DIFFERENTIAL EQUATIONS-NEXTGEN WILEYPLUS
3rd Edition
ISBN: 9781119764564
Author: BRANNAN
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 4.1, Problem 15P
A mass weighing
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
The force P = 15 lb is applied to the cable and the cords slip on the smooth surfaces of the non-
rotating pulleys. Determine the magnitude and direction of the acceleration of the 36-lb cylinder if
(a) the pulleys are massless, (b) the pulleys are 4 lb each. (a = 21.5 ft/sec², a = = 6.9 ft/sec²)
P
W
An object is shot straight upward from sea level with an initial velocity of 400 ft/sec.
a. Assuming that gravity is the only force acting on the object, give an upper estimate for its velocity after 5 sec have elapsed. Use g = 32 ft/sec2 for the gravitational acceleration.
b. Find a lower estimate for the height attained after 5 sec.
A shot putter threw an 8 lb 13 oz shot 71 ft, 8 in. Assuming the shot putter launched the shot at a 60° angle to the horizontal from 5.5 ft above
the ground, what was the shot's initial speed? The acceleration due to gravity is 32 ft/sec².
The shot's initial speed was vo
=
ft/sec.
Chapter 4 Solutions
DIFFERENTIAL EQUATIONS-NEXTGEN WILEYPLUS
Ch. 4.1 - In Problems 1 through 7, determine whether the...Ch. 4.1 - In Problems 1 through 7, determine whether the...Ch. 4.1 - In Problems 1 through 7, determine whether the...Ch. 4.1 - In Problems 1 through 7, determine whether the...Ch. 4.1 - In Problems 1 through 7, determine whether the...Ch. 4.1 - In Problems 1 through 7, determine whether the...Ch. 4.1 - In Problems 1 through 7, determine whether the...Ch. 4.1 - A mass weighing stretches a spring . What is the...Ch. 4.1 - A mass attached to a vertical spring is slowly...Ch. 4.1 - A mass weighing stretches a spring . The mass is...
Ch. 4.1 - A mass of stretches a spring. The mass is set in...Ch. 4.1 - A mass weighing 3lb stretches a spring 3in. The...Ch. 4.1 - A series circuit has a capacitor of 0.25...Ch. 4.1 - A mass of stretches a spring . Suppose that the...Ch. 4.1 - A mass weighing 16lb stretches a spring 3in. The...Ch. 4.1 - A spring is stretched by a force of (N). A mass...Ch. 4.1 - A series circuit has a capacitor of 105farad, a...Ch. 4.1 - Suppose that a mass m slides without friction on a...Ch. 4.1 -
Duffing’s Equation
For the spring-mass system...Ch. 4.1 - A body of mass is attached between two springs...Ch. 4.1 - A cubic block of side and mass density per unit...Ch. 4.1 - In Problems through , we specift the mass, damping...Ch. 4.1 - In Problems 22 through 26, we specift the mass,...Ch. 4.1 - In Problems through , we specift the mass, damping...Ch. 4.1 - In Problems 22 through 26, we specift the mass,...Ch. 4.1 - In Problems 22 through 26, we specift the mass,...Ch. 4.1 - The Linear Versus the Nonlinear Pendulum.
Convert...Ch. 4.1 - (a) Numerical simulations as well as intuition...Ch. 4.2 - In each of the Problems 1 through 8, determine the...Ch. 4.2 - In each of the Problems through, determine the...Ch. 4.2 - In each of the Problems 1 through 8, determine the...Ch. 4.2 - In each of the Problems through, determine the...Ch. 4.2 - In each of the Problems 1 through 8, determine the...Ch. 4.2 - In each of the Problems through, determine the...Ch. 4.2 - In each of the Problems 1 through 8, determine the...Ch. 4.2 - In each of the Problems through, determine the...Ch. 4.2 - In each of the Problems through, find the...Ch. 4.2 - In each of the Problems through, find the...Ch. 4.2 - In each of the Problems through, find the...Ch. 4.2 - In each of the Problems 9 through 14, find the...Ch. 4.2 - In each of the Problems 9 through 14, find the...Ch. 4.2 - In each of the Problems through, find the...Ch. 4.2 - Verify that and are two solutions of the...Ch. 4.2 - Consider the differential operator T defined by...Ch. 4.2 - Can an equation y+p(t)y+q(t)y=0, with continuous...Ch. 4.2 - If the Wronskian W of f and g is 3e2t, and if...Ch. 4.2 - If the Wronskian W of f and g is t2et, and if...Ch. 4.2 - If W[f,g] is the Wronskian of f and g, and if...Ch. 4.2 - If the Wronskian of f and g is tcostsint, and if...Ch. 4.2 - In each of problem 22 through 25, verify that the...Ch. 4.2 - In each of problem 22 through 25, verify that the...Ch. 4.2 - In each of problem 22 through 25, verify that the...Ch. 4.2 - In each of problem 22 through 25, verify that the...Ch. 4.2 - 26. Consider the equation
(a). Show that and ...Ch. 4.2 - 27. Prove Theorem 4.2.4 and Corollary 4.2.5....Ch. 4.2 - In each of problem 28 through 38, use method of...Ch. 4.2 - In each of problem 28 through 38, use method of...Ch. 4.2 - In each of problem 28 through 38, use method of...Ch. 4.2 - In each of problem 28 through 38, use method of...Ch. 4.2 - In each of problem 28 through 38, use method of...Ch. 4.2 - In each of problem 28 through 38, use method of...Ch. 4.2 - In each of problem 28 through 38, use method of...Ch. 4.2 - In each of problem 28 through 38, use method of...Ch. 4.2 - In each of problem 28 through 38, use method of...Ch. 4.2 - 37. The differential equation
Where N is...Ch. 4.2 - The differential equation y+(xy+y)=0 arises in the...Ch. 4.3 - In each of Problems 1 through 26: (a) Find the...Ch. 4.3 - In each of Problems 1 through 26: (a) Find the...Ch. 4.3 - In each of Problems 1 through 26:
(a) Find the...Ch. 4.3 - In each of Problems 1 through 26: (a) Find the...Ch. 4.3 - In each of Problems 1 through 26: (a) Find the...Ch. 4.3 - In each of Problems 1 through 26: (a) Find the...Ch. 4.3 - In each of Problems 1 through 26:
(a) Find the...Ch. 4.3 - In each of Problems 1 through 26:
(a) Find the...Ch. 4.3 - In each of Problems 1 through 26: (a) Find the...Ch. 4.3 - In each of Problems 1 through 26: (a) Find the...Ch. 4.3 - In each of Problems 1 through 26:
(a) Find the...Ch. 4.3 - In each of Problems 1 through 26: (a) Find the...Ch. 4.3 - In each of Problems 1 through 26: (a) Find the...Ch. 4.3 - In each of Problems 1 through 26:
(a) Find the...Ch. 4.3 - In each of Problems 1 through 26: (a) Find the...Ch. 4.3 - In each of Problems 1 through 26: (a) Find the...Ch. 4.3 - In each of Problems 1 through 26: (a) Find the...Ch. 4.3 - In each of Problems 1 through 26:
(a) Find the...Ch. 4.3 - In each of Problems 1 through 26: (a) Find the...Ch. 4.3 - In each of Problems 1 through 26:
(a) Find the...Ch. 4.3 - In each of Problems 1 through 26:
(a) Find the...Ch. 4.3 - In each of Problems 1 through 26: (a) Find the...Ch. 4.3 - In each of Problems 1 through 26: (a) Find the...Ch. 4.3 - In each of Problems 1 through 26: (a) Find the...Ch. 4.3 - In each of Problems 1 through 26: (a) Find the...Ch. 4.3 - In each of Problems 1 through 26:
(a) Find the...Ch. 4.3 - In each of Problems 27 through 43, solve the given...Ch. 4.3 - In each of Problems 27 through 43, solve the given...Ch. 4.3 - In each of Problems 27 through 43, solve the given...Ch. 4.3 - In each of Problems 27 through 43, solve the given...Ch. 4.3 - In each of Problems through, solve the given...Ch. 4.3 - In each of Problems through, solve the given...Ch. 4.3 - In each of Problems 27 through 43, solve the given...Ch. 4.3 - In each of Problems 27 through 43, solve the given...Ch. 4.3 - In each of Problems through, solve the given...Ch. 4.3 - In each of Problems through, solve the given...Ch. 4.3 - In each of Problems 27 through 43, solve the given...Ch. 4.3 - In each of Problems 27 through 43, solve the given...Ch. 4.3 - In each of Problems 27 through 43, solve the given...Ch. 4.3 - In each of Problems 27 through 43, solve the given...Ch. 4.3 - In each of Problems through, solve the given...Ch. 4.3 - In each of Problems 27 through 43, solve the given...Ch. 4.3 - In each of Problems through, solve the given...Ch. 4.3 - Find a differential equation whose general...Ch. 4.3 - Find a differential equation whose general...Ch. 4.3 - Find a differential equation whose general...Ch. 4.3 - In each of Problems and , determine the values of...Ch. 4.3 - In each of Problems 47 and 48, determine the...Ch. 4.3 - If the roots of the characteristic equation are...Ch. 4.3 - Consider the equation ay+by+cy=d, where a,b,c and...Ch. 4.3 - Consider the equation , where and are constants...Ch. 4.3 - Prob. 52PCh. 4.3 - If , use the substitution to show that the...Ch. 4.3 - In each of Problems through, find the general...Ch. 4.3 - In each of Problems 54 through 61, find the...Ch. 4.3 - In each of Problems through, find the general...Ch. 4.3 - In each of Problems through, find the general...Ch. 4.3 - In each of Problems 54 through 61, find the...Ch. 4.3 - In each of Problems through, find the general...Ch. 4.3 - In each of Problems 54 through 61, find the...Ch. 4.3 - In each of Problems through, find the general...Ch. 4.3 - In each of Problems 62 through 65, find the...Ch. 4.3 - In each of Problems through, find the solution of...Ch. 4.3 - In each of Problems through, find the solution of...Ch. 4.3 - In each of Problems through, find the solution of...Ch. 4.4 - In each of Problems through , determine and so...Ch. 4.4 - In each of Problems through , determine and so...Ch. 4.4 - In each of Problems 1 through 4, determine 0,R,...Ch. 4.4 - In each of Problems 1 through 4, determine 0,R,...Ch. 4.4 - (a) A mass weighing lb stretches a spring in. If...Ch. 4.4 - (a) A mass of 100 g stretches a spring 5 cm. If...Ch. 4.4 - A mass weighing 3 lb stretches a spring 3 in. If...Ch. 4.4 - A series circuit has a capacitor of 0.25...Ch. 4.4 - (a) A mass of g stretches a spring cm. Suppose...Ch. 4.4 - A mass weighing 16 lb stretches a spring 3in. The...Ch. 4.4 - (a) A spring is stretched cm by a force of ...Ch. 4.4 - (a) A series circuit has a capacitor of farad, a...Ch. 4.4 - A certain vibrating system satisfies the equation...Ch. 4.4 - Show that the period of motion of an undamped...Ch. 4.4 - Show that the solution of the initial value...Ch. 4.4 - Show that Acos0t+Bsin0t can be written in the form...Ch. 4.4 - A mass weighing 8 lb stretches a spring 1.5 in....Ch. 4.4 - If a series circuit has a capacitor of C=0.8...Ch. 4.4 - Assume that the system described by the equation...Ch. 4.4 - Assume that the system described by the equation...Ch. 4.4 - Logarithmic Decrement For the damped oscillation...Ch. 4.4 - Referring to Problem , find the logarithmic...Ch. 4.4 - For the system in Problem , suppose that and ....Ch. 4.4 - The position of a certain spring-mass system...Ch. 4.4 - Consider the initial value problem . We wish to...Ch. 4.4 - Consider the initial value problem...Ch. 4.4 - Use the differential equation derived in Problem...Ch. 4.4 - Draw the phase portrait for the dynamical system...Ch. 4.4 - The position of a certain undamped spring-mass...Ch. 4.4 - The position of a certain spring-mass system...Ch. 4.4 - In the absence of damping, the motion of a...Ch. 4.4 - If the restoring force of a nonlinear spring...Ch. 4.5 - In each of problems 1 through 16, find the general...Ch. 4.5 - In each of problems 1 through 16, find the general...Ch. 4.5 - In each of problems 1 through 16, find the general...Ch. 4.5 - In each of problems 1 through 16, find the general...Ch. 4.5 - In each of problems 1 through 16, find the general...Ch. 4.5 - In each of problems 1 through 16, find the general...Ch. 4.5 - In each of problems 1 through 16, find the general...Ch. 4.5 - In each of problems 1 through 16, find the general...Ch. 4.5 - In each of problems 1 through 16, find the general...Ch. 4.5 - In each of problems 1 through 16, find the general...Ch. 4.5 - In each of problems 1 through 16, find the general...Ch. 4.5 - In each of problems 1 through 16, find the general...Ch. 4.5 - In each of problems 1 through 16, find the general...Ch. 4.5 - In each of problems 1 through 16, find the general...Ch. 4.5 - In each of problems 1 through 16, find the general...Ch. 4.5 - In each of problems 1 through 16, find the general...Ch. 4.5 - In each of problems 17 through 22, find the...Ch. 4.5 - In each of problems 17 through 22, find the...Ch. 4.5 - In each of problems 17 through 22, find the...Ch. 4.5 - In each of problems 17 through 22, find the...Ch. 4.5 - In each of problems 17 through 22, find the...Ch. 4.5 - In each of problems 17 through 22, find the...Ch. 4.5 - In each of problems 23 through 30: Determine a...Ch. 4.5 - In each of problems 23 through 30:
Determine a...Ch. 4.5 - In each of problems 23 through 30:
Determine a...Ch. 4.5 - In each of problems 23 through 30: Determine a...Ch. 4.5 - In each of problems 23 through 30: Determine a...Ch. 4.5 - In each of problems 23 through 30:
Determine a...Ch. 4.5 - In each of problems 23 through 30: Determine a...Ch. 4.5 - In each of problems 23 through 30: Determine a...Ch. 4.5 - Consider the equation
(i)
From...Ch. 4.5 - Nonhomogeneous Cauchy-Euler Equations. In each of...Ch. 4.5 - Nonhomogeneous Cauchy-Euler Equations. In each of...Ch. 4.5 - Nonhomogeneous Cauchy-Euler Equations. In each of...Ch. 4.5 - Nonhomogeneous Cauchy-Euler Equations. In each of...Ch. 4.5 - Determine the general solution of
,
Where and ...Ch. 4.5 - In many physical problems, the nonhomogeneous term...Ch. 4.5 - Follow the instructions in Problem 37 to solve the...Ch. 4.6 - In each of Problems 1 through 4, write the given...Ch. 4.6 - In each of Problems 1 through 4, write the given...Ch. 4.6 - In each of Problems 1 through 4, write the given...Ch. 4.6 - In each of Problems 1 through 4, write the given...Ch. 4.6 - A mass weighing 4 pounds (lb) stretches a spring...Ch. 4.6 - A mass of 4 kg stretches a spring 8 cm. The mass...Ch. 4.6 - (a) Find the solution of Problem 5. (b) Plot the...Ch. 4.6 - 8.
Find the solution of the initial value problem...Ch. 4.6 - If an undamped spring-mass system with a mass that...Ch. 4.6 - A mass that weighs 8 lb stretches a spring 24 in....Ch. 4.6 - A spring is stretched 6 in. by a mass that weighs...Ch. 4.6 - A spring-mass system has a spring constant of 3...Ch. 4.6 - Furnish the details in determining when the gain...Ch. 4.6 - Find the solution of the initial value problem...Ch. 4.6 - A series circuit has a capacitor of 0.25...Ch. 4.6 - 16. Consider a vibrating system described by the...Ch. 4.6 - Consider the forced but undamped system described...Ch. 4.6 - Consider the vibrating system described by the...Ch. 4.6 - For the initial value problem in Problem 18, plot ...Ch. 4.6 - Problems 20 through 22 deal with the initial value...Ch. 4.6 - Problems 20 through 22 deal with the initial value...Ch. 4.6 - Problems 20 through 22 deal with the initial value...Ch. 4.6 - A spring-mass system with a hardening spring...Ch. 4.6 - Suppose that the system of Problem 23 is modified...Ch. 4.7 - (a) If
and ,
show that .
(b) Assuming that is...Ch. 4.7 - In each of Problems 2 through 5, use the method of...Ch. 4.7 - In each of Problems 2 through 5, use the method of...Ch. 4.7 - In each of Problems 2 through 5, use the method of...Ch. 4.7 - In each of Problems 2 through 5, use the method of...Ch. 4.7 - In each of Problems 6 through 9, find the solution...Ch. 4.7 - In each of Problems 6 through 9, find the solution...Ch. 4.7 - In each of Problems 6 through 9, find the solution...Ch. 4.7 - In each of Problems 6 through 9, find the solution...Ch. 4.7 - In each of Problems 10 through 13, use the method...Ch. 4.7 - In each of Problems 10 through 13, use the method...Ch. 4.7 - In each of Problems 10 through 13, use the method...Ch. 4.7 - In each of Problems 10 through 13, use the method...Ch. 4.7 - In each of Problems 14 through 21, find the...Ch. 4.7 - In each of Problems 14 through 21, find the...Ch. 4.7 - In each of Problems 14 through 21, find the...Ch. 4.7 - In each of Problems 14 through 21, find the...Ch. 4.7 - In each of Problems 14 through 21, find the...Ch. 4.7 - In each of Problems 14 through 21, find the...Ch. 4.7 - In each of Problems 14 through 21, find the...Ch. 4.7 - In each of Problems 14 through 21, find the...Ch. 4.7 - In each of Problems 22 through 27, verify that the...Ch. 4.7 - In each of Problems 22 through 27, verify that the...Ch. 4.7 - In each of Problems 22 through 27, verify that the...Ch. 4.7 - In each of Problems 22 through 27, verify that the...Ch. 4.7 - In each of Problems 22 through 27, verify that the...Ch. 4.7 - In each of Problems 22 through 27, verify that the...Ch. 4.7 - In each of Problems 28 through 31, find the...Ch. 4.7 - In each of Problems 28 through 31, find the...Ch. 4.7 - In each of Problems 28 through 31, find the...Ch. 4.7 - In each of Problems 28 through 31, find the...Ch. 4.7 - Show that the solution of the initial value...Ch. 4.7 - By choosing the lower limit of integration in Eq....Ch. 4.7 - (a) Use the result of Problem 33 to show that...Ch. 4.7 - Use the result of Problem 33 to find the solution...Ch. 4.7 - Use the result of Problem 33 to find the...Ch. 4.7 - Use the result of Problem 33 to find the solution...Ch. 4.7 - By combining the results of the problems 35...Ch. 4.7 - The method of reduction of order (see the...Ch. 4.7 - In each of problems 40 and 41, use the method...Ch. 4.7 - In each of problems and , use the method outlined...Ch. 4.P1 - Denote by the displacement of the platform from...Ch. 4.P1 - Denote by the frequency response of , that is,...Ch. 4.P1 - Plot the graphs of versus the dimensionless ratio...Ch. 4.P1 - The vibrations in the floor of an industrial plant...Ch. 4.P1 - Test the results of your design strategy for the...Ch. 4.P2 - Show that the differential equation describing the...Ch. 4.P2 - (a) Find the linearization of at .
(b) In the...Ch. 4.P2 - Subject to the initial conditions , draw the graph...Ch. 4.P3 - Assuming that both springs have spring constant ...Ch. 4.P3 - The Heaviside, or unit step function, is defined...Ch. 4.P3 - Is the differential equation derived in Problems ...Ch. 4.P3 - In the case that the damping constant 0, find the...Ch. 4.P3 - Consider the case of an undamped problem using...Ch. 4.P3 - Consider the damped problem using the parameter...Ch. 4.P3 - Describe some other physical problems that could...Ch. 4.P4 - Problems 1 through 3 are concerned with one...Ch. 4.P4 - Problems 1 through 3 are concerned with one...Ch. 4.P4 - Problems 1 through 3 are concerned with one...Ch. 4.P4 - Problems and are concerned with systems that...Ch. 4.P4 - Problems and are concerned with systems that...Ch. 4.P4 - Carry out the calculations that lead from Eq. to...
Additional Math Textbook Solutions
Find more solutions based on key concepts
Earnings A sociologist says, “Typically, men in the United States still earn more than women.” What does this s...
Introductory Statistics
The 16 sequences in the sample space S.
Probability And Statistical Inference (10th Edition)
Testing Hypotheses. In Exercises 13-24, assume that a simple random sample has been selected and test the given...
Elementary Statistics (13th Edition)
Fill in each blank so that the resulting statement is true. The quadratic function f(x)=a(xh)2+k,a0, is in ____...
Algebra and Trigonometry (6th Edition)
Explain the meaning of the term “statistically significant difference” in statistics terminology.
Intro Stats, Books a la Carte Edition (5th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- A helicopter flies over the arctic ice pack at a constant altitude, towing an airborne 147-kg laser sensor which measures the thickness of the ice (see the drawing). The helicopter and the sensor move only in the horizontal direction and have a horizontal acceleration of magnitude 2.54 m/s2. Ignoring air resistance, find the tension in the cable towing the sensor.arrow_forwardThe 0.50 lb ball is shot from the spring device shown. The spring has a stiffness k = 10 lb/in. and the four cords C and plate P keep the spring compressed 2 in. when no load is on the plate. The plate is pushed back 3 in. from its initial position. (Eigure 1) If it is then released from rest, determine the speed of the ball when it travels 23 in. up the smooth plane. Express your answer to three significant figure and include the appropriate units. HA Value ft/s v = 30arrow_forwardA firework of mass 0.4 kg is fired vertically upwards with initial speed 40 m/s. The firework itself provides a force of 2 N upwards. The firework explodes after 6s. Find the height at which it explodes.arrow_forward
- Use the concept of Particular Antiderivatives and Rectilinear Motion to answer the problem below: On the edge of an 8m building, Sam throws his toy vertically upwards at initial velocity = 28 m/s. If the only force that acts on the toy is accelerationdue to gravity (-32 ft/s), a. How many seconds will it take for the toy to reach its maximum height?b. What is the toy's speed when it hits the ground?arrow_forwardA trough whose cross-section is a trapezoid, measures 6 meters across the bottom and 8 meters across the top, and is 3 meters deep. If the trough is filled with a liquid of mass density p, what is the force due to hydrostatic pressure on one end of the trough? Write your answer in terms of p.arrow_forwardA hand truck is used to move two kegs, each of a mass 32 kg. Assume g=9.8 m.s²² and neglect the weight of the hand truck. a=35 deg. 80 mm 350 mm 500 mm •G2 B 300 mm A P Determine in N the vertical force P that should be applied to the handle to maintain equilibrium when a=35 deg.arrow_forward
- A cable exerts a constant upward tension of magnitude 2.14 ✕ 104 N on a 2.00 ✕ 103 kg elevator as it rises through a vertical distance of 3.90 m. HINT (a) Find the work done by the tension force on the elevator (in J). J (b) Find the work done by the force of gravity on the elevator (in J). Jarrow_forwardThe weight of an individual walking is 824N. The hill they are walking on has a slope of 10 degrees. Assuming they are in a static equilibrium what is their normal force?arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningElementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Elementary Geometry for College Students
Geometry
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Cengage Learning
Use of ALGEBRA in REAL LIFE; Author: Fast and Easy Maths !;https://www.youtube.com/watch?v=9_PbWFpvkDc;License: Standard YouTube License, CC-BY
Compound Interest Formula Explained, Investment, Monthly & Continuously, Word Problems, Algebra; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=P182Abv3fOk;License: Standard YouTube License, CC-BY
Applications of Algebra (Digit, Age, Work, Clock, Mixture and Rate Problems); Author: EngineerProf PH;https://www.youtube.com/watch?v=Y8aJ_wYCS2g;License: Standard YouTube License, CC-BY