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andrew-mc [135]

3 years ago

13

Can someone please help me with the question?

1 answer:

lys-0071 [83]3 years ago

6 0

Answer:

y would be 90 degrees

Step-by-step explanation:

The triangle has a right angle which is where y is located. A right angle is usually 90 degrees.

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Find a formula for the sum of n terms. Use the formula to find the limit as n → [infinity]. lim n → [infinity] n 2 + i n 8 n i =

Masteriza [31]

Complete Question

Find a formula for the sum of n terms. $\sum\limits_{i=1}^n ( 8 + \frac{i}{n} )(\frac{2}{n} )$

Use the formula to find the limit as $n \to \infty$

Answer:

$K_n = \frac{n + 73 }{n}$

$\lim_{n \to \infty} K_n = 1$

Step-by-step explanation:

So let assume that

$K_n = \sum\limits_{i=1}^n ( 8 + \frac{i}{n} )(\frac{2}{n} )$

=> $K_n = \sum\limits_{i=1}^n ( \frac{16}{n} + \frac{2i}{n^2} )$

=> $K_n = \frac{2}{n} \sum\limits_{i=1}^n (8) + \frac{2}{n^2} \sum\limits_{i=1}^n(i)$

Generally

$\sum\limits_{i=1}^n (k) = \frac{1}{2} n (n + 1)$

So

$\sum\limits_{i=1}^n (8) = \frac{1}{2} * 8* (8 + 1)$

$\sum\limits_{i=1}^n (8) = 36$

$K_n = \frac{2}{n} \sum\limits_{i=1}^n (8) + \frac{2}{n^2} \sum\limits_{i=1}^n(i)$

and

$\sum\limits_{i=1}^n (i) = \frac{1}{2} n (n + 1)$

Therefore

$K_n = \frac{72}{n} + \frac{2}{n^2} * \frac{1}{2} n (n + 1 )$

$K_n = \frac{72}{n} + \frac{1}{n} (n + 1 )$

$K_n = \frac{72}{n} + 1 + \frac{1}{n}$

$K_n = \frac{72 + 1 + n }{n}$

$K_n = \frac{n + 73 }{n}$

Now $\lim_{n \to \infty} K_n = \lim_{n \to \infty} [\frac{n + 73 }{n} ]$

=> $\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [\frac{n}{n} + \frac{73 }{n} ]$

=> $\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [1 + \frac{73 }{n} ]$

=> $\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [1 ] + \lim_{n \to \infty} [\frac{73 }{n} ]$

=> $\lim_{n \to \infty} [\frac{n + 73 }{n} ] = 1 + 0$

Therefore

$\lim_{n \to \infty} K_n = 1$

5 0

3 years ago

What is the value of 25

Umnica [9.8K]

<h3> $\large\pink{\sf{25}}$ </h3><h3 /><h3>Scientific notation:</h3>

$\begin{gathered}\\ \sf\longmapsto 2.5×10\end{gathered}$

<h3>Round the number to nearest ten:</h3>

$\begin{gathered}\\ \sf\longmapsto 30\end{gathered}$

<h3>Write in expanded form using exponents:</h3>

$\begin{gathered}\\ \sf\longmapsto 2×10^{1}\end{gathered}$

<h3>Rewrite in exponential form:</h3>

$\begin{gathered}\\ \sf\longmapsto 5^{2}\end{gathered}$

8 0

3 years ago

Read 2 more answers

Point Q is located at (-4, 6). Point R is located at (8, 6).

Bess [88]

Step-by-step explanation:

Hi there!

Given;

Point Q is located at (-4, 6). Point R is located at (8, 6).

Note: Use distance formula.

Now;

$(d) = \sqrt{( {x2 - x1)}^{2} + ( {y2 - y1)}^{2} }$

Keep all values;

$(d) = \sqrt{ {(8 + 4)}^{2} + ( {6 - 6)}^{2} }$

Simplify;

$(d) = \sqrt{( {12)}^{2} }$

Therefore, the distance is 12 units.

<u>Hope</u><u> it</u><u> helps</u><u>!</u>

8 0

3 years ago

A car moved at a speed of 90km/hr for 3 minutes.What distance did it cover?

aniked [119]

Answer:

270kilometers

Step-by-step explanation:

To find the distance, all you have to do is the speed · time

In these types of distance time and word problems, you multiply the other factors, 90 and 3, The time(T) · The speed(S)

So. 90(S) · 3(T) = 270(D)

5 0

3 years ago

What is the meaning of proportional and non-proportional?

frutty [35]

Answer:

Proportional: Non-Proportional: How to tell the difference: A proportional graph is a straight line that always goes through the origin. A non-proportional graph is a straight line that does not go through the origin.

Step-by-step explanation:

<h3>hope it helps</h3>

4 0

2 years ago