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3 years ago

PLEASE ANSWER RIGHT AWAY

Mathematics

1 answer:

Gala2k [10]3 years ago

4 0

Answer:

D) 43.1

Step-by-step explanation:

What we want to do here is find the total volume of the box in cubic inches, then divide it by the number of apples inside. This will tell us how big one apple is in cubic inches.

Box One:

20×13×12 = 3120

3120÷72 apples = 43.3 inches³

Box Two:

12×12×12 = 1728

1728 ÷ 40 = 43.2 inches³

Box Three:

20×10×6 = 1200

1200÷28 = 42.8 inches³

Take those three numbers and find their mean. Add them up and divide by three. You will get 43.1 inches ³.

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3 years ago

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timurjin [86]

B A C

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3 years ago

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Vlad1618 [11]

Answer:

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Step-by-step explanation:

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3 years ago

Find cos θ given that cos 2θ = 5/6 and 0 ≤ θ < π/2. Give an exact answer

trasher [3.6K]

$\bf \textit{Double Angle Identities}
\\ \quad \\
sin(2\theta)=2sin(\theta)cos(\theta)
\\ \quad \\
cos(2\theta)=
\begin{cases}
cos^2(\theta)-sin^2(\theta)\\
1-2sin^2(\theta)\\
\boxed{2cos^2(\theta)-1}
\end{cases}
\\ \quad \\
tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}\\\\
-------------------------------\\\\
$

$\bf cos(2\theta)=\cfrac{5}{6}\implies 2cos^2(\theta)-1=\cfrac{5}{6}\implies 2cos^2(\theta)=\cfrac{5}{6}+1
\\\\\\
2cos^2(\theta)=\cfrac{11}{6}\implies cos^2(\theta)=\cfrac{11}{12}\implies cos(\theta)=\pm\sqrt{\cfrac{11}{12}}$

now, bear in mind, the square root gives us +/- versions, so, which is it? well, we know the angle is in the range of "<span>0 ≤ θ < π/2", that simply means the 1st quadrant, so, we'll use the positive one then

</span> $\bf cos(\theta)=\cfrac{\sqrt{11}}{\sqrt{12}}\implies cos(\theta)=\cfrac{\sqrt{11}}{2\sqrt{3}}
\\\\\\
\textit{now, let's rationalize the denominator}
\\\\\\
\cfrac{\sqrt{11}}{2\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}}\implies \cfrac{\sqrt{11}\cdot \sqrt{3}}{2\sqrt{3^2}}\implies \cfrac{\sqrt{11\cdot 33}}{2\cdot 3}\implies \boxed{\cfrac{\sqrt{33}}{6}}$ <span>
</span>

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4 years ago