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3 years ago

How many bucketloads would it take to bucket out the world’s oceans? Write your answer in scientific notation.

Mathematics

1 answer:

kodGreya [7K]3 years ago

5 0

Answer: $7\times10^{19} buckets$

Step-by-step explanation:

Given: A cubic kilometer= $10^{15}$ cubic centimeters

The volume of world’s oceans= $1.4\times10^{9}$ cubic kilometers of water.

⇒ The volume of world’s oceans= $1.4\times10^{9}\times10^{15}$ cubic centimeters of water.

Volume of a bucket = 20,000 cubic centimeters of water.

The number of bucket-loads would it take to bucket out the world’s oceans

$n=\frac{\text{volume of ocean}}{\text{volume of bucket}}=\frac{1.4\times10^{9}\times10^{15}}{20000}$

$\Rightarrow\ n=\frac{1.4\times10^{9+15}}{0.2\times10^5}......[a^n\times a^m=a^{m+n}]\\\Rightarrow\ n=7\times10^{24-5}.....[\frac{a^m}{a^n}=a^{m-n}]\\\Rightyarrow\ n=7\times10^{19}$

hence, $7\times10^{19}$ bucketloads would it take to bucket out the world’s oceans.

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4. Name the first five terms of the arithmetic sequence. a1 = -35, d=4

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Answer:

Step-by-step explanation:

We first have to write the equation for the sequence, then finding the first five terms will be easy. Follow the formatting:

$a_n=a_1+d(n-1)$ and we are given enough info to fill in:

$a_n=-35+4(n-1)$ and

$a_n=-35+4n-4$ and

$a_n=-39+4n$ or in linear format:

$a_n=4n-39$ where n is the position of the number in the sequence. We already know the first term is -35.

The second term:

$a_2=4(2)-39$ so

$a_2=8-39$ and

$a_2=-31$

The third term:

$a_3=4(3)-39$ and

$a_3=12-39$ so

$a_3=-27$ and we could go on like this forever, but the nice thing about this is when we know the difference all we have to do is add it to each number to get to the next number.

That means that the fourth term will be -27 + 4 which is -23.

The fifth term then will be -23 + 4 which is -19. You can check yourself by filling in a 5 for n in the equation and solving:

$a_5=4(5)-39$ and

$a_5=20-39$ so

$a_5=-19$

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2 years ago

Find the slope. ( include whether positive or negative.)

dsp73

Answer:

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Step-by-step explanation:

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Eli lives 3 3/4 miles from the library. He decided to bike from his home to the library to return some books. Eli biked 1 1/10 m

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Answer:

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What is the partial product for 652 x 4= 2,608

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To find out the answer of the two multiplied products with the help of partial products we separate into unit based numbers so as to, for easier calculation and simplification with units of zeroes. So, in this case we are given the product of 4 times of 652.

Here we need to expand this product of higher number to zeroes and take aside the added numbers to come back to the original multiple of a product. That is:

$\huge{652}$

$\begin{bmatrix}652 \\ + \\ 0 \end{bmatrix}$

We just separated and expanded the product to be multiplied by removing other units following it. Same goes for other units at Hundredth, tenth and unitary position.

Therefore,

$\begin{bmatrix}600 \\ + \\ 52 \end{bmatrix}$

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$\begin{bmatrix}50 \\ + \\ 2 \end{bmatrix}$

The terms after splitting and expanding the product before multiplication is:

$\begin{bmatrix}600 \\ 50 \\ 2 \end{bmatrix}$

Multiply the product elements in individual manner and add the elements forged by individual multiplication to get the required solution.

$\therefore \quad \begin{bmatrix}600 \times 4 \\ 50 \times 4 \\ 2 \times 4 \end{bmatrix}$

$\begin{bmatrix}600 \times 4 \\ + \\ 200 \\ + \\ 2 \times 8 \end{bmatrix}$

$\begin{bmatrix}2400 \\ + \\ 200 \\ + \\ 2 \times 8 \end{bmatrix}$

$\begin{bmatrix}2600 \\ + \\ 8 \end{bmatrix}$

$\boxed{\mathbf{Final \: \: Answer \: = \: 2,608}}$

Hope it helps.

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