CPhill

We can rewrite this as

f(x)  =  - 2sin (1/4)(x) + 3

We can find the period, P as

P = 2pi / (1/4)  =  2pi * 4   =  8pi

And the frequency   = 1/ Period  =  1 / P   =    1 / (8 pi)

A  =  (-2,1)   B  =  (4,1)

The side length of AB  = 6

And C  will have an x coordinate value  of  (4 - 2) / 2  =  2/2   =  1

So...C  = (1, y)

So....we can find the possible y values  of C  by setting the distance between A and C = 6...so we have

sqrt [ (-2 - 1)^2 + ( y - 1)^2 ]  =  6          square both sides

(-2 - 1)^2 + (y - 1)^2   =  36       simplify

(-3)^2 + (y - 1)^2  =  36

9 + (y - 1)^2  = 36   subtract 9 from both sides

(y - 1)^2 = 27      take both roots

y -  1  = ±√27

y =  ±3√3 + 1      =   -4.2   and  6.2

So...the possible coordinates for C are

(1, -4.2)     and   (1, 6.2)

1. 

6 * 12  =   72 different choices

2. 

8!  =  40320  ways

3.

P(10,2)   =  90 ways

                          H   3.1     FS

                                          1.7

Middle School      4.3        TH

Distance between School and Fire Station  =  sqrt ( 4.3^2 + 1.7^2 )  = 4.6 miles

Distance between  School and Hospital  =  sqrt [ (4.3 - 3.1)^2 + 1.7^2 ] = 

sqrt [ ( 1.2)^2 + 1.7^2 ]  =  2.1 miles

The  area  of the actual house  =

Square footage of the model  *  scale factor^2   =

7 * 16^2  =

1792  sq ft

9, 6,  4

We can find the common ratio  as

Succssive Term  / Previous Term 

So.using the first two terms, we have

6 / 9   =    2 / 3   = common ratio

So....the next term after 4  is    4(2/3)   =  8/3

38       13    35   13

The length of the diagonal  at the base of the box  is :

sqrt  ( 13^2 + 35^2 )  = 37.3  inches...so...it WON'T fit   !!!

The length of the interior diagonal  is

sqrt  ( 13^2  + 35^2 + 13^2)  =  39.5 in.....so...it WILL fit     !!!!

Volume  =  (1/3) ( 54^2) (260)    =  252720 m^3

NO.... in all three cases  !!!

(Maybe the easiest question I've ever had to answer on  here...LOL!!! )

Volume of a pyramid  = 

(1/3) ( base  area)  *  (height)

Because the base area is a square  with a side of 10...its area  is 10^2  =  100m^2

The height  is 12 m

So....the area  is

(1/3) (100m^2) * 12m  =   400m^3