CPhill

V_cube   =  side^3

So

698  =  side^3     take the cube root of each side

³√698   =  side  ≈   8.9  cm

y   =  -2*3^x

The graph of the function passes through the point (0,−2)

The range of the function is the set of all real numbers less than 0.

The domain of the function is all real numbers.

Very nice, MIRB16  !!!

The directrix  is 8  units below the focus

So...the vertex  is  ( 2, (6 + -2)/2 )  =  (2, 4/2) =  (2, 2)

And  p  is the distance between the vertex  and directrix  =  [2 - (-2)]  =  4

So....we have the form

4p(y - k)  = (x  - h)^2       where  (h, k) is the vertex  and p  = 4

So  we have

4(4)(y - 2)  = (x - 2)^2

16 (y - 2)  = (x - 2)^2

(y - 2)  = (1/16)(x - 2)^2

y  =  (1/16)(x - 2) + 2

Angle  C  = Angle R

And  angle  C  =   180  - 45  - 60   =  75°  =  angle  R

The area  of  the triangle  is

(1/2) (3)^2 √3/2  =  (9/4)√3  units^2

The  area  that is no more than  unit from A  is (1/6) of a circle with a center at A and a radius of 1 =

pi *(1/6)(1)^2   =   pi / 6  units' 2

So....the probability  that X  is no more than 1 unit from A  is

[pi / 6 ]   /  [(9/4)√3 ]  =

4 pi  / [ 54√3]  =

2pi / [27√3 ]  ≈  0.134  ≈   13.4 %

8)The center of a regular octahedron is 1 foot away from every vertex. What is the volume of the octahedron in cubic feet?

The octahedron will form two congruent pyramids

The edge of  one of these  is   2/√2  = √2

So....the area of the base of one of the pyramids is (√2)^2  =  2 ft^2

And the height  = 1 ft

So.....the volume  of one of the pyramids  is

(1/3) (area of base)  ( height)  =

(1/3) (2) (1)  =  2/3  ft^3

And by symmetry we have    

4/3  ft^3

First one 

The scale factor is 2

Second  one...the triangles are similar...so..we can solve this...

n / 6  =  5 / 3         multiply both sides by 6

n  =    6 ( 5/3)  =  30/3   =  10

Thanks, Alan.....here's  the last two

c)

[ 8*2  + 4*4]  / [ 8 + 4 ]  = [ 16 + 16] / [ 12 ]   =  32/12  =  8/3  

d) We need to solve this for N

[ 8*2  + N*4] / [ 8  + N ]  =  3

[ 16 + 4N]  =  3 [ 8 + N ]

16 + 4N  =  24 + 3N  

N  =  8  ⇒  number of 4's  we need to have to have an expected value of 3

So....we need to add N - 2  =   8 - 2   =   6 

Hang in there, DC...!!!!