ElectricPavlov

Yes, ....it is.   And so is 'x' .

Look under the heading 'Possible Outcomes'.....and COUNT them.

Hit the equal sign again after your result to get there.....or once if you just entered a value.

What is the equation of the curve ?    1x + 4x = 5x

    I think you ment   1/x + 4x

    x^-1 +4x     the derivative will tell you the slope at a given point

Derivative

-x^-2  + 4        at x = -1    yields  -1 +4 = 3 = slope      Normal (perpindicular ) slope will be   - 1/3

y = -1/3 x +b    contains the point    -1,-5    sub that in

-5 = -1/3 (-1) + b

-5 = 1/3 +b     b = -5 1/3

y = -1/3 x  - 16/3 

area of piston end = pi r^2   = pi (1.5/2)^2  in^2

pi (.75)^2  in^2   x   60 lb/in^2 = 106.03 lb

The numbers   a   and  b   must multiply to 15    and add to k

a   b        can be        added =k

1  15                             16

3   5                                8

-1  -15                           -16

-3   -5                              -8

all of the k's multiplied results in   16384

2

Cross multiply to get

x^2 +3x = -9x-36

x^2+12x+36=0

(x+6)(x+6) = 0    x = - 6

3

x^2 -12x +32 -12 = 0

    x^2-12x+20 = 0

    (x-10)(x-2) = 0     so x = 10 or 2

4

x^2-7x -98 =0    use quadratic formula to find x = 14  or -7

OK....  Let 'x' = the number

He subtracts 8        x-8

Multiplies the result by 5       5(x-8)

And that = 20                         5(x-8) = 20    

Now solve for x

5(x-8) = 20

5x - 40 = 20

5x = 60

x = 12

F= mg    = 4(1000)(10) = 40000 kg-m/s^2 = 40000 N

W= F x d = 40,000(3) = 120,000 kg-m^2/s^2= 120,000 j

P= W/t = 120000/60 = 2000 j/s

NOT positive about this....

100 thru 999 is 900 3-digit numbers

there are 180 multiples of 5

there are 128 multiples of 7

there are 26 multiples of 35  (which must be subtraced to avoid double counting)

900 - (180+128-26) = 618       Corrected after input from Rom....Thanx ! 

Let's look at triangle BPC

Angle C is 45 degrees (bisected by the diagonal)

Angle ABE is 60 degrees due to equilateral triangle so angle B = 30 degrees

180 -30 - 45 = angle BPC = 105 degrees