(a)
To find the number of subscribers in 1st year.
(a)

Answer to Problem 6PS
The matrix is-
Explanation of Solution
Given Information:
The percentage changes in satellite subscriptions each year by the competing companies Gold and Galaxy and the non-subscribers respectively from company to
company is given by the element
in the matrix:
The following matrix represents the total number of subscribers and non-subscribers of the companies Gold and Galaxy.
The total number of subscribers each company will have 1 in year is found by the multiplication of the percentage subscribers of the company with the total number of subscribers of each company.
The percentage of subscribers in the company is found by the transpose of the given matrix of percentage subscription.
So,
The percentage of subscribers of a company and the non-subscribers is given by the matrix:
Thus, the total number of subscribers can be found by the multiplication of the matrices N and A.
So,
Hence, the total number of subscribers each company will have 1 in year is given by the matrix.
b.
To find the number of subscribers in 2nd year.
b.

Answer to Problem 6PS
The matrix is-
Explanation of Solution
The total number of subscribers each company will have 2 in years is found by the multiplication of the percentage subscribers of the company with the total number of subscribers of each company in 1 year.
Thus, the total number of subscribers can be found by the multiplication of the matrices N1 and A.
So,
Hence, the total number of subscribers each company will have 1 in year is given by the matrix.
c.
To find the number of subscribers after 3rd year.
c.

Answer to Problem 6PS
Explanation of Solution
The total number of subscribers each company will have 3 in years is found by the multiplication of the percentage subscribers of the company with the total number of subscribers of each company in 2 years.
Thus, the total number of subscribers can be found by the multiplication of the matrices N2 and A.
So,
Hence, the total number of subscribers each company will have 1 in year is given by the matrix.
The number of non-subscribers is decreasing each year.
d.
To find how does the number of subscribers vary each year.
d.

Answer to Problem 6PS
Explanation of Solution
The number of subscribers in each year is increasing year by year.
The number of non-subscribers is decreasing each year.
Chapter 8 Solutions
EBK PRECALCULUS W/LIMITS
- 2. Consider the following: Prove that x, x2, and 1/x are the solutions to the homogeneous equation corresponding to x³y"" + x²y" + 2xy' + 2y = 2x4. b. use variation of parameters to find a particular solution and complete the general solution to the differential equation. I am interested in process. You may use a computer for integration, finding determinants and doing Kramer's.arrow_forward3. A spring is stretched 6 in. by a mass that weighs 8 lb. The mass is attached to a dashpot mechanism that has a damping constant of 0.25 lb-sec./ft. and is acted on by an external force of 4 cos 2t lb. a. Set-up the differential equation and initial value problem for the system. b. Write the function in phase-amplitude form. C. Determine the transient solution to the system. Show your work. d. Determine the steady state of this system. Show your work. e. Is the system underdamped, overdamped or critically damped? Explain what this means for the system.arrow_forward4. Suppose that you have a circuit with a resistance of 20, inductance of 14 H and a capacitance of 11 F. An EMF with equation of E(t) = 6 cos 4t supplies a continuous charge 60 to the circuit. Suppose that the q(0)= 8 V and the q'(0)=7. Use this information to answer the following questions a. Find the function that models the charge of this circuit. b. Is the circuit underdamped, overdamped or critically damped?arrow_forward
- 1. Solve the initial value problem: y" -11y' + 30y = x³e6x y(0) 11, y'(0) = 36 =arrow_forwardWhat is the particular solution to the differential equation y′′ + y = 1/cos t ?arrow_forwardWhich of the following is the general solution to y′′ + 4y = e^2t + 12 sin(2t) ?A. y(t) = c1 cos(2t) + c2 sin(2t) + 1/8 e^2t − 3t cos(2t)B. y(t) = c1e^2t + c2e^−2t + 1/4 te^2t − 3t cos(2t)C. y(t) = c1 + c2e^−4t + 1/12 te^2t − 3t cos(2t)D. y(t) = c1 cos(2t) + c2 sin(2t) + 1/8 e^2t + 3 sin(2t)E. None of the above. Please include all steps! Thank you!arrow_forward
- Show that i cote +1 = cosec 20 tan 20+1 = sec² O २ cos² + sin 20 = 1 using pythagon's theoremarrow_forwardFind the general solution to the differential equationarrow_forwardcharity savings Budget for May travel food Peter earned $700 during May. The graph shows how the money was used. What fraction was clothes? O Search Submit clothes leisurearrow_forward
- Exercise 11.3 A slope field is given for the equation y' = 4y+4. (a) Sketch the particular solution that corresponds to y(0) = −2 (b) Find the constant solution (c) For what initial conditions y(0) is the solution increasing? (d) For what initial conditions y(0) is the solution decreasing? (e) Verify these results using only the differential equation y' = 4y+4.arrow_forwardAphids are discovered in a pear orchard. The Department of Agriculture has determined that the population of aphids t hours after the orchard has been sprayed is approximated by N(t)=1800−3tln(0.17t)+t where 0<t≤1000. Step 1 of 2: Find N(63). Round to the nearest whole number.arrow_forward3. [-/3 Points] DETAILS MY NOTES SCALCET8 7.4.032. ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the integral. X + 4x + 13 Need Help? Read It SUBMIT ANSWER dxarrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning





