(-0.5x-0.4)-8(0.75x-0.6)

The fish tank has side lengths 20in, 10in and height 15in. The water level is two inches below the top of the tank. A glass sphe

Kitty [74]

Answer:

Part 1) The new distance from the water to the top of the tank is $1.979\ in$

Part 2) The maximum number of balls that can be put into the tank with the tank not overflowing is 95

Step-by-step explanation:

step 1

Find the total volume of the tank

$V=20*10*15=3,000\ in^{3}$

step 2

Find the volume of the tank if the water level is two inches below the top of the tank

$V=20*10*(15-2)=2,600\ in^{3}$

step 3

Find the volume of the glass sphere

The volume of the glass sphere is equal to

$V=\frac{4}{3}\pi r^{3}$

we have

$r=1\ in$

assume

$\pi=3.14$

substitute

$V=\frac{4}{3}(3.14)(1)^{3}$

$V=4.2\ in^{3}$

step 4

What is the new distance from the water to the top of the tank?

we know that

$2 in -----> represent (3,000-2,600)=400\ in^{3}$

so

using proportion

Find how many inches correspond a volume of $4.2\ in^{3}$

$\frac{2}{400}\frac{in}{in^{3}}=\frac{x}{4.2}\frac{in}{in^{3}}\\ \\x=4.2*2/400\\ \\x=0.021\ in$

The new distance from the water to the top of the tank is

$2-0.021=1.979\ in$

step 5

Find how many of these balls can be put into the tank with the tank not overflowing

we know that

The volume of one ball is equal to $4.2\ in^{3}$

using proportion

$\frac{1}{4.2}=\frac{x}{400}\\ \\x=400/4.2\\ \\x=95.23\ balls$

therefore

The maximum number of balls that can be put into the tank with the tank not overflowing is 95

4 0

3 years ago

Solve on the interval (0,pi)<br> 1+cosθ=((sqrt3)+2)/2

Oliga [24]

$\bf 1+cos(\theta )=\cfrac{\sqrt{3}+2}{2}\implies cos(\theta )=\cfrac{\sqrt{3}+2}{2}-1
\\\\\\
cos(\theta )=\cfrac{\sqrt{3}+2}{2}-\cfrac{2}{2}\implies cos(\theta )=\cfrac{\sqrt{3}\underline{+2-2}}{2}\implies cos(\theta )=\pm\cfrac{\sqrt{3}}{2}
\\\\\\
cos^{-1}[cos(\theta )]=cos^{-1}\left( \pm\cfrac{\sqrt{3}}{2} \right)\implies \measuredangle \theta =
\begin{cases}
\frac{\pi }{6}\\\\
\frac{5\pi }{6}\\\\
\frac{7\pi }{6}\\\\
\frac{11\pi }{6}
\end{cases}$

8 0

3 years ago

sub to hxlloween so you get free points and a xbox make sure to like and sub i will be checking if you subbed

photoshop1234 [79]

Answer:

Done! :)

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

3p-2 greater than or equal to 4 or 7p>-28

Leona [35]

Answer:

$\large \boxed{\boxed{p>-4}}}$

Step-by-step explanation:

$3p-2\geq4\ or\ 7p>-28\\\\(1)\\3p-2\geq4\qquad\text{add 2 to both sides}\\3p-2+2\geq4+2\\3p\geq6\qquad\text{divide both sides by 3}\\\dfrac{3p}{3}\geq\dfrac{6}{3}\\\boxed{p\geq2}\\\\(2)\\7p>-28\qquad\text{divide both sides by 7}\\\dfrac{7p}{7}>-\dfrac{28}{7}\\\boxed{p>-4}\\\\\text{From (1) and (2) we have:}\\\\p\geq2\ or\ p>-4\Rightarrow \boxed{\boxed{p>-4}}$

3 0

3 years ago

Please answer the questions in the image plsss

stepan [7]

pt 1: possibilities for Joel winning a point- 1+1, 2+2, 3+3, 4+4, 5+5, 6+6, 1+3, 1+5 2+4, 2+6, 3+5, 4+6. Possibilities for Hiram winning a point- 1+2, 1+4, 1+6, 3+2, 3+4, 3+6, 5+2, 5+4, 5+6.

I am a little confused to why this would be something to ask about; it is straight forward. List the possible outcomes.

3 0

3 years ago

(-0.5x-0.4)-8(0.75x-0.6)​

(-0.5x-0.4)-8(0.75x-0.6)