ElectricPavlov

See diagram below:

  Use pythagorean theorem to calculate ?    and ??  below

   sqrt ( 12^2 + 4^2)    +  sqrt ( 12^2 + 10^2) = rope length

10x²  sqrt ( 3x³ )

= sqrt  (10x²)² * 3x³)

=\(\sqrt{300x^7}\)

Angle bisector theorem

56/xb = 14/ax          note that xb = 50 -ax   sub that in

56 / (50 - ax) = 14/ax

56 ax = 14 (50 - ax)

70 ax = 700

ax = 10

\(\sqrt[3]{432x}\)                 this is    cubrt ( 6³ *2 x)    by moving the 6 into the radical

I THINK:

Any digit repeated    4 x 4 x 4 x 4 =  256   four-digit numbers possible

No repeats    4 x 3 x 2 x 1     = 24          256 -24 = 232 with repeats

232/256 = 29/32   

2/5 z  = 12 + 2/3 l    or

   z = 5/2 (12 + 2/3 l)           given

z-50 = l + 50        sub in the red equation

5/2 ( 12 + 2/3 l ) = l + 50

30 + 10/6 l   -50  = l +50

-70   = - 4/6 l

l = $ 105 originally

(10 b /20 d ) / 5c    = 1/10  b / cd

 1/10   b / (cd)   *  18 c  = 1.8 b/d

100 b / (1.8 b/d) = 55.56 d

1 lawn / (5 people 12 hours)  =   1 l / 60 p-h

1 / 60 p-h  x 3 hr = 3/(60  p)           60/3 = 20 people    needed      or      15 MORE people needed

In a right triangle , recall that   tangent of angle = oppsosite side / hypotenuse

tan? = 23/20

? = arctan ( 23/20) = ..........

c = 2/3 a

then

c -12  =  1/9 (a+12)    sub in the red equation  

2/3 a  - 12 = 1/9a + 12/9

a = 24 originally