hectictar

I am NO expert at this, but I think I found the original binomial,

and putting that into WolframAlpha gives the answer:

cos a = adjacent / hypotenuse

cos a = 10/35

a = arccos(10/35)

a ≈ 73.398º

\((63)6\div65 \\~\\ =\frac{63*6}{65} \\~\\ =\frac{378}{65}\\~\\ \approx 5.815\)

radius = diameter / 2

r   =   6/2   =   3

volume of toy = volume of hemisphere + volume of cylinder + volume of cone

volume of toy = ( \(\frac12*\frac43*\pi*r^3\) ) + ( \(\pi*r^2*\text{cylinder height}\) ) + ( \(\frac13*\pi*r^2*\text{cone height}\) )

volume of toy = ( \(\frac12*\frac43*\pi*3^3\) ) + ( \(\pi*3^2*10\) ) + ( \(\frac13*\pi*3^2*8\) )

volume of toy = ( \(\frac12*\frac43*\pi*27\) ) + ( \(\pi*9*10\) ) + ( \(\frac13*\pi*9*8\) )

volume of toy = ( \(18\pi\) ) + ( \(90\pi\) ) + ( \(24\pi\) )

volume of toy = 132π   cubic centimeters               ≈ 414.69 cubic cm

Sometimes taking a little break definitely helps!

Hmmm, I don't really know if prime factorization has to do with the LCD ...

I'm glad it helped!  

If this is exactly as the question is written...

(n - 6) / (2n)

This is also

=   n / (2n)   -   6 / (2n)

We can reduce the first fraction by n .

=   1 / 2        -   6 / (2n)

We can reduce the second fraction by 2.

=   1 / 2        -   3 / n

..........

I don't really know what you mean by " divide the LCD " .  Why do you want to divide the LCD ?

Is that what the instructions tell you to do?

Maybe the problem is

n - 6 / (2n)           ?

Reduce the second fraction by 2.

=   n - 3/n

We can get the LCD by multiplying the first term by n/n ,

which gives us

=   n² / n   -   3 / n

=   (n² - 3) / n

....

BTW, I see you became a member! Welcome aboard! 

If    \(x=\,-\,\frac83\)   , does    \(2(3x^2+24x+48)+1(x-6)=2(1)\)   ?

Replace every   " x "   with   \( -\,\frac83 \)   in the second equation.

\(2(3(-\frac83)^2+24(-\frac83)+48)+1((-\frac83)-6)\stackrel{?}{=}2(1) \\~\\ 2(3(\frac{64}{9})-64+48)+(-\frac{26}3)\stackrel{?}{=}2 \\~\\ 2(\frac{64}{3}-16)-\frac{26}3\stackrel{?}{=}2 \\~\\ 2(\frac{16}{3})-\frac{26}3\stackrel{?}{=}2 \\~\\ \frac{32}{3}-\frac{26}3\stackrel{?}{=}2 \\~\\ \frac63\stackrel{?}{=}2 \\~\\ 2=2\quad\text{ true!}\)

n - 6/2n

Is this the problem?

If it is..it that exactly how it is written? Or is it

n - 6/(2n)

? 

\(\frac{2n^2}{2n} \\~\\ =\frac{2\,\cdot \, n\,\cdot \, n}{2\,\cdot\, n}\)

The   2's   in the numerator and denominator cancel.

\(=\frac{\not2\,\cdot \, n\,\cdot \, n}{\not2\,\cdot\, n} \\~\\ =\frac{n\,\cdot \, n}{n}\)

The   n's   in the numerator and denominator cancel.

\(=\frac{n\,\cdot\, \not{n}}{\not{n}} \\~\\ =n\)

(Also, when we canceled the n from the denominator we should say n ≠ 0 )

This image may help. To look at a cross section, imagine slicing through it with a knife, and look at the shape you just formed from the slicing.

Also, I have a tip for how to remember parallel from perpendicular.

The two L's in " Parallel " are two parallel lines! 

To Melody, I have a question...aren't there two ways to get a perpendicular cross section???