CPhill

Take the derivative of the function

h' t =  -6.22t + 9.33

At 1 sec we have

h'(1)  =   -6.22 (1)  + 9.33  ≈   3.1  ft/s

f(-2)  = (-2)^2 - 2  =  2

f(2) =  2 (2)+ 20  =  24

So

2 +  24   + f(a)  =  0

26  + f(a)  = 0

f(a)  =  -26

So either                                       or                 

a^2 - 2 =  -26                             2a + 20  =  -26                                                                                                

a^2  =  -24                                   2a  = -46

not possible                                  a  = -23     { but a must be >=  0 }

No answer to this one

When it hits the surface, the height = 0...so

-t^2  + 8t + 10  = 0

Use the quad formula

-8  ±  sqrt [ 8^2 -  4 * -1 * 10 ]                   -8 ± sqrt [ 104]           -8 ± 2sqrt (26)

_______________________  =             _____________  =   _____________  = 

           2 (-1)                                                      -2                                -2

4 -sqrt (26) sec  (reject)  or

4  + sqrt (26)sec ≈   9.1 sec

We have  the form

y = a ( x - h)^2  + k

(h,k)   = the vertex =  ( -1, 7)   

So we have

y  = a( x  - -1)^2  + 7

y = a ( x + 1)^2  + 7

And the point (0,20) is on the graph so

20  = a ( 0 +1)^2 + 7

20 - 7  =   a * 1^2

13  = a

The equation is

y =  13 ( x + 1)^2  + 7

Here's a graph :  https://www.desmos.com/calculator/hnmgnpsmel

f(f(x))  + 2x - 1 = (x^2 -2x)^2 - 2 (x^2 - 2x) + 2x - 1 =   [ x^4 - 4x^3 + 4x^2 ] - 2x^2 + 4x + 2x- 1 =

x^4 - 4x^3 + 2x^2 + 6x - 1

So

x^2 - 2x =  x^4 - 4x^3 + 2x^2 + 6x - 1            rearrange as

x^4 - 4x^3 + x^2 + 8x - 1   =  0

See the graph here :  https://www.desmos.com/calculator/os2uyqpfze

The real numbers that make this true   are     x ≈ -1.209   and x ≈ .124

1)  Quarter circle at the top with a radius   =  3.....area =  pi (3)^2 / 4  =  (9/4)pi

2)  A    (4 + 2) x 4  = 6 x 4  rectangle in the middle =  24

3) A 1 x 4  rectangle at the bottom

Again....add these together....answer is in km^2

h(t)  = -(t -14)^2 + 74

The first statement is true

To see why, whenever   t is anything but 14, the first part of the function is negative.....adding this to 74  gives us something < 74

But when t =14, the first part of the function =  0^2....adding this to 74    =   74

Break it up into pieces

1) A 5 x 5  square on the left  = 30

2) A 4 x 8  rectangle at the bottom =  32

3) A (8+1) x 5 rectangle in the middle  = 9 x 5 =  45

4) A triangle at top with a base of   (8 + 5) - (6 + 4)  =  3   and a height of 3 =  (3 * 3) / 2  = 4.5

Now....just add the areas together

Let the amount that Joseph paid =  N

The amount that Tony paid =  3N

The amount that Andy paid  =  2 [3n]  = 6n

N + 3N + 6N  = 126

10N = 126

N = 126/10 =  $12.60

Sharing the cost equally each would pay   126/3 =  $42

So    Joseph would have to pay Andy    42 -12.60  = $29.40

And Tony would have to pay Andy    42 - 3(12.60)  = 42 -  37.80  =  $4.20

Normal  price of the towel set  =   15.96 / (4/5)   =  19.95

floor  [ 200 / 19.95 ]  =  10  sets

floor [ 200 /15.96]  =  12 sets