All categories

3 years ago

-8n+4(1+5n)=-6n-14 show your work

Mathematics

1 answer:

dmitriy555 [2]3 years ago

6 0

Answer:

n = -1

Step-by-step explanation:

-8n + 4 (1 + 5n) = -6n - 14

-8n + 4 + 20n = -6n - 14 Distribute

12n + 4 = -6n - 14 Combine Like Terms

18n + 4 = -14 Add 6 on Both Sides

18n = -18 Subtract 4 on Both Sides

n = -1 Divide Both Sides by 18

You might be interested in

I need help with this problem from the calculus portion on my ACT prep guide

LenaWriter [7]

Given a series, the ratio test implies finding the following limit:

$\lim _{n\to\infty}\lvert\frac{a_{n+1}}{a_n}\rvert=r$

If r<1 then the series converges, if r>1 the series diverges and if r=1 the test is inconclusive and we can't assure if the series converges or diverges. So let's see the terms in this limit:

$\begin{gathered} a_n=\frac{2^n}{n5^{n+1}} \\ a_{n+1}=\frac{2^{n+1}}{(n+1)5^{n+2}} \end{gathered}$

Then the limit is:

$\lim _{n\to\infty}\lvert\frac{a_{n+1}}{a_n}\rvert=\lim _{n\to\infty}\lvert\frac{n5^{n+1}}{2^n}\cdot\frac{2^{n+1}}{\mleft(n+1\mright)5^{n+2}}\rvert=\lim _{n\to\infty}\lvert\frac{2^{n+1}}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^{n+1}}{5^{n+2}}\rvert$

We can simplify the expressions inside the absolute value:

$\begin{gathered} \lim _{n\to\infty}\lvert\frac{2^{n+1}}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^{n+1}}{5^{n+2}}\rvert=\lim _{n\to\infty}\lvert\frac{2^n\cdot2}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^n\cdot5}{5^n\cdot5\cdot5}\rvert \\ \lim _{n\to\infty}\lvert\frac{2^n\cdot2}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^n\cdot5}{5^n\cdot5\cdot5}\rvert=\lim _{n\to\infty}\lvert2\cdot\frac{n}{n+1}\cdot\frac{1}{5}\rvert \\ \lim _{n\to\infty}\lvert2\cdot\frac{n}{n+1}\cdot\frac{1}{5}\rvert=\lim _{n\to\infty}\lvert\frac{2}{5}\cdot\frac{n}{n+1}\rvert \end{gathered}$

Since none of the terms inside the absolute value can be negative we can write this with out it:

$\lim _{n\to\infty}\lvert\frac{2}{5}\cdot\frac{n}{n+1}\rvert=\lim _{n\to\infty}\frac{2}{5}\cdot\frac{n}{n+1}$

Now let's re-writte n/(n+1):

$\frac{n}{n+1}=\frac{n}{n\cdot(1+\frac{1}{n})}=\frac{1}{1+\frac{1}{n}}$

Then the limit we have to find is:

$\lim _{n\to\infty}\frac{2}{5}\cdot\frac{n}{n+1}=\lim _{n\to\infty}\frac{2}{5}\cdot\frac{1}{1+\frac{1}{n}}$

Note that the limit of 1/n when n tends to infinite is 0 so we get:

$\lim _{n\to\infty}\frac{2}{5}\cdot\frac{1}{1+\frac{1}{n}}=\frac{2}{5}\cdot\frac{1}{1+0}=\frac{2}{5}=0.4$

So from the test ratio r=0.4 and the series converges. Then the answer is the second option.

8 0

1 year ago

The value of x can be 3 or 7.<br>The value of y can be 4 or 9.<br>a. List the possible values of xy

aleksklad [387]

Answer:

7, 27, 28, 63

Step-by-step explanation:

The possible values of xy are

3 × 4 = 12

3 × 9 = 27

7 × 4 = 28

7 × 9 = 63

4 0

3 years ago

I NEED HELP!!<br><br> How can you rewrite the number 1 as 2 to a power?

hoa [83]

Take any number but 0 and raise it to the 0th power, and you'll get 1.

So in terms of an equation, I mean x^0 = 1 is true for any x value as long as x is nonzero.

So this means 2^0 = 1 if we replace x with 2.

7 0

3 years ago

What does inversely proportional mean? bro why my stuff keep getting deleted instantly lol

IrinaK [193]

Answer:

corresponding in size or amount to something else.

Step-by-step explanation:

3 0

2 years ago

If a coin is flipped five times, the probability of getting heads all five times is ___________.

sergejj [24]

5 coin tosses. This means,

Total observations =25=25

Required outcome → 5 Heads {H,H,H,H,H}

This can occur only ONCE!

Thus, required outcome =1=1

Probability (5 Heads) =125=132

7 0

3 years ago