The triangles legs are 5 and 12 y (via pythagorean theorem ) = 13 cm
origianl area of rectangle was 15 x 20 = 300 cm2
less the triangle 300 - 1/2 *5*12 = x = 270 cm2
Maximum value of y occus at the vale of x = - b/2a a = -2 b = 8
put this value of 'x' in the equation to calculate the max value (y) =.......
240 boxes / ( 30 box/min + 20 box/min) = 240 / 50 min = 4.8 min = 288 seconds
slope, m , between the two points (y1-y2) / (x1-x2) = -2
perpindicular slope would be - 1/m = 1/2
60 x + 72 (1-x) = 70 (1)
- 12x = -2
x = 1/6 per kilo of x 5/6 per kilo of y
ratio x:y = 1:5
216 x 66 = 6 (6x)
36 x 66 = 6x
62 x66
68 = 6x x = 8
The minimum ocurrs at x = 0 y = -3
two units left means x = -2 three units down means y = -6
Using law of sines
2/ sin45 = x/sin60
sin60 * 2/sin45 = x
sqrt3 / (sqrt2/2) = x
x = 2 sqrt3 / sqrt2 = ~ 2.4494897
x6 = 1/93 = 1/729 = 1/36
Take 6th root of both sides
x = 1/ 3 (for the positive root x >0)
He starts with 1/3
eats 5/8
He has 1/3 x 3/8 left = 3/24
he eats 2/5 of this 2/5 x 3/24 = 6/72 = 1/ 12 for dinner
