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3 years ago

Convert 12 pints to gallons

Mathematics

2 answers:

EleoNora [17]3 years ago

6 0

12 pints=
1.5 gallons

mel-nik [20]3 years ago

4 0

1 pint = 0.125 gallons

12 * 0.125 =

1.5 gallons

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Show Work Please Thank You

Misha Larkins [42]

Answer:

$\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}$

Step-by-step explanation:

We are given the trigonometric equation of:

$\displaystyle{\sin 4x = \dfrac{\sqrt{3}}{2}}$

Let u = 4x then:

$\displaystyle{\sin u = \dfrac{\sqrt{3}}{2}}\\\\\displaystyle{\arcsin (\sin u) = \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}\\\\\displaystyle{u= \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}$

Find a measurement that makes sin(u) = √3/2 true within [0, π) which are u = 60° (π/3) and u = 120° (2π/3).

$\displaystyle{u = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}$

Convert u-term back to 4x:

$\displaystyle{4x = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}$

Divide both sides by 4:

$\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}$

The interval is given to be 0 ≤ 4x < π therefore the new interval is 0 ≤ x < π/4 and these solutions are valid since they are still in the interval.

Therefore:

$\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}$

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