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creativ13 [48]
3 years ago
9

What is the factorization of 729^15+1000​

Mathematics
1 answer:
Nesterboy [21]3 years ago
3 0

\bf \textit{difference and sum of cubes} \\\\ a^3+b^3 = (a+b)(a^2-ab+b^2) \\\\ a^3-b^3 = (a-b)(a^2+ab+b^2) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} 729=27^2\\ \qquad (3^3)^2\\ 1000=10^3 \end{cases}\implies 729^{15}+1000\implies ((3^3)^2)^{15}+10^3 \\\\\\ ((3^2)^{15})^3+10^3\implies (3^{30})^3+10^3\implies (3^{30}+10)~~[(3^{30})^2-(3^{30})(10)+10^2] \\\\\\ (3^{30})^3+10^3\implies (3^{30}+10)~~~~[(3^{60})-(3^{30})(10)+10^2]

now, we could expand them, but there's no need, since it's just factoring.

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Answer:

$960

Step-by-step explanation:

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Find the distance between the points given.
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Use the distance formula

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Input corresponding numbers

d = \sqrt {\left( {2- 6} \right)^2 + \left( {5-8} \right)^2

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Directions: for questions 1 through 4, find the diagonal length of each solid figure.
Alex787 [66]
\text{The length of the diagonal is }11.2\text{ mm}

Here, we want to find the diagonal of the given solid

To do this, we need the appropriate triangle

Firstly, we need the diagonal of the base

To get this, we use Pythagoras' theorem for the base

The other measures are 6 mm and 8 mm

According ro Pythagoras' ; the square of the hypotenuse equals the sum of the squares of the two other sides

Let us have the diagonal as l

Mathematically;

\begin{gathered} l^2=6^2+8^2 \\ l^2\text{ = 36 + 64} \\ l^2\text{ =100} \\ l\text{ = }\sqrt[]{100} \\ l\text{ = 10 mm} \end{gathered}

Now, to get the diagonal, we use the triangle with height 5 mm and the base being the hypotenuse we calculated above

Thus, we calculate this using the Pytthagoras' theorem as follows;

\begin{gathered} d^2=5^2+10^2 \\ d^2\text{ = 25 + 100} \\ d^2\text{ = 125} \\ d\text{ = }\sqrt[]{125} \\ d\text{ = }11.2\text{ mm} \end{gathered}

7 0
11 months ago
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