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statuscvo [17]
3 years ago
6

What is the equivalent recursive definition for an = 12+ (n - 1)3?

Mathematics
1 answer:
Verdich [7]3 years ago
6 0

Answer:

A_1 = 12

A_n = A_{n-1} + 3

Step-by-step explanation:

Given

A_n =12+(n-1)3

Required

Write as recursive

We have:

A_n =12+(n-1)3

Open bracket

A_n =12+3n-3

A_n =12-3+3n

A_n =9+3n

Calculate few terms

A_1 =9+3*1 = 9 + 3 = 12

A_2 =9+3*2 = 9 + 6 = 15

A_3 =9+3*3 = 9 + 9 = 18

The above shows that the rule is to add 3.

So, we have:

A_1 = 12

A_n = A_{n-1} + 3

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A boat on a river travels downstream between two points, 90 mi apart, in 1 h. The return trip against the current takes 2 1 2 h.
docker41 [41]

Answer:

A)63miles per hour.

B)27 miles per hour

Step-by-step explanation:

HERE IS THE COMPLETE QUESTION

boat on a river travels downstream between two points, 90 mi apart, in 1 h. The return trip against the current takes 2 1 2 h. What is the boat's speed (in still water)??b) How fast does the current in the river flow?

Let the speed of boat in still water = V(boat)

speed of current=V(current)

To calculate speed of boat downstream, we add speed of boat in still water and speed of current. This can be expressed as

[V(boat) +V(current)]

It was stated that it takes 1hour for the

boat to travels between two points of 90 mi apart downstream.

To calculate speed of boat against current, we will substact speed of current from speed of boat in still water. This can be expressed as

[V(boat) - V(current)]

and it was stated that it takes 2 1/2 for return trip against the Current

But we know but Speed= distance/time

Then if we input the stated values we have

V(boat) + V(current)]= 90/1 ---------eqn(1)

V(boat) - V(current) = 90/2.5----------eqn(2)

Adding the equations we have

V(boat) + V(current) + [V(boat) - V(current)]= 90/2.5 + 90/1

V(boat) + V(current) + V(boat) - V(current)]=90+36

2V(boat)= 126

V(boat)=63miles per hour.

Hence, Therefore, the speed of boat in still water is 63 miles per hour.

?b) How fast does the current in the river flow?

the speed of the current in the river, we can be calculated if we input V(boat)=63miles per hour. Into eqn(1)

V(boat) + V(current)]= 90/1

63+V(current)=90

V(current)= 27 miles per hour

Hence,Therefore, the speed of current is 27 miles per hour.

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3 years ago
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kakasveta [241]

Answer:

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Step-by-step explanation:

if they had letters it would be

A     B

C     D

options B and D are similar

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