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Vaselesa [24]
3 years ago
11

Set up the characteristic equation, which is given by r2 − 5r − 6 = 0. The roots of this equation are given by r1 = 6 and r2 = −

1. Thus a general solution for the recurrence is given by an = a6 n + b(−1)n . To find a and b, we use the initial conditions. a0 = 1 implies a + b = 1, while a1 = 3 implies 6a − b = 3.
Mathematics
1 answer:
s344n2d4d5 [400]3 years ago
4 0

Answer:

Step-by-step explanation:

From your characteristic equation, your recursive equation is

f(n+2) = 5 f(n=1) +6f(n)

the general solution:

f(n) = A6^n + B(-1)^n

The initial conditions are

f(0) =1 ~~~and~~~ f(1) = 3

For f(0) = 1, that is

f(0) = A6^0 + B(-1)^0 = A+ B=1 (*)

For f(1) = 3, that is

f(1) = A6^1 + B(-1)^1 = 3

6A- B = 3 (**)

From (*) and (**) you solve for A and B

you have A = 4/7 and B= 3/7

Replace A, B into the general one, you have the particular solution for the given condition

f(n) = 4/7 *6^n +3/7*(-1)^n

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Dale drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took hours. When Dale drove hom
IrinaK [193]

Dale drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took 7 hours. when dale drove home, there was no traffic and the trip only took 5 hours. if his average rate was 18 miles per hour faster on the trip home, how far away does dale live from the mountains? do not do any rounding.

Answer:

Dale live 315 miles from the mountains

Step-by-step explanation:

Let y be the speed  of Dale to the mountains

Time taken by Dale to the mountains=7 hrs

Therefore distance covered by dale to the mountain = speed × time = 7y ......eqn 1

Time taken by Dale back home = 5hours

Since it speed increased by 18 miles per hour back home it speed = y+18

So distance traveled home =speed × time = (y+18)5 ...... eqn 2

Since distance cover is same in both the eqn 1 and eqn 2.

Eqn 1 = eqn 2

7y = (y+18)5

7y = 5y + 90

7y - 5y = 90 (collection like terms)

2y = 90

Y = 45

Substitute for y in eqn 1 to get distance away from mountain

= 7y eqn 1

= 7×45

= 315 miles.

∴ Dale leave 315 miles from the mountains

4 0
3 years ago
In the diagram, AB=18. find AC and BC
LuckyWell [14K]

Answer:

b

Step-by-step explanation:

In a 30-60-90 right triangle, the hypotenuse is twice the length of the short leg.

The hypotenuse is AB and is 18.

The short leg is BC and is 9.

The only choice with BC = 9 is b.

Answer: b

3 0
2 years ago
Plz help worth 40 points
denis23 [38]

Answer:    

Answer is B

6 0
3 years ago
Read 2 more answers
Independent Practice
motikmotik
The answer you’re looking for is a yes the domain value five corresponds to two range values -8 and five
5 0
2 years ago
10=Z+6 can u please solve it in evaluate the expression
Eva8 [605]

Answer: z=4

Step-by-step explanation:

Subtract 6 on both sides and 10-6=4 and then plug 4 into z and the equation is true

8 0
3 years ago
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