Mathematics: How much apple juice does each person get if 6 people share 2 and 2/3 quarts equally

4.5.6.7.8. [ follow steps of no.6 ]factorization9.10.11, 12, and 13: follow expansion step in question 614:• rationalise the denominator:...

How much apple juice does each person get if 6

Ответ:

huddyxo

05.08.2020

Mathematics

${ \tt{ { \sin }^{4} \theta - { \cos }^{4} \theta = ( { \sin }^{2} \theta) {}^{2} - ( { \cos }^{2}\theta) {}^{2} }} \\ \\ = { \tt{( { \sin }^{2}\theta - { \cos }^{2} \theta)( { \sin }^{2} \theta + { \cos }^{2}\theta) }} \\ \\ = { \boxed{ \tt{ { \sin }^{2}\theta - { \cos }^{2} \theta}}}$

${ \tt{ { { \sin }^{4} A} + { \cos }^{4} A = { {( { \sin }^{2}A) }^{2} + ( { \cos }^{2} A)}^{2} }} \\ \\ = { \tt{( { \sin }^{2}A + { \cos}^{2}A) {}^{2} - 2( \sin A. \cos A) }} \\ \\ = { \tt{1 {}^{2} - 2( \sin A. \cos A)}} \\ \\ = { \boxed{ \tt{1 -2( \sin A. \cos A) }}}$

${ \tt{ {( \sin A - \cos A)}^{2} = ( \sin A - \cos A)(\sin A - \cos A)}} \\ \\ = { \tt{ { \sin }^{2} A - 2 \sin A \cos A + { \cos }^{2} A}} \\ \\ = { \tt{( { \sin }^{2} A + { \cos }^{2} A) -2 \sin A \cos A }} \\ \\ = { \boxed{ \tt{1 - 2 \sin A \cos A}}}$

${ \tt{ { \sin }^{4} \alpha + 2 { \sin }^{2} \alpha { \cos }^{2} \alpha + { \cos }^{4} \alpha }} \\ = { \tt{ {( { \sin }^{2} \alpha + { \cos }^{2} \alpha) }^{2} }} \\ \\ = { \tt{ {1}^{2} }} \\ \\ = { \boxed{ \tt{1}}}$

8. [ follow steps of no.6 ]

factorization

${ \tt{ \tan(x) + \cot(x) = \frac{ \sin(x) }{ \cos(x) } + \frac{ \cos(x) }{ \sin(x) } }} \\ \\ = { \tt{ \frac{ { \sin }^{2} x + { \cos }^{2}x }{ \cos(x) \sin(x) } }} \\ \\ ={ \tt{ \frac{1}{ \cos(x) \sin(x) } }} \\ \\ = { \tt{ \frac{1}{ \cos(x) }. \frac{1}{ \sin(x) } }} \\ \\ = { \boxed{ \tt{ \sec(x) . \csc(x) }}}$

10.

${ \tt{ \cos(x) + \sin(x). \tan(x) }} \\ = { \tt{ \cos(x) + \frac{ { \sin }^{2} x}{ \cos(x) } }} \\ \\ = { \tt{ \frac{ { \cos }^{2}x + { \sin }^{2}x }{ \cos(x) } }} \\ \\ = { \tt{ \frac{1}{ \cos(x) } }} \\ \\ { \boxed{ \tt{ = \sec(x) }}}$

11, 12, and 13: follow expansion step in question 6

14:

${ \tt{ \frac{1 - \tan( \theta) }{1 + \tan(\theta) } }} \\$

• rationalise the denominator:

${ \tt{ = \frac{ \{1 - \tan(\theta ) \}. \{1 - \tan(\theta ) \} }{ \{1 + \tan(\theta ) \}. \{1 - \tan(\theta ) \} } }} \\ \\ = \frac{ { \{1 - \tan(\theta ) \}}^{2} }{1 - { \tan}^{2} \theta} \\ \\ = { \tt{ \frac{(1 - 2 \tan(\theta ) + { \tan}^{2} \theta)}{1 - \tan {}^{2} \theta } }} \\ \\ { \tt{ = \frac{(1 - 2 \tan(\theta ) + { \tan }^{2} \theta)}{ { \sec}^{2} \theta } }} \\ \\ = { \tt{}}$

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How much apple juice does each person get if 6 people share 2 and 2/3 quarts equally

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