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goblinko [34]
3 years ago
6

Write the five term sequence that would represent each recursive rule f(x) = f(x-1) -7; f(2) = 12

Mathematics
1 answer:
barxatty [35]3 years ago
8 0

<u>Answer: </u>

Required five terms of sequence are 19 , 12 , 5 , -2 and -9 .

<u> Solution: </u>

Need to find the five terms of the sequence.

Given recursive rule is f(x) = f(x-1) -7

Substituting x = 2 , f(2) = f(2-1)-7

= f(2) = f(1) – 7    ------(1)

Also given that f(2) = 12.  

On substituting the given value of f(2) in eq (1) we get

12 = f(1) – 7

f(1) = 12 + 7 = 19

Using given recursive rule and given value of f(2) calculating f(3)

Substituting x = 3 ,  

f(3) = f(3-1) – 7  

= f(2) – 7  

= 12 – 7  

= 5

Using given recursive rule and calculated  value of f(3) calculating f(4)

Substituting x = 4,  

f(4) = f(4-1) – 7  

= f(3) – 7  

= 5– 7  

= -2

Using given recursive rule and calculated  value of f(4) calculating f(5)

Substituting x = 5,  

f(5) = f(5-1) – 7  

= f(4) – 7  

= -2– 7  

= -9

Hence required five terms of sequence are 19 , 12 , 5 , -2 and -9 .

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Bill wanted to try out different water craft he went 62 mikes downstream in a motor boat and 27 mikes down stream on a jest ski
valina [46]

Answer:

The speed on motorboat is 20 mph

Step-by-step explanation:

here, we want to find the speed on the motorboat

if he has a speed of x mph on the motor boat, his speed on the ski will be (x + 10) mph

The total hours is 4 hours

Mathematically; speed = distance/time

Time on ski is 27/x+ 10

Time on motor boat is 62/x

The addition of both is 4

Thus;

27/(x + 10) + 62/x = 4

27(x) + 62(x + 10) = 4(x)(x + 10)

27x + 62x + 620 = 4(x^2 + 10x)

89x + 620 = 4x^2 + 40x

4x^2 -49x-620 = 0

using the quadratic formula;

{-b ± √(b^2-4ac)}/2a

where a = 4, b = -49 and c = -620

= 49 ± √(-49)^2-4(4)(-620)/8

So we have

49+ 111/8 or 49-111/8

Speed cannot be negative

(49 + 111)/8

= 20 mph

3 0
2 years ago
Discrete MathA coin is flipped four times. For each of the events described below, express the event as a set in roster notation
Vladimir79 [104]

Answer:

a) 25%

b) 50%

c) 87.5%

Step-by-step explanation:

There are 2^4 = 16 number of outcome in total.

a)First and last flips come up heads. There are 4 outcomes here. Probability of the event is 4/16 = 1/4, or 25%.

- HHHH

- HHTH

- HTHH

- HTTH

b) at least 2 Consecutive flips that is heads. There are 8 outcomes. Probability of event is 8/16 = 1/2, or 50%

- HHHH

- HHHT

- HHTH

- HHTT

- THHH

- THHT

- HTHH

- TTHH

c) At least 2 consecutive flips that are the same. There are 14 outcomes. Probability of 14/16 = 7/8, or 87.5%

- HHHH

- HHHT

- HHTH

- HHTT

- THHH

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- HTHH

- TTHH

- TTTT

- TTTH

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6 0
2 years ago
3 9/12 + (4 7/12 + 5/12) = 3 9/12 + ____?
Maru [420]

Answer:

5

Step-by-step explanation:

4 7/12 + 5/12 = 4 12/12 which equals 5

8 0
3 years ago
Read 2 more answers
7. The height of each story of an apartment
ivanzaharov [21]
How many stories does it have?
3 0
3 years ago
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Solve 3x + 2 = 15 for x using the change of base formula log base b of y equals log y over log b. −1.594 0.465 2.406 4.465
disa [49]

<u>Answer:</u>

The value in 3x + 2 = 15 for x using the change of base formula is 0.465 approximately and second option is correct one.

<u>Solution:</u>

Given, expression is 3^{(x+2)}=15

We have to solve the above expression using change of base formula which is given as

\log _{b} a=\frac{\log a}{\log b}

Now, let us first apply logarithm for the given expression.

Then given expression turns into as, x+2=\log _{3} 15

By using change of base formula,

x+2=\frac{\log _{10} 15}{\log _{10} 3}

x + 2 = 2.4649

x = 2.4649 – 2  = 0.4649

Hence, the value of x is 0.465 approximately and second option is correct one.

3 0
3 years ago
Read 2 more answers
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