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3 years ago

2. Use the diagram below to answer the following questions,

Mathematics

1 answer:

astra-53 [7]3 years ago

4 0

Answer:

give me the answer step by step please

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Solve the following recurrence relation: <br> <img src="https://tex.z-dn.net/?f=A_%7Bn%7D%3Da_%7Bn-1%7D%2Bn%3B%20a_%7B1%7D%20%3D

-Dominant- [34]

By iteratively substituting, we have

$a_n = a_{n-1} + n$

$a_{n-1} = a_{n-2} + (n - 1) \implies a_n = a_{n-2} + n + (n - 1)$

$a_{n-2} = a_{n-3} + (n - 2) \implies a_n = a_{n-3} + n + (n - 1) + (n - 2)$

and the pattern continues down to the first term $a_1=0$ ,

$a_n = a_{n - (n - 1)} + n + (n - 1) + (n - 2) + \cdots + (n - (n - 2))$

$\implies a_n = a_1 + \displaystyle \sum_{k=0}^{n-2} (n - k)$

$\implies a_n = \displaystyle n \sum_{k=0}^{n-2} 1 - \sum_{k=0}^{n-2} k$

Recall the formulas

$\displaystyle \sum_{n=1}^N 1 = N$

$\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2$

It follows that

$a_n = n (n - 2) - \dfrac{(n-2)(n-1)}2$

$\implies a_n = \dfrac12 n^2 + \dfrac12 n - 1$

$\implies \boxed{a_n = \dfrac{(n+2)(n-1)}2}$

4 0

2 years ago

An exercise class had 20 people. If each person produced 2,200 BTUs of body heat during the class and the room is 30 ft × 40 ft

nika2105 [10]

We are given the average body heat equal to 2200 BTU. In this problem, we are asked to determine the total body heat in BTU per cubic foot given the dimensions of the room. The volume of the room is 18000 ft3. we multiply the average heat by 20 persons.hence the answer to this problem is 2.44 BTU/ft3.

8 0

3 years ago

2/13 divided by 1/6 need help

tia_tia [17]

Dividing by a fraction means the same as multiplying by its reciprocal.

In other words, change the division sign to multiplication

and flip or take the reciprocal of the second fraction.

So we can rewrite 2/13 ÷ 1/6 as 2/13 × 6/1.

Now multiply across the numerators and denominators to get 12/13.

8 0

2 years ago

Read 2 more answers

What’s the correct answer for this question?

vladimir2022 [97]

Answer:

Step-by-step explanation:

A cone with a radius of 1-unit will be obtained by rotating the 3-D figure.

8 0

3 years ago

Hey ya'll don't scroll please, just look at the attachment and answer every single question please- thank you very much.

Crazy boy [7]

Answer:

a. is B b. is D

Step-by-step explanation:

3 0

3 years ago