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i think you have to add to move the -9 over. so 9 plus -74. am i right? im confused.

This means x - y= The difference so 

\(x - (-9) = -74 <=> x= -74 - 9 = -83 \)

so the number is \(-83\)

Hope this helps! 

Why? Where is my false? 

Last one.....a little more conceptual

Radius of cylinder and hemisphere = r

Height of cylinder  =   h - r

Height of hemisphere = r

Total  volume of cylinder  =   pi  [ r^2]  * [ h - r ]

Total volume of hemisphere  = pi  (4/3) (r^2) * (r)  * (1/2)  =  (2/3) pi r^3 = pi ( 2/3) r^3

(2/3) pi r^3  + pi r^2 ( h - r )   ⇒  "C"

^^ thats not correct

the correct answer was -√35 / 6

and - √13 / 4

Second.....easier than the first one   !!!

Volume of cone  = (1/3)  3.14  * ( radius of cone)^2 * height of cone  =

(1/3) (3.14) * (2^2) * 6  =     25.12   (1)

Volume of cylinder  = pi * radius^2 * height  =

pi * 2^2 * 12  =      150.72     (2)

So....total volume is    (1) + (2)  =  175.84  in^3

1) \(sinθ=\frac{1}{6}\)

and  \(tanθ=\frac{sinθ}{cosθ}\) <=> \(cosθ=\frac{sinθ}{tanθ}=\frac{\frac{1}{6}}{\frac{-\sqrt{35}}{35}}=\frac{-\sqrt{35}}{6 }\) 

so \(cosθ= \frac{-\sqrt{35}}{6}\)

2) \(cosθ=cos(-θ)=\frac{\sqrt{3}}{4}\)

and \(cos^2θ + sin^2θ =1 \) 

so  \(sinθ =\sqrt{1-cos^2θ} = \sqrt{\frac{16}{16}-\frac{3}{16}}=\sqrt{\frac{13}{16}}=\frac{\sqrt{13}}{-4}\)

so \(sinθ=-\frac{\sqrt{13}}{4}\)

Hope this helps! 

First one

We need to find the height of the pyramid

Cone volume  =  (1/3) (3.14)  * ( radius of cone )^2 * ( height of cone )

1884  =  (1/3) (3.14) * (10)^2 * (height of cone)

1884 = (100/ 3)) (3.14) * height of cone   

Divide both sides by  (100/3) (3.14)

Height of cone  =  1884 /   [ (100/3) (3.14)]  =  18  =  height of pyramid

Volume of (square ) pyramid  =   (1/3)  [ side of base ]^2 * 18  =

(1/3)* ( 20^2] * 18  =  2400 in^3

So....the difference is    2400 - 1884  =     516 in^3

deleted

thx dimitristhyn

\(sin^2θ +cos^2θ =1\)

so \(sinθ =\sqrt{1-cos^2θ}=\sqrt{\frac{36}{36}-\frac{1}{36}}=\sqrt{\frac{35}{36}}=\frac{\sqrt{35}}{6}\)

so \(tanθ=\frac{sinθ}{cosθ}= \frac{{\frac{\sqrt{35}}{6}}}{\frac{-1}{6}}=-\sqrt{35}\)

Hope this helps! 

 √ [ 125 x^3 ] 

√25 *  √5 *  √x^2 *  √ x

5  * √5  * x  * √ x

5x √ [ 5x ]

Generally its: 

\(sin^2θ + cos^2θ=1 \)

so \(cosθ=\sqrt{1 - sin^2θ }=\sqrt{1 - \frac{4}{25} }=\sqrt{\frac{25}{25}-\frac{4}{25}}=\sqrt{\frac{21}{25}}=\frac{\sqrt{21}}{5}\)

LOL!!!!!

Thanks for that solution,  Dimitristhym.......!!!!

Let the smaller number   = N

The greater number  = 4 times N   = 4N

And we know that 

N + 4N   = 155

5N    = 155      divide both sides by 5

N =  31     [ the smaller number ]

And the larger number is  4 ( 31)  =  124

I kind of don't get your question, but ... 

The first one (THTHTHTHHT). More even probability of Heads and Tails. 

Sorry if you don't understand my solution sent me message to explain it step by step 

Thank you CPhill and thanks to dimitristhym as well!

2 fast :p

No prob   !!!

\(\sqrt{128r^3}=\sqrt{64 \times 2 \times r^2 \times r }=\sqrt{64} \sqrt{r^2} \sqrt{2r}=8r\sqrt{2r}\)

Hope this helps!

8r sqrt 2r. 

Welcome.

Hope this helps a little bit, sorry I don't have too much time for explanation. (and I don't understand why latex does not work here)

√ [ 128 r^3 ]  =

√64 *  √2 *    √ r^2   *   √ r   =

8 * √2 * r   * √ r  =

8r √ [ 2r ]

Thank you!