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matrenka [14]
3 years ago
11

The combined volume of all the tanks at an aquarium is 1.25 X 106 gallons. The aquarium plans to install a new dolphin tank with

a volume of 250,000 gallons. What will be the total volume of all of the tanks at the aquarium after the new dolphin tank is installed?
Mathematics
1 answer:
DaniilM [7]3 years ago
3 0

1. The combined volume of all the tanks at the aquarium is written in Scientific notation. Keeping this on mind, you can write it as following:

(1.25)(10^{6})=1,250,000gallons

2. Now, you must sum the combined volume of all the tanks and the volume of  the new tank to calculate the total volume of all of them:Vt=1,250,000gallons+250,000gallons\\Vt= 1,500,000gallons

3. Now, you can write the result in Scientific notation, as following:

Vt=(1.5)(10^{6}) gallons

The answer is: (1.5)(10^{6}) gallons

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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.

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kumpel [21]

Answer:

Step-by-step explanation:

1. y = 2x

       y = 2*4 = 8  Checks, therefore

y = 20  for x = 10

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y =  3*(1.5) = 4.5  

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3. y = 5/x

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x = 5/3

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5 m = Kn/p  [Add the K as a constant that will make m = Knp true at some value of K]

9 = K*2/(1/3)

27 = (K*2)

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K = (3/2)

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        m = 1

   

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