CPhill

We have

73.9 * ( 1/2)^ ( t / 3.8)         where t  is the number of days...so....

73.9 * (1/2) ^ (23/ 3.8)  ≈  1.11  g

(1 + tan x  )  / sin x  - sec  x = csc x

(1 + tan x) / sin x  -    1 / cos x

(1 + sin x / cos x) /  sin x  - 1 / cos x

1/sin x + sinx / [ cos x sin x]  - 1/cos x

1 / sin x  + sin x / [ cos x sin x ]  - sin x / [ sinx cos x]

1 / sin x  + sin x [ sin x cos x] -  sin x / [ sin x cos x ]

1 / sin x   =    csc x

E  is true

The function is defined at  x  = 0   as   1

The  limit as  x → 0  exists

F is continuous at  x  = 0    [ the second  part of the piecewise  function "fills in" the "hole' that exists at x = 0  ]

(a)

Find the z score

[ 20555 - 20500 ] / 55  =  .1

This z score  equates to  .8413  =  84.13% of the days

(b)

Find the z  score

[20610 - 20500] / 55 =  2

This score equates to .9772.....so the % days that the factory  produced  20610 or more skateboards  =

1 - .9772 = .0228  =  2.28%  of the days

(c)

Find the z score

[20445 - 20500 ]  / 55  = -1

This z score equates to .1587 = 15.87%  of the days

Notice the pattern : 

1, 4, 3, -1, -4, -3, 1, 4, 3, -1, -4, -3

The series has a cycle of 6.....and the sum of these terms  = 0

So

2014 mod 6 =  4

So we will have   2010/6  = 335 of these cycles  and  the last  4 terms after that are   1,4,3  -1

So....the sum  =  7

Center of  P =  (-9, 1)     radius  =  5 

Center  of Q  =( -2, -3)   radius  = 6

So...the answers are

7

right

4

below

a longer radius

y=1/2x^2+6x+24     factor out the 1/2

y  = (1/2) [ x^2 + 12x + 48  ] completet te square on x

y  = (1/2)  [ x^2  + 12 x  + 36  + 48 - 36 ]    factor the first three terms in the parenthses, simplify the rest

y =  (1/2)  [ ( x + 6)^2    + 12 ]      

y  =(1/2) ( x + 6)^2  + 6    

y - 6  =  (1/2)( x + 6)^2    multiply both sides by 2

2 ( y - 6)  = (x+ 6)^2

The vertex  is   ( --6, 6)

To find the directrix

4p  = 2

p = 2/4

p =  1/2

The parabola turns upward...so the  directrix   is   y  = 6  - 1/2   =  5.5

y = -(1/6)x^2  + 7x  - 80    factor out the  -1/6

y  = -(1/6)  [ x^2  - 42x + 480 ]      complete the square  on  x

y = -(1/6)  [ x^2 - 42x + 441 + 480 - 441 ]

y  = -(1/6)  [  ( x - 21)^2 + 39 ]

y = (-1/6)(x - 21)^2   - 39/6

 (y +39/6) = (-1/6) (x - 21)^2     multiply both sides by -6

-6(y  + 39/6)  = ( x - 21)^2

-6 ( y + 6.5)  = (x - 21)^2

4p  = -6

p = -6/4  = -3/2

The vertex is  ( 21, -6.5)

The directrix is given by :  y   = -6.5  - p  =  -6.5  - (-3/2)  = -5

Let  the airplane be represented by the  vector     < 0, 400 >

Let the wind be represented  by the vector    < -100, 0 >

The components of the  airplane  vector  are     400 cos 90  = 0     and   400 sin 90  = 400

The components of the wind vector  are   -100 cos 180  = 100    and -100 sin180  = 0

So....the resultant vector  is found as    

sqrt [ ( 0 + 100 )^2  + ( 400 + 0 )^2  ] = 

sqrt  [ 10000 + 160000 ] =

sqrt [ 170000]  = 

412.3 km / h   =  412 km/h  [rounded ] 

The focus is above the directrix....so this parabola turns downward

The vertex  is given as  ( 3, (-7 + -4) / 2  )   =  (3, -5.5  )

And we have this equation

( x - h)^2   = 4p ( y - k)  where  the  vertex   is  ( h, k)   and p  is the (negative) distance between  the focus and the vertex and is given by: 

p  = ( -7 - - 5.5)  

p = (-7 + 5.5)

p = -1.5

So...the equation is :

( x - 3)^2   =  4(-1.5) ( y + 5.5)

(x - 3)^2  = -6(y + 5.5)   ⇒    Answer "D"