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3 years ago

7

A large box shaped arena has a rectangular floor that measures 200 feet by 150 feet and a flat ceiling that is 35 feet above the

floor. Find the area of the floor and the volume of the arena.

1 answer:

Andrew [12]3 years ago

8 0

200 I’m pretty sure Yea your gonna have to trust your gut with this one

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A teacher pays $39 for 10 books.What is the unit price of each book?

zheka24 [161]

To find the cost of each book, you need to divide the money spent on all of the books by the number of books.

$39 / 10 = $3.90 per book

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4 years ago

Read 2 more answers

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

2|4x-1|=38 I need to solve this

umka21 [38]

First you have to have the absolute value isolated so the 2 has to be divided. Then set up the two cases and solve.

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3 years ago

Nearest Integer of the square root of -61?

OLga [1]

You cannot take the square root of a negative number and get a real number answer. You can only get an imaginary root.

square root of 49 = 7 and square root of 64 = 8
square root of 61 is between 7 and 8.
It would be closer to 8.

square root of -49 = 7i and square root of -64 = 8i
square root of -61 would be closer to 8i

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4 years ago

Key: 0.40x+15 [pens] 1.50y+30 [sportpack]

Marina CMI [18]

$\bf \stackrel{\textit{cost of the pens}}{0.40x+15}\qquad \qquad \qquad \stackrel{\textit{cost of the sportpacks}}{1.50y+30}
\\\\\\\
\stackrel{x=500}{[0.40(500)+15]}~~+~~[1.50y+30] \le 3330
\\\\\\
200+15~~+~~1.5y+30\le 3330\implies 245+1.5y \le 3330
\\\\\\
1.5y\le 3085\implies y\le \cfrac{3085}{1.5}\implies y\le \cfrac{6170}{3}\implies y\le 2056\frac{2}{3}$

or namely 2056 sportpacks if we toss away the fraction.

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3 years ago