Pearson eText for Business Math -- Instant Access (Pearson+)
11th Edition
ISBN: 9780137518883
Author: Cheryl Cleaves, Margie Hobbs
Publisher: PEARSON+
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Chapter 21.2, Problem 1-1SC
To determine
To calculate: The gross profit and net income for accompany for the year ending if the company had net sales of $5385920, cost of goods sold on $2073587 and the operating expenses of $498507.
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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.
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Chapter 21 Solutions
Pearson eText for Business Math -- Instant Access (Pearson+)
Ch. 21.1 - Prob. 1-1SCCh. 21.1 - Prob. 1-2SCCh. 21.1 - Prob. 1-3SCCh. 21.1 - Prob. 1-4SCCh. 21.1 - Prob. 2-1SCCh. 21.1 - Prob. 2-2SCCh. 21.1 - Prob. 2-3SCCh. 21.1 - Prob. 2-4SCCh. 21.1 - Prob. 3-1SCCh. 21.1 - Prob. 3-2SC
Ch. 21.1 - Prob. 3-3SCCh. 21.1 - Prob. 3-4SCCh. 21.1 - Prob. 1SECh. 21.1 - Prob. 2SECh. 21.1 - Prob. 3SECh. 21.1 - Prob. 4SECh. 21.1 - Prob. 5SECh. 21.1 - Prob. 6SECh. 21.1 - Prob. 7SECh. 21.1 - Prob. 8SECh. 21.1 - Prob. 9SECh. 21.1 - Prob. 10SECh. 21.1 - Prob. 11SECh. 21.1 - Prob. 12SECh. 21.2 - Prob. 1-1SCCh. 21.2 - Prob. 1-2SCCh. 21.2 - Prob. 1-3SCCh. 21.2 - Prob. 1-4SCCh. 21.2 - Prob. 2-1SCCh. 21.2 - Prob. 2-2SCCh. 21.2 - Prob. 2-3SCCh. 21.2 - Prob. 2-4SCCh. 21.2 - Prob. 1SECh. 21.2 - Prob. 2SECh. 21.2 - Prob. 3SECh. 21.2 - Prob. 4SECh. 21.2 - Prob. 5SECh. 21.2 - Prob. 6SECh. 21.2 - Prob. 7SECh. 21.3 - Prob. 1-1SCCh. 21.3 - Prob. 1-2SCCh. 21.3 - Prob. 1-3SCCh. 21.3 - Prob. 1-4SCCh. 21.3 - Prob. 1-5SCCh. 21.3 - Prob. 1-6SCCh. 21.3 - Prob. 1-7SCCh. 21.3 - Prob. 1-8SCCh. 21.3 - Prob. 1-9SCCh. 21.3 - Prob. 1-10SCCh. 21.3 - Prob. 1SECh. 21.3 - Prob. 2SECh. 21.3 - Prob. 3SECh. 21.3 - Prob. 4SECh. 21.3 - Prob. 5SECh. 21.3 - Prob. 6SECh. 21.3 - Prob. 7SECh. 21.3 - Prob. 8SECh. 21.3 - Prob. 9SECh. 21.3 - Prob. 10SECh. 21 - Prob. 1ESCh. 21 - Prob. 2ESCh. 21 - Prob. 3ESCh. 21 - Prob. 4ESCh. 21 - Prob. 5ESCh. 21 - Prob. 6ESCh. 21 - Prob. 7ESCh. 21 - Prob. 8ESCh. 21 - Prob. 9ESCh. 21 - Prob. 10ESCh. 21 - Prob. 11ESCh. 21 - Prob. 12ESCh. 21 - Prob. 13ESCh. 21 - Prob. 14ESCh. 21 - Prob. 15ESCh. 21 - Prob. 16ESCh. 21 - Prob. 17ESCh. 21 - Prob. 18ESCh. 21 - Prob. 19ESCh. 21 - Prob. 20ESCh. 21 - Prob. 21ESCh. 21 - Prob. 22ESCh. 21 - Prob. 23ESCh. 21 - Prob. 24ESCh. 21 - Prob. 25ESCh. 21 - Prob. 26ESCh. 21 - Prob. 1PTCh. 21 - Prob. 2PTCh. 21 - Prob. 3PTCh. 21 - Prob. 4PTCh. 21 - Prob. 5PTCh. 21 - Prob. 6PTCh. 21 - Prob. 7PTCh. 21 - Prob. 8PTCh. 21 - Prob. 9PTCh. 21 - Prob. 10PTCh. 21 - Prob. 11PTCh. 21 - Prob. 12PTCh. 21 - Prob. 1CTCh. 21 - Prob. 2CTCh. 21 - Prob. 3CTCh. 21 - Prob. 4CTCh. 21 - Prob. 5CTCh. 21 - Prob. 6CTCh. 21 - Prob. 7CTCh. 21 - Prob. 8CTCh. 21 - Prob. 9CTCh. 21 - Prob. 10CTCh. 21 - Prob. 11CTCh. 21 - Prob. 1CPCh. 21 - Prob. 2CPCh. 21 - Prob. 3CPCh. 21 - Prob. 1CS1Ch. 21 - Prob. 2CS1Ch. 21 - Prob. 3CS1Ch. 21 - Prob. 1CS2
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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) 6arrow_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_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_forward
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