ElectricPavlov

Here is an easier way ...the hour hand moves 1/12th as far as the MINUTE hand

the minute hand moved 165%    165/12 = 13.75%  is how far the hour hand moves!

 .....as a further follow up      the HOUR hand will move how far?

12 hours = full rotation = 360 degrees

12 hours = 12 x 60 = 720 minutes

360 degrees/ 720 minutes  =  x degrees / 99 minutes

360/720  x  99 =  49.5 degrees

49.5 / 360 = 13.75% of the clock face is how far the HOUR hand moves !!

10:44  to 11:44     is 60 minutes      

11:44  to  12:00    is 16 minutes      

12:00  to  12:23    is 23 minutes      

TOTAL                =   99 minutes     

One FULL ROTATION is 60 minutes

99 minutes / 60 minutes/full rotation = 1.65 Rotations       1.65 rotations x 100% = 165 %

Set it up as a ratio:

90/100 = x/70

90/100 * 70 = x = 63 questions answered correctly

This is an error.....   sin only goes from -1 to +1     you have   + 1.5     

Let's say the mural originally is 100 x 100 = 10000 sq ft

 new size will be   124 x 112 = 13888 sq ft           

13888/10000 = 1.3888 times bigger  ...or   38.88 percent bigger   ~~ 39 percent

They should charge the cost plus  43% of the cost    :     

(1 + .43)

4.23(1.43) = 6.05

To get lumens per watt  (l/w)  just divide the lumens by the watts 

You have the correct answers......the most efficient one will be the one with the highest l/w number (66.66 l/w)

Least efficient is smalles l/w ( 13.33 l/w)

w= width

l= 2w + 5    (given)

circumference =  2 x w + 2 x l

2 x w + 2 x(2w+5) = 82

2w + 4w +10 = 82

6w=72

w = 12

l = 2w + 5 = 29

12 + 12 + 29 + 29 = 82   CHECK!

So you are given    b = ka +m     then move -l

                                     k(a-l) +m

                                      ka-kl  +m

                                      (ka + m) -kl        remember we were givien ka+m = b  (see above)

                                       b - kl        equals the new 'y'

the new points would be

x,y =  ( (a-l) , (b-kl) )