CPhill

2x^2 - 3x + 27 = 0          

Let the roots be p and q

The sum of these roots =  3/2

The product of these roots =  27/2

So

p + q   =  3/2       (1)

And

pq =  27/2           

2 pq =  27        (2)

Square both sides of (1)

p^2 + 2pq  + q^2  = 9/4         sub (2) into this

p^2 + (27) + q^2 = 9/4

p^2 + q^2 =      9 / 4 - 27 

p^2 + q^2 =   9/4 - 108 / 4

p^2 + q^2 =  -99 / 4

p^2 + q^2 =  -24.75

If a circle has a radius of 1, its curvature is inversely proportional to this = 1

A circle with a curvature of 1/3 of this must have a radius of 3

So....the circumference of this circle  =  2 pi * radius =  2 pi * 3 =  6pi ≈ 18.85 units

The function y=-16t^2+8t represents the height y (in feet) of a grasshopper jumping straight up from the ground t seconds after the start of the jump. After how many seconds is the grasshopper 1 foot off the ground?

We need to solve this

-16t^2+ 8t  =  1      subtract 1 from both sides

-16t^2 + 8t - 1  = 0           multiply through by - 1

16t^2 - 8t + 1 =  0           factor

(4t - 1) (4t - 1) = 0

(4t - 1)^2 =  0           take the square root

4t - 1 = 0       add 1 to both sides

4t  = 1           divide both sides by 4

t =  1/4   seconds

The scale factor is given by

 JK  / EF  =  11.2 / 28    =  2 / 5 =  0.4

No prob....!!!

OK.....let's take it from here

( [ (3/2) (a) +  5 ]  -  [ (3/2) (b) + 5 ] )  / [ a - b ]  =

[ (3/2)a + 5 - (3/2)b - 5 ]  / [ a - b ]  =

[ (3/2) a - (3/2)(b)] / [ a - b]  =

 (3/2) (a - b) / ( a - b)  =

3/2

I think I forgot to close the parentheses  on the (a) term above....sorry....!!! 

Taking what you have literally written, we have

{ |-2(-5)-38|+2} / 3 * [-9+7]^3  =

(1/3)  {   l  10 - 38  l  + 2 }  * ( -9 + 7)^3  =

(1/3)  { l - 28 l + 2 }  * (-2)^3  =

(1/3) ( 30) * (-2)^3  =

10 * ( -8)  =

-80

Excellent, PM....!!!!

Good job, PM....!!!

Thanks, EP....Here's another way

Just add the equations and we get that

2x  = 4 + 4

2x = 8

x = 4

Sub this back into the first equation to find y

4 + y  = ( 5 - 4) + ( 5 - y)

4 + y   =  6 - y

2y = 2

y = 1