Concept explainers
(a)
the product of factors that are irreducible over the rationals.
(a)

Answer to Problem 52E
The polynomial as a product of factors that is irreducible over rationales
Explanation of Solution
Given information:
The given polynomial function as following below,
Formula used:
Factors are used
Calculation:
Let us assume the above polynomial is an in terms of
Now the above equation is
Therefore,
Hence the polynomial as a product of factors that is irreducible over rationales
Conclusion:
The polynomial as a product of factors that is irreducible over rationales
(b)
The product of linear and quadratic factors that are irreducible over the real’s.
(b)

Answer to Problem 52E
The polynomial as a product of factors that is irreducible over rationales
Explanation of Solution
Given information:
The given polynomial function as following below,
Formula used:
The factor is equated to zero
Calculation:
Similarly take from the part (a) is
To get the real solution put
Therefore,
Hence the polynomial as a product of factors that is irreducible over rationales
Conclusion:
The polynomial as a product of factors that is irreducible over rationales
(c)
The factored form.
(c)

Answer to Problem 52E
The polynomial in complete factored form is
Explanation of Solution
Given information:
The given polynomial function as following below,
Formula used:
The polynomial both irreducible over real and rationales
Calculation:
As we have already discussed the factor of the polynomial both irreducible over real and rationales. So the polynomial in complete factored form is
Conclusion:
The polynomial in complete factored form is
Chapter 2 Solutions
EBK PRECALCULUS W/LIMITS
- 3. 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_forward1. Solve the initial value problem: y" -11y' + 30y = x³e6x y(0) 11, y'(0) = 36 =arrow_forward
- What 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_forwardShow that i cote +1 = cosec 20 tan 20+1 = sec² O २ cos² + sin 20 = 1 using pythagon's theoremarrow_forward
- Find 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_forwardExercise 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_forward
- Aphids 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_forwardEvaluate the limit, and show your answer to 4 decimals if necessary. Iz² - y²z lim (x,y,z)>(9,6,4) xyz 1 -arrow_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





