All Answers 358481 Answers

The base of EFGH  = the base of DEFG

The height of pyramid EFGH is (1/2) that of pyramid DEFG

So....the volume  of  pyramid EFGH =  (1/2)(18)  =  9

Im 99% sure that the prism is also a cube, so in that case then the answer wouuld be \(\sqrt{10}^3\)or \(10\sqrt{10}\) (simplifed)

Thanks a lot for the answer, but I think using only one of each number is allowed... Thanks again though!

All real numbers is correct

|x-2| represents the distance between 2, and |x-7| represents the distance between 7.

The sum of the distance between a number and 2 and a number and 7 is a minimum of 5. 

So x is all real numbers.

tan x + sec x =  2

sin x / cos x  + 1 /cosx  = 2

[ sinx + 1 ]  = 2 cosx             square both sides

sin^2 x  + 2sinx + 1 =  4cos^2x

sin^2x + 2sinx + 1  = 4 (1 - sin^2x)

5sin^2x + 2sinx - 3  =  0       factor as

(5sinx - 3) (sinx + 1) =  0 

5sinx - 3 = 0             sinx + 1 =  0

5sinx = 3                  sinx = -1   (reject as x = -pi/2)

sinx = 3/5

cos x  =  sqrt [ 5^2 - 3^2 ] /  5  =   sqrt [ 16 ] / 5  =   4 / 5

I think it's 4/5

Law of Cosines

AC^2  = AB^2 + BC^2  - 2 (AB * BC)cos (ABC)

30^2 = 25^2  + 25^2   - 2 (25 * 25)cos (ABC)

[ 30^2 - 25^2 - 25^2 ] / [ -2 (25*25) ] =  cos (ABC)

7 / 25  = cos (ABC)

sin (ABC)  =  sqrt  [ 25^2 - 7^2 ] /  25  = sqrt [ 576 ] / 25  =  24 / 25

4. 

( 1x + 4) (1x + 3)  = 1x^2  + 7x + 12

Thank you so much, CPhill!!!!

As a side note, I don't mean to be arrogant. When I named myself "ImCool" I was 9 years old, and had no idea how much time I would spend on this great website. Is there like any way to change your name?

(4) 

Surface area

SA  = pi  * L *  ( R + r)  +   pi ( R^2 + r^2)

Where L  = the slant height  = sqrt [ H^2  +  (R - r)^2 ]  = sqrt [ 4^2  + (6-3)^2 ] = sqrt [ 16 + 9 ] =  5

So

SA =  pi * 5 (6 + 3) + pi  ( 6^2 + 3^2)  = 

pi (45)  + pi ( 45)  = 

90 pi

4. Volume of a Frustum  =

(1/3) pi * h * ( r^2  + Rr + R^2)

Where  

h = height

r = radius of smaller base

R = radius of larger base

So

(1/3) pi* 4  * (3^2 + 6*3 + 6^2)  =

(4/3) ( 9 + 18 + 36) pi  =

(4/3) (63)  pi  =

84 pi

It's correct, thanks!

Sorry....see my corrected anwser to (2).....

Questions 1 and 3 were right, but not question 2. Could you please do question 4 too?

Correct, ImCool !!!

3. We can find the radius of the circle, r,  as

14pi =  pi*r^2

14  = r^2

r =sqrt (14)

We can find the radius of the sphere, R,  using the Pythagorean Theorem

R = sqrt [ (sqrt (14))^2  + 2^2  ] = sqrt  [ 18] 

Surface area of sphere =

4 pi ^ R^2  =

4 * pi * 18   =

72 pi

2.  The height of the triangle is   sqrt [ 5^2 - 4^2 ] = sqrt [9] = 3 

Rotating this triangle in space around BC produces identical  cones with radiuses = 3  and  heights =  4

So.....the volume is

2 * [  pi * radius^2 * height   / 3 ]  =

2 * [  pi * (3)^2  * 4   / 3 ]   =

24 pi

CORRECTED