CPhill

b 

s ' (t)   =  -32t + Vo

c

Vo  = 0     [ the object is dropped...so the initial velocity = 0 ]

So  =   initial height  = 64 ft

So we have

0   = -16t^2 + 64       add 16t^2 to both sides

16t^2   = 64       divide both sides by 16

t^2   = 4       take the positive root

t  = 2   (seconds to hit the ground)

d

Velocity at impact

-32(2)   =   -64 ft/ s

5.50  *  [ 100000/25000 ]   +   3.50   *  [ 75000 / 25000]    =  $32.50 per month

208   [ ( 1 + .05 / 12)^(25 * 12)  - 1]   /  (.05 / 12 ) =

$123866.02

Smoking  

9.00 x   [ 75000 / 25000] x 12   =  $324

Non-Smoking

5.50  x   [ 75000 /  25000 ] x 12    = $198

Can  you take it from here, NSS ???

Here's a simple formula for this, NSS

Applicable Category Price x     [ Amt of Requested Coverage / 25000]

So...in this case....we have

6.75   x     [ 125000/25000]  =  $33.75

Remember that this is the monthly premium.....if they want yearly, we need to multiply the answer by 12....

Her probability of dying is  1958.7 / 100000

So...the probability of her living   is

1  -  probability of dying   =

1 - 1958.7 / 100000   ≈  .98

HAHAHA!!!!!....don't feel bad.....I took 4 semesters of Calculus and can barely do a derivative, now   !!!!

 Use it... or Lose It.......!!!!

A long time ago for me too, EP....LOL!!

1 False.....the function   y = abs (x)  is continuous, but not differentiable at x = 0

2 True....Remember the motto..."Differentability implies Continuity....but Continuity does not imply Differentiability "

3 Just as EP said

4  Remember that we can take as many non-zero derivatives of a polynomial as its degree

For instance  x^2   ⇒  2x  ⇒ 2   ⇒ 0    [ two non-zero derivatives ]

So....just as EP said !!!

5  sin x   ⇒ cos x ⇒ - sin x ⇒ - cos x  ⇒ sin x    ..... true   !!!!

This is known as the "Chain Rule"

d/dx   [ f(x) }^n   =

n * [ f(x)] ^(n - 1) * [ f ' (x) ]

Where f ' x   is the derivative of f(x)

I just keyed in the points and let the website generate the graph [ and function ] based on that.....it's probably pretty similar to what you would do in Desmos...but.....I'm not sure