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3 years ago

Multiply. Enter the product in simplest form.

Mathematics

1 answer:

iVinArrow [24]3 years ago

4 0

Answer:

1. {1/20} 2. {7/36} 3. {1/2} 4. {8/21} 5. {4/15}

6.{1/6} 7.{ 20} 8. {15} 9. {1.2} 10. {1.25}

Step-by-step explanation:

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I’m stuck on this, can someone explain please? Thanks!

ololo11 [35]

first off, I'd like to point out that for the 5th test, he has 96, and that's +6 above 90, and therefore it should be 6.

if all the above/below numbers, summed up yield 0, that simply means the average is an even 90 on average for all 6 tests, if they yield above 0, is above on the average, and if it's below 0, a negative value, he needs to do more work.

-7+4-11+7+6-3 = -4.

you can think of it this way, if he had 90 on all 6 tests, the above/below row will show 0, 0, 0, 0, 0, 0. If any of the tests was above 90, that row will yield a sum more than 0, and if any of the tests were below, that sum will be a negative value.

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4 years ago

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.

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2 years ago

Sumo-Sumo Gas Company has a tanker-truck for hauling gasoline. The cylindrical tank has a

atroni [7]

422.72 is your answer vote me brainliest if you liked it

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3 years ago

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Liula [17]

Answer:

Yes

Step-by-step explanation:

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3 years ago

Rachel really wants to purchase a new skateboard and her mother has agreed to give her a weekly allowance that she can save unti

Slav-nsk [51]

Answer:

Step-by-step explanation:

10x+ 150=220 is the equation for the second plan you subtract 150 from 220 to get 70 and divide that by 10 and you get 7 which is the number of weeks it'll take

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I dont understand what the second one is asking so sorry dude but I think that's right

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3 years ago

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