Year 12 Maths revision unit 3 and 4

A Newly manufactured car is priced at $24000. each year, the car depreciates by 25%. write a recurrence relation to model this scenario?

Step 1: Which formula are we using

• An+1 = r x An - R

• An+1= r x An

A Newly manufactured car is priced at $24000. each year, the car depreciates by 25%. write a recurrence relation to model this scenario?

Step 2: If the value of the car decreases by 25% what is the remaining percentage in a decimal

• 0.025

• 0.25

• 0.075

• 0.75

A Newly manufactured car is priced at $24000. each year, the car depreciates by 25%. write a recurrence relation to model this scenario?

Step 3: What is the final equation

• Ao = 18000,

  An+1 = 0.25 x An

• Ao = 18000,

  An+1 = 0.75 x An

• Ao = 24000,

  An+1 = 0.25 x An

• Ao = 24000,

  An+1 = 0.75 x An

A company invests 130'000 into a perpetuity at an interest rate of 3.91% p.a. compounding semiannually to create a steady stream of income for a retiree

Calculate the amount of payment that is received every 6 months?

Step 1: choose formula

A company invests 130'000 into a perpetuity at an interest rate of 3.91% p.a. compounding semiannually to create a steady stream of income for a retiree

Calculate the amount of payment that is received every 6 months?

Step 2: what is the A and i value

• A = 130 000

  i = 0.01955

• A = 130 000

  i = 0.1955

• A = 130 000

  i = 0.0391

• A = 130 000

  i = 0.03258

A company invests 130'000 into a perpetuity at an interest rate of 3.91% p.a. compounding semiannually to create a steady stream of income for a retiree

Calculate the amount of payment that is received every 6 months?

Step 3: substitute in and calculate answer

• 423.58

• 1270.75

• 2541.50

• 6'649'616.37

• 111.2 x angular distance

 

Calculate the shortest distance between Sakhalin, Russia (50°05′ N, 142°25′ E)  and Calgary, Canada (50°05′ N, 113°56′ W)  

Step 2: find angular distance

• 142°25′ + 113°56' = 256°21'

• 142°25′ - 113°56 = 28°29'

 

Calculate the shortest distance between Sakhalin, Russia (50°05′ N, 142°25′ E)  and Calgary, Canada (50°05′ N, 113°56′ W)  

Step 2: find the shortest angular distance

•  256°21′ - 360° = -103°29'

•  360° - 256°21′ = 103°29′

Calculate the shortest distance between Sakhalin, Russia (50°05′ N, 142°25′ E)  and Calgary, Canada (50°05′ N, 113°56′ W)  

Step 4: which was the shortest distance

• 103°29′ 

• 256°21′