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3 years ago

Friends?.............................

Mathematics

1 answer:

Vlad [161]3 years ago

7 0

Ok sure—————-_______—-____

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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

Plz help me i need help

natali 33 [55]

Ok so you know the first garden needs 1 and 2/5 bags of soil. Now first we need to find one fifth of that. So let's make this mied number into an improper fraction:

1 2/5 = 7/5

Ok now let's divide 7/5 by 5:

7/5 divided by 5/1 = 7/25

So Jared will need 7/25 bags of soil for his second garden, but we're STILL not done. now we have to add for the TOTAL.

1 2/5 + 7/25 > 7/5 + 7/25 > 7 x 5 = 35 > 35/25 + 7/25 = 42/25
_________
5x 5 = 25

Now let's simplify it to 1 and 17/25

8 0

3 years ago

PLEASE HELP ME!!!<br> Which Choice is equivalent to the product below?

skad [1K]

It’s B

6x3=18
sqrt18 simplifies to sqrt9 x sqrt2
sqrt9 is 3 for 3sqrt2

8 0

3 years ago

Three friends earned more than $200 washing cars. They paid their parents $28 for supplies and divided the rest of the money equ

Ksenya-84 [330]

Answer: 3x + 28 > 200

Step-by-step explanation:

$$$Let $x$ be the amount each friend received. Since there are 3 friends, then $3 x$ is the amount of money they split evenly. The amount of money they split evenly was the amount left over after paying their parent's $\$ 28$. Therefore $3 x+28$ is the total amount they earned.$

7 0

2 years ago

Which equation is correct? Cos G= 8/15 ...

Troyanec [42]

Answer:

Step-by-step explanation:

For angle G, opp = 15, adj = 8, hyp = 17.

cos G = adj/hyp = 8/17

sin G = opp/hyp = 15/17

Answer: (d) sin G = 15/17

3 0

3 years ago