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3 years ago

The area of room in a dollhouse is 1248 sq in. the width of the room is 8 in. how long is the room?

Mathematics

1 answer:

Tanzania [10]3 years ago

6 0

The length of the room is 156 sq in

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The surface area of a cube is 24 square inches.<br> What is the side length of the cube?

Alex777 [14]

Answer:

2 inches

Step-by-step explanation:

A cube has 6 faces. Therefore, each face is 4 square inches. (24/6) The side length of the square (face of the cube) is the square root of the area. The square root of 4 is 2. There is your answer :)

3 0

3 years ago

If cos theta= -8/17 and theta is in quadrant 3, what is cos2 theta and tan2 theta

Karo-lina-s [1.5K]

$\bf cos(\theta)=\cfrac{adjacent}{hypotenuse}\qquad 
\begin{array}{llll}
\textit{now, hypotenuse is always positive}\\
\textit{since it's just the radius}
\end{array}
\\\\\\
thus\qquad cos(\theta)=\cfrac{-8}{17}\cfrac{\leftarrow adjacent=a}{\leftarrow hypotenuse=c}$

since the hypotenuse is just the radius unit, is never negative, so the - in front of 8/17 is likely the numerator's, or the adjacent's side

now, let us use the pythagorean theorem, to find the opposite side, or "b"

$\bf c^2=a^2+b^2\implies \pm\sqrt{c^2-a^2}=b\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite
\end{cases}
\\\\\\
\pm\sqrt{17^2-(-8)^2}=b\implies \pm\sqrt{225}=b\implies \pm 15=b$

so... which is it then? +15 or -15? since the root gives us both, well
angle θ, we know is on the 3rd quadrant, on the 3rd quadrant, both, the adjacent(x) and the opposite(y) sides are negative, that means, -15 = b

so, now we know, a = -8, b = -15, and c = 17
let us plug those fellows in the double-angle identities then

$\bf \textit{Double Angle Identities}
\\ \quad \\
sin(2\theta)=2sin(\theta)cos(\theta)
\\ \quad \\
cos(2\theta)=
\begin{cases}
cos^2(\theta)-sin^2(\theta)\\
\boxed{1-2sin^2(\theta)}\\
2cos^2(\theta)-1
\end{cases}
\\ \quad \\
tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}\\\\
-----------------------------\\\\
cos(2\theta)=1-2sin^2(\theta)\implies cos(2\theta)=1-2\left( \cfrac{-15}{17} \right)^2
\\\\\\
cos(2\theta)=1-\cfrac{450}{289}\implies cos(2\theta)=-\cfrac{161}{289}$

$\bf tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}\implies tan(2\theta)=\cfrac{2\left( \frac{-15}{-8} \right)}{1-\left( \frac{-15}{-8} \right)^2}
\\\\\\
tan(2\theta)=\cfrac{\frac{15}{4}}{1-\frac{225}{64}}\implies tan(2\theta)=\cfrac{\frac{15}{4}}{-\frac{161}{64}}
\\\\\\
tan(2\theta)=\cfrac{15}{4}\cdot \cfrac{-64}{161}\implies tan(2\theta)=-\cfrac{240}{161}$

6 0

3 years ago

Simplify 15a^2 * 4c * 5ab

gulaghasi [49]

Answer: 300a^3cb

Step-by-step explanation:

$Simplify the following:$$15 \times 4 \times 5 a^{2} c a b$$$$\begin{aligned}&15 a^{2} \times 4 c \times 5 a b=15 a^{2+1} \times 4 c \times 5 b: \\ \\&15 \times 4 \times 5 a^{2+1} c b\end{aligned}$$$$\begin{aligned}&2+1=3 \\ \\&15 \times 4 \times 5 a^{3} c b \end{aligned}$$$$\begin{aligned}&15 \times 4=60 \\ \\&60 \times 5 a^{3} c b\end{aligned}$$$$60 \times 5=300$$Answer:$$300 a^{3} c b$

6 0

2 years ago

Maxwell wants to know how much space his globe occupies. Should he find its surface area or volume? Explain your answer

Elenna [48]

Since, Maxwell wants to know how much space his globes occupies he has to find its volume.

<h3>What is a volume?</h3>

Volume is the amount of space an object or substance occupies.

Every three dimensional object occupies a space.

Volume is measured in cubic units.

Therefore, the three dimensional object that has a width, length and height will have its volume as follows;

volume = lwh

where

l = length
w = width
h = height

Therefore, the space occupied by the globe is the volume of the globe.

learn more on volume here: brainly.com/question/9950097

#SPJ1

4 0

2 years ago

Apples cost $3.99 for 3 lbs. Susan wants to buy 5 lbs. How much will it cost her?

SSSSS [86.1K]

Answer: $5.99 is the answer hope this helps!

8 0

1 year ago