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3 years ago

A vial contains 20mL of medicine.If each dose is 1/3 of the vial,how many mL is each dose.Express your answer as a decimal

Mathematics

1 answer:

Genrish500 [490]3 years ago

4 0

Answer:

each dose = 6.7 mL ( to 1 decimal place)

Step-by-step explanation:

Total volume of vial = 20mL

each dose of vial = 1/3 of the total volume

let us express this fraction as a real number:

1/3 of 20 = 1/3 × 20

Since we are to express the answer as a decimal, let us convert the fraction to decimal:

1/3 = 0.3333

∴ 1/3 × 20 = 0.3333 × 20 = 6.667 mL

since we are dealing with drugs, it'll be appropraite to express the answer to 1 d.p

∴ each dose = 6.7 mL

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$\rm\displaystyle 0,\pm\pi$

Step-by-step explanation:

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===========================

we want to find all possible values of α+β+γ when tanα+tanβ+tanγ = tanαtanβtanγ to do so we can use algebra and trigonometric skills first

cancel tanγ from both sides which yields:

$\rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \alpha ) \tan( \beta ) \tan( \gamma ) - \tan( \gamma )$

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$\rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \gamma ) (\tan( \alpha ) \tan( \beta ) - 1)$

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multiply both numerator and denominator by-1 which yields:

$\rm\displaystyle \tan( \gamma ) = - \bigg(\frac{ \tan( \alpha ) + \tan( \beta ) }{ 1 - \tan( \alpha ) \tan( \beta ) } \bigg)$

recall angle sum indentity of tan:

$\rm\displaystyle \tan( \gamma ) = - \tan( \alpha + \beta )$

let α+β be t and transform:

$\rm\displaystyle \tan( \gamma ) = - \tan( t)$

remember that tan(t)=tan(t±kπ) so

$\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm k\pi )$

therefore when k is 1 we obtain:

$\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm \pi )$

remember Opposite Angle identity of tan function i.e -tan(x)=tan(-x) thus

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recall that if we have common trigonometric function in both sides then the angle must equal which yields:

$\rm\displaystyle \gamma = - \alpha - \beta \pm \pi$

isolate -α-β to left hand side and change its sign:

$\rm\displaystyle \alpha + \beta + \gamma = \boxed{ \pm \pi }$

when is 0:

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isolate -α-β to left hand side and change its sign:

$\rm\displaystyle \alpha + \beta + \gamma = \boxed{ 0 }$

and we're done!

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3 years ago

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