75ECh. A.1 - Prob. 76ECh. A.1 - Prob. 77ECh. A.1 - Prob. 78ECh. A.1 - Prob. 79ECh. A.1 - Prob. 80ECh. A.1 - Prob. 81ECh. A.1 - Prob. 82ECh. A.1 - Prob. 83ECh. A.1 - Prob. 84ECh. A.1 - Prob. 85ECh. A.1 - Prob. 86ECh. A.1 - Prob. 87ECh. A.1 - Prob. 88ECh. A.1 - Prob. 89ECh. A.1 - Prob. 90ECh. A.1 - Prob. 91ECh. A.1 - Prob. 92ECh. A.1 - Prob. 93ECh. A.1 - Prob. 94ECh. A.1 - Prob. 95ECh. A.1 - Prob. 96ECh. A.1 - Prob. 97ECh. A.1 - Prob. 98ECh. A.1 - Prob. 99ECh. A.1 - Prob. 100ECh. A.1 - Prob. 101ECh. A.1 - Prob. 102ECh. A.1 - Prob. 103ECh. A.1 - Prob. 104ECh. A.1 - Prob. 105ECh. A.1 - Prob. 106ECh. A.1 - Prob. 107ECh. A.1 - Prob. 108ECh. A.1 - Prob. 109ECh. A.1 - In Exercises 101-134, simplify each expression....Ch. A.1 - Prob. 111ECh. A.1 - Prob. 112ECh. A.1 - Prob. 113ECh. A.1 - Prob. 114ECh. A.1 - Prob. 115ECh. A.1 - Prob. 116ECh. A.1 - Prob. 117ECh. A.1 - Prob. 118ECh. A.1 - Prob. 119ECh. A.1 - Prob. 120ECh. A.1 - Prob. 121ECh. A.1 - Prob. 122ECh. A.1 - Prob. 123ECh. A.1 - Prob. 124ECh. A.1 - Prob. 125ECh. A.1 - Prob. 126ECh. A.1 - Prob. 127ECh. A.1 - Prob. 128ECh. A.1 - Prob. 129ECh. A.1 - Prob. 130ECh. A.1 - Prob. 131ECh. A.1 - Prob. 132ECh. A.1 - Prob. 133ECh. A.1 - Prob. 134ECh. A.1 - Prob. 135ECh. A.1 - Prob. 136ECh. A.1 - Prob. 137ECh. A.1 - Prob. 138ECh. A.1 - Prob. 139ECh. A.1 - Prob. 140ECh. A.1 - Prob. 141ECh. A.1 - Prob. 142E
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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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