Solve the exponential equation: 4x – 2 = 2x

Mathematics

1 answer:

Tems11 [23]3 years ago

6 0

Answer:

x=1

Step-by-step explanation:

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Cos ( α ) = √ 6/ 6 and sin ( β ) = √ 2/4 . Find tan ( α − β )

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Answer:

$\purple{ \bold{ \tan( \alpha - \beta ) = 1.00701798}}$

Step-by-step explanation:

$\cos( \alpha ) = \frac{ \sqrt{6} }{6} = \frac{1}{ \sqrt{6} } \\ \\ \therefore \: \sin( \alpha ) = \sqrt{1 - { \cos}^{2} ( \alpha ) } \\ \\ = \sqrt{1 - \bigg( {\frac{1}{ \sqrt{6} } \bigg )}^{2} } \\ \\ = \sqrt{1 - {\frac{1}{ {6} }}} \\ \\ = \sqrt{ {\frac{6 - 1}{ {6} }}} \\ \\ \red{\sin( \alpha ) = \sqrt{ { \frac{5}{ {6} }}} } \\ \\ \tan( \alpha ) = \frac{\sin( \alpha ) }{\cos( \alpha ) } = \sqrt{5} \\ \\ \sin( \beta ) = \frac{ \sqrt{2} }{4} \\ \\ \implies \: \cos( \beta ) = \sqrt{ \frac{7}{8} } \\ \\ \tan( \beta ) = \frac{\sin( \beta ) }{\cos( \beta ) } = \frac{1}{ \sqrt{7} } \\ \\ \tan( \alpha - \beta ) = \frac{ \tan \alpha - \tan \beta }{1 + \tan \alpha . \tan \beta} \\ \\ = \frac{ \sqrt{5} - \frac{1}{ \sqrt{7} } }{1 + \sqrt{5} . \frac{1}{ \sqrt{7} } } \\ \\ = \frac{ \sqrt{35} - 1 }{ \sqrt{7} + \sqrt{5} } \\ \\ \purple{ \bold{ \tan( \alpha - \beta ) = 1.00701798}}$

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kelly is using a bucket to fill up a barrel with water from a well. The barrel holds 25.5 liters.the bucket holds 800 millileter

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To determine how much of the barrel is left to fill, you must subtract the amount of water already in it from the total mass of the bucket.

25.5 - 5.2 = 20.3 Litres

In order to the fill the entire barrel, Kelly must collect 20.3 Litres of water. You must then covert the measurement from litres to millilitres so that the bucket and barrel are measured in the same units.

20.3L = 20300mL

You must then divide the amount of space left by the mass of the bucket. This will determine the least number of buckets needed to fill the barrel.

20300 <span>÷ 800 = 25.375

That means the you would have to do a minimum on 25.375 buckets to fill the barrel, or 26.

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