CPhill

The time for the  stone to fall can be calculated by

0  = -4.9t^2  + 19.6

-19.6  = -4.9t^2

t^2 =  19.6 / 4.9  

t  =sqrt (19.6 / 4.9)  = 2 seconds

The boat must travel  27 - 3  =  24 m  in this time

So

D / T  = R

24 /2   = 12m/s        you are correct!!!!

4. The normal to the cirlcle x^2 - 4x + y^2 = 9 at (5,2)

Let's complete the square to find the center

x^2 -4x + 4  + y^2 =  4 + 9

(x - 2)^2  + (y - 0)^2  = 13

The center is   (2, 0)

The slope between this point and ( 5,2)  is 

[ 2- 0 ] / [ 5 - 2 ] = 2/3  = slope of the normal line

The equation of the normal line  at  (5,2) is

y  = (2/3) (x - 5) + 2

y = (2/3)x - 10/3 + 2

y= (2/3)x - 4/3

Here's the graph : https://www.desmos.com/calculator/u8n7sc01uh

Ker - rect  !!!!!!

3. The tangent to the circle with C(1,2), r= root 5 at (3,3)

The slope between  the center and  the point is 

[ 3 - 2] / [ 3 - 1] = 1/2

The tangent line  will have a negative reciprocal slope = -2

So.....the equation of the tangent line is

y = -2 ( x -3) + 3

y = -2x +  6 + 3

y = -2x + 9

Here's the graph : https://www.desmos.com/calculator/ve37r2kubn

P = 400

r = .075/12

n = 6 * 12  = 72

So we have

400  [ (1 + .075/12)^72  - 1 ]  / [ (.075/12) ( 1 + .075/12)^72 ]   ≈ $23,134.61 

Amt to be paid to Jake  =

Cost of repairs - deductible he pays  =

3425.75  - 250

Can you work to the answer, NSS  ???

Let's see how critical  might have gotten this

1600  = pi * r^2      divide both sides by pi

1600 / pi   = r^2

Take the square root of both sides

sqrt (1600 / pi )  = r   = 22.56

And the diameter is twice this ≈ 45.2

NSS......We need to divide yearly income by 12 to get the monthly income

29000/ 12   = $2416.66

The  montly housing budget is 25%  of this = 

2416.66 * .25  =  $604.17

2.the normal to the circle x^2 + 4x + y^2 - 6y = 0 at (1,1) 

The slope of a tangent line at any point is found as

2x + 4 + 2yy' - 6y'  = 0

y' [ 2y - 6] =  - [2x + 4]

y '  =  - [2x + 4 ]  / [2y - 6]

At (1,1), the slope is

-[2(1) + 4 ] / [ 2(1)  - 6 ]  =   - 6 / -4  =  3/2

Since we want a normal line at this point...the slope of our line  is  -2/3

So...the equation of the normal line is

y = (-2/3) ( x - 1) + 1

y =(-2/3)x +  2/3 + 1

Here's the graph :  https://www.desmos.com/calculator/1jrzfuhcxk

What is the "rule of housing??"