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Brums [2.3K]
4 years ago
10

How many 3/8s are in 6

Mathematics
1 answer:
dlinn [17]4 years ago
5 0

Answer:

16

Step-by-step explanation:

6 divided by 3/8=6*8/3=48/3=16

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What will be the value of
madreJ [45]

The expression as given doesn't make much sense. I think you're trying to describe an infinitely nested radical. We can express this recursively by

\begin{cases}a_1=\sqrt{42}\\a_n=\sqrt{42+a_{n-1}}\end{cases}

Then you want to know the value of

\displaystyle\lim_{n\to\infty}a_n

if it exists.

To show the limit exists and that a_n converges to some limit, we can try showing that the sequence is bounded and monotonic.

Boundedness: It's true that a_1=\sqrt{42}\le\sqrt{49}=7. Suppose a_k\le 7. Then a_{k+1}=\sqrt{42+a_k}\le\sqrt{42+7}=7. So by induction, a_n is bounded above by 7 for all n.

Monontonicity: We have a_1=\sqrt{42} and a_2=\sqrt{42+\sqrt{42}}. It should be quite clear that a_2>a_1. Suppose a_k>a_{k-1}. Then a_{k+1}=\sqrt{42+a_k}>\sqrt{42+a_{k-1}}=a_k. So by induction, a_n is monotonically increasing.

Then because a_n is bounded above and strictly increasing, the limit exists. Call it L. Now,

\displaystyle\lim_{n\to\infty}a_n=\lim_{n\to\infty}a_{n-1}=L

\displaystyle\lim_{n\to\infty}a_n=\lim_{n\to\infty}\sqrt{42+a_{n-1}}=\sqrt{42+\lim_{n\to\infty}a_{n-1}}

\implies L=\sqrt{42+L}

Solve for L:

L^2=42+L\implies L^2-L-42=(L-7)(L+6)=0\implies L=7

We omit L=-6 because our analysis above showed that L must be positive.

So the value of the infinitely nested radical is 7.

4 0
3 years ago
A new car is purchased for $33,000 and over time its value depreciates by one half
densk [106]

Answer: 26 years

Step-by-step explanation:

3 0
3 years ago
HELLLPPP!!! how many gallons of oil were introduced into the gulf of ecosystem in 7 weeks?
Mashcka [7]
62,000x42= 2,604,000 gallons a day
Times that by 7 to get one week
Then by 7 again for 7weeks then 4 to get 28 weeks :)
7 weeks= 127,596,000
28 weeks= 510,384,000
7 0
3 years ago
Please help I will reward brainly! Need done ASAP
hoa [83]
Fort Sumter, Battle of Bull Run, <span>Battle of Shiloh, Battle of Vicksburg and Battle of </span>Gettysburg
6 0
4 years ago
PLEASE ANSWER QUICKLY!!!!! FIRST ANSWER WILL BE MARKED BRAINLIST!!!
Allushta [10]

Answer:

1. $6000

2. 40.9%

3. 51.6%

4. Misc

Explained :

1. 1800 + 150 + 2450 + 1300 + 300 = 6000

2. 2450/6000 = 0.409 = 40.9%

3. 1800 + 1300 = 3100 ; 3100/6000 = 0.516 = 51.6%

4. 300/6000 = 0.005 = 5%

8 0
3 years ago
Read 2 more answers
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