CPhill

x^5 = 200

We need to take the fifth root of both sides (not divide by 5...)

Doing this, we have

x =  ⁵√200 = about 2.885

3.41 x 10^-4

We just move the decimal back 4 places to the left

= .000341

a) From E, draw a perpendicular to AD  and a perpendicular to DC. The length of each of these will be the radius of the circle centered at E. Then, DE is just the hypotenuse of a isoceles right triangle and its length is just 4√2 cm.

By similar reasoning, BF = 6√2cm

b) So, the length of the diagonal will be 4√2 + 4 + 6 + 6√2  = 10 + 10√2

c) The length of the side of the square will be  [10 + 10√2] / √2.....and the area will be

([10 + 10√2] / √2)^2 = [100 + 200√2 + 200] / 2 =  [300 + 200√2] / 2 =

[150 + 100√2]cm^2

d) The area of the two circles = pi(4^2 + 6^2] =pi[16 + 36] = 52pi cm^2

e) The % area occupied by the two circles will be [52pi / (150 + 100√2) ] = about 56% of the total area of the square

Of course......"permutes"  permutes to  "tee-rumps" which is what one has when he is holding all the cards....

Not to mention......all the medals.....in some combination, of course.......

My answer assumes that the total paid to the players and other workers is $2000 and $1600, respectively.....

Of course.....Anonymous has the correct idea if the amounts are per player and per worker.......we wouldn't have enough info to give an exact answer....

√[5 /(9a^2)] = √5 / (3a)

√(120 / 121)  = √120 / 11  = √(4 * 30) / 11  = (√4 * √30) / 11 = (2/11)√30

Notice that 10% of 280 is just 28

So....30% must be three times as much....

I'll let you take it from here....

I'm assuming this is

[2√3+9√2] /  6

We can split this up into

(2√3 / 6 )  + ( 9√2) / 6 =

(√3/3) + (3/2)√2

The only way that x = 6 is if the other two sides are √15 - √3  and √15 + √3

Proof

√[(√15 - √3)^2 + (√15 + √3)^2 ] =

√(15 - 2√45 + 3) + (15 +2√45 + 3) =

√(30 + 6) = √36 = 6

Assuming the above is true....the area =

(1/2)[√15 - √3][√15 +√3] =

(1/2)[15 - 3] = (1/2)(12) = 6 sq units

And the perimeter is just [√15 - √3] + [√15 +√3] + 6  =  6 + 2√15

12 -5y = 3y -12  add 5y and 12 to both sides

24 = 8y       divide both sides by 8

3 = y