CPhill

[ f(3 + h)   - f(3) ]  / h   =

[ (3 + h)^3 - 14 (3 + h)  -  [ (3)^3 - 14(3)] ]  / h    =

[ 27 + 3*3^2*h + 3*3*h^2 + h^3 - 42 - 14h  - 27 + 42]  / h  =

[  27h + 9 h^2 + h^3  - 14h   ] / h =

[13 + 9h + h^2]   =

[ 13 + 9(0.1) + (0.1)^2]  = 13.91

f (2)  = - 4         f  ' (2)  = 5

So......the equation of the tangent line at x =  2   is given by  :

y - (-4)  = 5(x - 2)

y + 4  = 5x -10

y  = 5x - 14

P(Green)  = Number of Green / Total  of Red, Yellow and Green   =  8 / 18  = 4 / 9

P(Red)  =  Number of Red / Total  of Red, Yellow and Green   =  6 / 18  =  1 / 3

Here's the visual proof of this.....

Draw a circle centered at the origin with a radius of 29  with the specified triangles inscribed in the bottom half of this circle

Triangle ECD  is isosceles with sides = 29, a base of 42  and a height, GC = 20

Triangle  BCA  is iscosceles with sides = 29, a base of 40  and a height,  FC = 21

So....area of ECD = [42 * 20]/2  =  840/2 = 420 cm^2

And BCA has an area of [ 40 * 21] / 2  = 840/2  =  420 cm^2

Thus   area of ECD  = area of BCA   ....!!!!

100% older means twice as old

20%  older means 6/5 as old

Let  Rebecca's current age  = x      so....Bill's = 2x

In 8 years we have........his age =  6/5 her age 

2x + 8 =  (6/5) [ x + 8]   simplify

2x + 8 = (6/5)x + 48/5

2x + 8 = (6/5)x + 48/5      subtract 8, (6/5)x from both sides

2x - (6/5)x  = 48/5 - 8        

(4/5)x  = 8/5   multiply through by 5

4x  = 8      divide both sides by 4

x  = 2       this is Rebecca's current age.......so Bill = 2x  =4

And...in 8 years, Rebecca will be 10 and Bill will be 12    .....and   12 is 6/5 of 10  →  20% more than 10

They have exactly the same area......believe it, or not.....!!!!!

Using Heron's formula to prove this, we have, for the 29,29,40 triangle

sqrt [49(20)(20)(9) ] =  about 420 cm^2

And for the 29,29, 42 triangle, we have

sqrt [ (50(21)(21)(8) ]  =  420 cm^2

Here is the explanation for the derivation of Heron's Formula along with a calculator to verify the above results :

http://www.mathsisfun.com/geometry/herons-formula.html

I think this is supposed to be :

5.91 x 10^9   =

five billiion, nine hundred ten million

Add the three side lengths of the triangle and divide this sum by two......this is known as the "semi-perimeter"   = s

The formula for the area is :

sqrt [ s (s - a) (s - b) (s - c) ]         where a, b and c are the side lengths

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Añadir las tres longitudes de los lados del triángulo y dividir esta suma por dos ...... esto se conoce como la "semi-perímetro" = s

La fórmula para el área es:

sqrt [s (s - a) (s - b) (s - c)]       donde a, byc son las longitudes de los lados

I think this is supposed to be :

f(x)= 5x^2 - 7x + 6 .......  if so, it cannot be factored and it has no real zeroes, either

The complex solutions are :

x = (1/10) (7 - i sqrt(71))  and x = (1/10 ) (7+ i sqrt(71))

I'll do the first one.....the rest are similar

d(0.15)  = 3tan [pi * 0.15]  = about 1.53 miles