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Marianna [84]
3 years ago
14

Find r(x + 1) if r(x) = x3 + x + 1

Mathematics
2 answers:
suter [353]3 years ago
7 0

Substitute x + 1 as x in the equation of the function:

r(x)=x^3+x+1\\\\r(x+1)=(x+1)^3+(x+1)+1=x^3+3(x^2)(1)+3(x)(1^2)+1^3+x+1+1\\\\=x^3+3x^2+3x+x+2=x^3+3x^2+4x+2

Used

(a+b)^3=a^3+3a^3b+3ab^3+b^3

Ad libitum [116K]3 years ago
4 0

Answer:

<em>r(x + 1) = x^3 + 3x^2 + 4x + 3</em>

Step-by-step explanation:

r(x) = x3 + x + 1

Replace x with x + 1 is r(x) and simplify.

r(x + 1) = (x + 1)^3 + x + 1 + 1

= (x^2 + 2x + 1)(x + 1) + x + 2

= x^3 + x^2 + 2x^2 + 2x + x + 1 + x + 2

r(x + 1) = x^3 + 3x^2 + 4x + 3

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5 0
3 years ago
Determine whether the series is convergent or divergent. if it is convergent, find its sum. (if the quantity diverges, enter div
Lemur [1.5K]

The geometric series is convergent and the value is 16.

<h3>How to illustrate the information?</h3>

Recall that the sum of an infinite geometric series, S, given first term, t_1, and common ratio, r, is given by:

S = t_1/(1 - r)

Note that:

3 = (4)(3/4)

9/4 = (3)(3/4)

27/16 = (9/4)(3/4)

So this a geometric series with t_1 = 4 and r = 3/4. Therefore:

4 + 3 + 9/4 + 27/16 + ... = 4/(1 - 3/4) = 4/(1/4) = 16

The correct option is 16.

Learn more about geometric series on:

brainly.com/question/24643676

#SPJ4

Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum

4+3+ 9/4 +27/16 +???

choices are

1. 3/4

2. 12

3. 4

4. divergent

5. 16

7 0
1 year ago
Simplify the expression below: 4+2×[(3+1)×5] (show work please need it for review)
____ [38]

Answer:

44

Step-by-step explanation:

Parenthesis

Exponents

Multiply

Divide

Add

Subtract

First we need to do the work inside the parenthesis that are in the boxed parenthesis

3 + 1 = 4

4 * 5 = 20

Now we multiply

20 * 2 = 40

Now we add

40 + 4 = 44

Best Of Luck,

- I.A. -

5 0
3 years ago
1. Mr. Jones is correcting math test. Here are the scores for the
iogann1982 [59]

Answer:

12

Step-by-step explanation:

12 doesn't fit the data because it is so much farther from the general average of the others.

12 affects the median because with it, the median is 74. but without 12, the median is 76.

12 affects the mean because with it, the mean is 68.36. but without 12, the mean is 72.69.

8 0
2 years ago
Carey, the music reporter for her high school newspaper, is writing an article about this year's school musical. Carey wants to
andreyandreev [35.5K]

Answer:

24 sets

Step-by-step explanation:

Carey, the music reporter for her high school newspaper, is writing an article about this year's school musical. Carey wants to interview one male and one female cast member, and there are 4 boys and 3 girls in the musical this year. Carey also wants to interview one of the 2 students working backstage on the tech crew. Therefore, there can be 24 different sets of people that Carey can interview.

4 boys x 3 girls = 12 people

12 people  x 2 students working = 24

7 0
3 years ago
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