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4 years ago

Express this in scientific notation 13,040,000

1 answer:

3 0

First, to rewrite something in scientific notation, we want to move the decimal point a number of times to the right or left to end with a number between 0 and 10. In this case, we want to move the decimal point 7 times to the left to get the number 1.304. In scientific notation, this would be the same as 1.304*10^7.

I hope this helps!

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Find tan2θ if θ terminates in Quadrant IV and cosθ = 3/5.

natali 33 [55]

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$\cos( \alpha ) = \frac{3}{5} \\$

${sin}^{2}( \alpha ) = 1 - {cos}^{2} ( \alpha )$

${sin}^{2}( \alpha ) = 1 - ({ \frac{3}{5} })^{2} \\$

${sin}^{2}( \alpha ) = 1 - \frac{9}{25} \\$

${sin}^{2}( \alpha ) = \frac{25}{25} - \frac{9}{25} \\$

${sin}^{2}( \alpha ) = \frac{16}{25} \\$

$sin( \alpha )= ± \sqrt{ \frac{16}{25} } \\$

In Quadrant IV , sin is negative .

Thus ;

$sin( \alpha ) = - \sqrt{ \frac{16}{25} } \\$

$\sin( \alpha ) = - \frac{4}{5} \\$

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$\tan(2 \alpha ) = \frac{ \sin(2 \alpha ) }{ \cos(2 \alpha ) } \\$

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$\sin(2 \alpha ) = 2. \sin( \alpha ). \cos( \alpha )$

$\sin(2 \alpha ) = 2 \times ( - \frac{4}{5} ) \times ( \frac{3}{5} ) \\$

$\sin(2 \alpha ) = - \frac{24}{25} \\$

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$\cos(2 \alpha ) = {cos}^{2}( \alpha ) - {sin}^{2}( \alpha )$

$\cos(2 \alpha ) = ({ \frac{3}{5} })^{2} - ({ - \frac{4}{5} })^{2} \\$

$\cos(2 \alpha ) = \frac{9}{25} - \frac{16}{25} \\$

$\cos(2 \alpha ) = - \frac{7}{25} \\$

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$\tan(2 \alpha ) = \frac{ \sin(2 \alpha ) }{ \cos(2 \alpha ) } \\$

$\tan(2 \alpha ) = \frac{ - \frac{24}{25} }{ - \frac{7}{25} } \\$

$\tan(2 \alpha ) = - \frac{24}{25} \div - \frac{7}{25} \\$

$\tan(2 \alpha ) = - \frac{24}{25} \times - \frac{25}{7} \\$

$\tan(2 \alpha ) = \frac{24}{7} \\$

Thus the correct answer is (( C )) .

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4 0

3 years ago

Read 2 more answers

andy picked 5 tulips.brianna picked 3 more tulips than andy , carley picked 16 tulips. how many times as many tulips did carley

tatyana61 [14]

Andy picked 5
brianna picked 3 more then andy...she picked 8
carley picked 16

carley picked 2 times as many tulips as brianne....because carley picked 16 and brianna picked 8

8 0

4 years ago

Read 2 more answers

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goldfiish [28.3K]

When a shape is rotated, it must be rotated around a point.

To determine the location of the new triangle, Sonja must subtract (5,-1) from the coordinates of the original triangle, before rotating by $90^o$ .