ElectricPavlov

Sorry.....I thought you knew I was being fecitious.    

The engine does (3850j - 2250j) of work = 1600 j    (or 1600 N-m)

The thermal efficiency is the amount of work produced divided by the heat provided.....

1600j / 3850j x 100% = 41.6 %  

This car's parking spot is  89.....I assigned the parking spots and this goofball parked in the wrong one.

I'm sure I am not going to re-invent THAT wheel.!!   .... here is a place to get you started:

https://en.wikipedia.org/wiki/Poker_probability

Then just find the area of the sector and subtract the area of the triangle

sector area     =   125/360 x  pi x 8^2 = 69.813 sq units

Now subtract the triangle for the area of the segment.....

The chord line and the the two  radii of 8  form a triangle of which one angle is 125 degrees and the other two are

27.5 degrees   (must add to 180 degrees)

  Draw a line of length 'h' perpindicular to the chord which bisects the 125 degree angle .

Now you have two equal triangles with angles of 90  125/2   and 27.5 degree angles

Now use law of sines to find 'h'  

sin 90 /8  = sin 27.5 /h = sin 62.5/(1/2chord)         

h = 3.694    and chord = 14.192

Then area of the triangle = 1/2 b h      where b is the chord

Area = 1/2 (14.192)(3.694) = 26.22 units^2

2x^2+kx+6 = -x+4

2x^2+ x(k+1) +2 = 0

(2x+     )(x+   ) = 0     the only two factors which multiply to '2' are 1 and 2   or -1 and -2

(2x+1) (x+2)              results in TWO values of x (-1/2 and -1)that would satisfy the system of equations...no good.

(2x+2)(x+1) = 0         would result in ONE values for 'x' :   (-1)    ....we want only ONE (Per the question)

                                     so this would make k+1 = 4   or k=3

Multiply this out to get     2 x^2 + 4x +2 =0        so  k+1 = 4   .... or  k=3

(2x-2)(x-1) =0                works  for only   x =1

    multiply it out     2x^2 -4x+2       means       k+1 = -4       or k=-5

(2x-1)(x-2)      has two solutions    x = 1/2   and x= 2     no good

SO k = 3  or -5    results in only one solution for the system of equations.

Graphically:

From the graph   f(x)   (which is 'y') is a constant value from   x =   -6  to 0

cylinder volume = area x height     area = pi x r^2      r = 1/2 diameter

3.14 x   2^2   x  5  

3.14 x 4 x 5

3.14 x 20    units^3

62.8 units^3

COS (28) = 11/x    Adjacent/hypotenuse