Volume and surface area question. show work pleaseee

Mathematics

1 answer:

Sever21 [200]2 years ago

4 0

Answer:

180 $cm^3$ can fit in the container will be your answer.

Step-by-step explanation:

Ok so... the equation is: 6 x 5 x 12 ÷ 2

Which will be 180.

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Find Sin (BAC+30) 80POINTS

Ann [662]

Answer:

$\dfrac{2}{5}\sqrt{3}+\dfrac{3}{10}$

Step-by-step explanation:

<u>Trigonometric Identities</u>

$\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B$

<u>Trigonometric ratios</u>

$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$

where:

$\theta$ is the angle
O is the side opposite the angle
A is the side adjacent the angle
H is the hypotenuse (the side opposite the right angle)

Using the trig ratio formulas for cosine and sine:

$\cos (\angle BAC)=\dfrac{12}{20}$

$\sin (\angle BAC)=\dfrac{16}{20}$

<u>Angles</u>

$\sin (30^{\circ})=\dfrac{1}{2}$

$\cos (30^{\circ})=\dfrac{\sqrt{3}}{2}$

Therefore, using the trig identities and ratios:

$\begin{aligned}\sin (\angle BAC + 30^{\circ}) & = \sin (\angle BAC) \cos (30^{\circ})+\cos (\angle BAC) \sin (30^{\circ})\\\\& = \dfrac{16}{20} \cdot \dfrac{\sqrt{3}}{2} + \dfrac{12}{20} \cdot \dfrac{1}{2}\\\\& = \dfrac{16}{40}\sqrt{3}+\dfrac{12}{40}\\\\& = \dfrac{2}{5}\sqrt{3}+\dfrac{3}{10}\end{aligned}$