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Add the two equations together to get

6x = 6

x = 1          then y = -2          you can finish......

b = 1/5 s      s = sibling     

b+9 = 1/2 (s+9)      sub in the red equation

1/5s + 9 = 1/2s + 4.5

4.5 = .3s

s = 15 y/o    b = 1/5 (15) = 3 y/o     You can finish......

Coordinates  =    

[  1 + (1/6)(10 - 1)   ,  -5 + (1/6) ( 1 - - 5)  ]    =

[ 1  + 9/6  ,  -5   + 1 ]  =

[ 1+ 3/2  , -4  ]   =

( 5/2  ,  -4 )

See the  graph  here  :  https://www.desmos.com/calculator/kblqq5fy8r

x = y^2    ⇒   sqrt (x)  =  y    ⇒  2y  = 2sqrt (x)  =  side  length of  one group of equilateral triangles

2y^2  =  3 - x

y^2   =  (3-x)/2

y =   sqrt  [  (3 - x) / 2 ]   ⇒   2y  = 2 sqrt [ (3 - x) /2  ] =  sqrt ( 6 - 2x)  side  length of the other equilateral triangles

We  have  two integrals

The   height  of  the first  group  of  equilateral triangles  =   2y * sqrt (3) / 2  =  y sqrt (3)  = sqrt x * sqrt 3

Part  of  the   volume   =

1                                                                                     1

∫    sqrt (x) * sqrt (x)  * sqrt (3)   dx  =    sqrt (3)  [ x^2  / 2]  =   sqrt  (3)  / 2

0                                                                                      0

The height  of  the other  group  of equilateral triangles  =   sqrt (6 - 2x) sqrt (3) / 2                                                                                    

The  other part  of  the  volume  is

3

∫  sqrt ( 6 -2 x) / 2 *  sqrt (6 - 2x)  *  sqrt (3) / 2   dx  =

1

                      3

(sqrt 3)  / 4 *  ∫   ( 6  - 2x) dx  = 

                     1

                                    3

sqrt (3)/4  * [  6x  - x^2 ]         =

                                    1

sqrt (3)  / 4 *   [   18 - 9  - 6  + 1  ]  =

sqrt (3)  / 4  *  [ 4]    =  sqrt (3)

So.....the total volume  is

sqrt (3)   / 2    +     sqrt (3) 

3sqrt (3)  / 2

j = n

m = 4n

l = 5 * 4n = 20n

n + 4n + 20n = 25n pencils

you referred to "v" as velocity, shouldn't it be speed?

(Because K.E. is scalar not vector, and scalar quantities must be of either: Vector x Vector or scalar x scalar).

That’s an interesting question.

Most equations use velocity to define kinetic energy. Though I have seen speed used. Kinetic energy is produced when mass is in motion without regard to its direction; however, in most closed systems there is at least an implied direction.  

In the case of the wind turbine, the implied direction is at zero (0) degrees relative to the face of blades. If the mass of the wind was vectored at 90 degrees to the face of the blade then none of the kinetic energy would translate to the mass of the blades. 

GA

Similarly, if the result is 0 when divided by (x-2) , then x = 2 is a root

sub in x = 2

-6 k^3 +2k - 2 = 0   simplify

3k^3 - k + 1 = 0

then the answer is  k =  -0.85138 as Chris found   ...... 

2  [  (-3k^3  + k)  -  2   ]

                           - 6k^3 + 2k

    _______________________

      -3k^3  + k       -6k^3  + 2k - 2

So

-6k^3 + 2k  - 2  = 0         divide through by  -2

3k^3  - k  + 1    =   0

Solving this  with a CAS, we  get that

k ≈  -.85138

Here's  (a)  and (b)

(a)  If AM  is  the midpoint of BC.....then  BC  = 2* AM  =   4 sqrt (37)

(b)   s  =   14 + 2sqrt (37)

Area   =   sqrt   [ (14 + 2sqrt 37)  ( 2sqrt (37) - 1)  ( 2sqrt (37)  + 1) ( 14 - 2sqrt (37 ))]   =  84

For this to occur, the discriminant of the Quadratic Formula must = 0

b^2 - 4 ac = 0

b^2 - 4 ( 1)( 16) = 0

b^2 = 64

b = +- 8

sqrt (2)  +  sqrt (3)  +   1  / [ (2sqrt (2)  + 3sqrt (3) ] 

[(sqrt (2) + sqrt (3) ) ( 2sqrt ( 2)  + 3 sqrt (3) )   + 1 ]  /  ( 2sqrt (2) + 3sqrt (3) )

[  4  + 5sqrt (6)  +  9   +  1  ]  / ( sqrt (8)  + sqrt (27))

[ 14  + 5sqrt (6)  ]  / ( sqrt 8  +  sqrt (27)     mult num/den  by  sqrt (8)  - sqrt (27)

[14 + 5sqrt (6) [ sqrt (8)   - sqrt (27)]  / ( 8 - 27)

[14sqrt (8)  + 5 sqrt (48)  - 14sqrt(27)  - 5sqrt (162) ]  / (-19)

[ 14 * 2sqrt (2)  + 5*4 sqrt (3)  - 14*3 sqrt (3)  - 5*9 sqrt ( 2)  ]   / (-19)

[  -17 sqrt 2    -  22 sqrt 3  ]   /  (-19)

[ 17 sqrt 2   +   22 sqrt (3)   ]   /  19

a = 17     b  = 22     c   =19

a + b + c  =   58

There is no need to delete your answer. I usually leave my mistakes, unless they are a major distraction to the continuity of the post. They are uinique monuments to exceedingly rare events.

Your solution is well thought out and explained; you just have mistakes in the application. The more complex the subject, the easier it is to make mistakes. Physics becomes very complex, very fast.  We learn from our mistakes; others learn from them too. It’s part of educating ourselves.

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After rereading the question, I realize I made a mistake too, so I’m adding my name to the list of dumb-dumbs.

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The initial energy of (0.5MW) is what passes through the wind turbine system—the input power, not the output power.  Doubling the wind speed increases the input power to (4MW). The input power is then multiplied by the coefficient of efficiency (4.0MW * 0.47407) giving the output power of 1.9MW.  (This is consistent with the OP’s answer, which I dismissed because there wasn’t any associated work product.)  

GA

The expected value is 47/11.

The probability is 8/25.

When it hits  the ground  y  = 0

So

-16t^2  + 28t  + 180   =  0       divide  through by  -4

4t^2  - 7t  - 45   =  0

Using the Quadratic Formula

t  =   7  +  sqrt  [ 7^2  - 4 * 4 * -45 ]                    7  +  sqrt 769

       __________________________  =         _____________   ≈   4.34  sec

                    2 * 4                                                        8

414n  =   9* 46n     so   this term  is always divisible by  9

12 / 9    leaves  a remainder of  3

675   / 3    =   225

225 / 3    =   75

75 / 3   =  25

25 is the last integer

So....8  integers

The  exterior   angles sum  to  360°

The  smallest interior angle  is  :

180  -  (8/17)(360)  =

180   - 2880 / 17  ≈   10.59°

2x^2  + 10x  + 2y^2  - 6y  =  48       divide through  by 2

x^2  + 5x   + y^2  - 3y  =   24          complete the  square on x  and  y

x^2  + 5x  +  25/4 +  y^2  - 3y + 9/4  =  24  + 25/4  + 9/4

r^2  =   24 + 25/4 + 9/4

r^2  = 24   +  34/4

r^2  =  24 +  17/2

r^2   =  (48 + 17)  / 2

r^2  =   65 / 2   =   32.5

The area  =    pi * r^2    =  

32.5 pi

a + b =  7       square both sides

a^2 + 2ab  + b^2   = 49

a^2 + b^2   =   49   - 2ab          

and

a^3 +  b^3  =    44

(a + b) ( a^2  - ab + b^2)   =  44

(7) ( a^2 + b^2   - ab)   = 44

(7)  (49   - 2ab  - ab)   =  44

49  - 3ab  =    44/7

49   - 44/7  =  3ab

299 / 7 =   3ab   divide both sides  by 3

299 / 21   = ab

1/a + 1/b   =   (a + b)  /ab  =      7  / ( 299/21)  =  147 / 299

x^2  + y^2   =  1      square both sides

(x^4  + 2(xy)^2  + y^4)   = 1

(x^4 + y^4)   +  2 (xy)^2    =1

(17/19)  +  2(xy)^2  = 1

2(xy)^2  =    1   -17/19

2 (xy)^2  =      2 / 19         divide both sides  by 2

(xy)^2   =   1 /19

xy  =  sqrt (1/19) = sqrt (19) / 19

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

2x^2 - 2x  - 4  =  0                divide through  by 2

x^2 - x  - 2  =  0                     factor as

( x - 2) ( x + 1)   = 0

Set  each factor to 0   and solve for x   and  we  get  that

x = 2  = c          and  x   =  -1   =  a

c - a   =

2 - (-1)   = 

3

L

M         N

LN   =   sqrt   [ 2^2   +  19]   =  sqrt (23)

sin L   =   MN / LN       =       2  / sqrt (23)  =     2sqrt (23)  /  23