Chapter 7.4, Problem 8E

Solve 6 Only Solve each equation by the method of inspection or any other method.

y? (x² + 1) x(y² + 1) 4. Solve the IVP y = y(-1) = 3. You may leave your answer in implicit form.

شكشكيمنسص

11 A ball is thrown vertically upwards from a ledge 1.45 m above the ground. The height, h metres, of the ball above the ground at / seconds can be modelled by the equation h = at² + bt+c. a State the value of c. The ball reaches its highest point above the ground when f = 1.4 seconds and hits the ground after a further 1.5 seconds. bi Write down two equations in a and b. ii Hence find the values of a and b. c Find the times when the ball is 5 m above the ground. TL

Can you double check my answers

The following difference equation describes a simple model of a certain economy, where Yk is the total income during year k, a is a constant less than 1, called the marginal propensity to consume, and b is a positive constant of adjustment that describes how changes in consumer spending affect the annual rate of private investment. YK+2- a(1+ b)YK+1 +abYk = 1 Find the general solution when a = 0.99 and b= 0.25. Find the general solution of the difference equation, rounding to two decimal places as needed. Choose the correct answer below. O A. YK = 100(0.99)k + 100(0.25)k O B. Yk =c1 (0.99)* .c2(0.25)* - 100 %3D Oc. Yk = C1 (0.99k) + c2(0.25k) + 100 O D. Yk =c1(1.24)*.cz(0.25)* O E. YK = (0.99)* + (0.25)* + 0.01 O F. YK =c4 (1.24)* +c2(0.25)* + 1 O G. Yk = C1 (1.24k) + c2(0.25k) + 1 O H. YK = c4 (0.99)* +c2 (0.25)* + 100

4.2

2 A stone is released from a catapult towards a castle. The castle is 120 m away, and is 10 m high. The stone moves with horizontal component - 30t metres and vertical component y = -4.9 + 201 +5 metres, where t is the time in seconds, t>0. a Find the position of the stone after 1 second. b Find the maximum height reached by the 4 height 10m -120m- distance stone. e Will the stone fly over the castle, hit the castle, or land in front of the castle? Explain your answer.

The following difference equation describes a simple model of a certain economy, where Yg is the total income during year k, a is a constant less than 1, called the marginal propensity to consume, and b is a positive constant of adjustment that describes how changes in consumer spending affect the annual rate of private investment. YK+2- a(1 + b)Yk+1 + abYk = 1 Find the general solution when a = 0.75 and b= 0.09. Find the general solution of the difference equation, rounding to two decimal places as needed. Choose the correct answer below. O A. Y = 4(0.72)k + 4(0.09)k O B. Y =c, (0.82)* .c2(0.07)* Oc. Yk =C1 (0.72k) + c2(0.09k) + 4 O D. Y =c, (0.82)* + c, (0.07)* + 1 O E. Y =c, (0.72)* .c2(0.09)* OF. Y =c, (0.72)* + c, (0.09)* + 4 •4 O G. Yk = C1 (0.82k) + c2(0.07k) + 1 O H. Y = (0.72)* + (0.09)* + 0.25