Find the loss in the value of diamond worth $10872 when it broke into 3 pieces with wt ratio as 1:2:3 and the value of each respective piece being proportional to the square of the of its wt?
2006-06-25 23:51:59 · 6 answers · asked by ved_vishwa 2 in Science & Mathematics ➔ Mathematics
Let the weight of the original piece be y and the weight of the smallest piece be x. Then x + 2x + 3x=y → 6x=y → x=y/6. If K is our constant of proportionality, then Ky²=10872 and the value of our three smaller pieces is K((y/6)²+(2y/6)²+(3y/6)²). Simplifying, this is K(y²/36+4y²/36+9y²/36) or (14/36)Ky². Substituting, we get the value of our pieces as (14/36)10872 which is 4228. $10872-$4228 is $6644, thus the value dropped by $6644 when you dropped it.
2006-06-26 00:38:22 · answer #1 · answered by Pascal 7 · 1⤊ 0⤋
If the smallest piece has a weight of one unit (this is arbitrary) the total weight was 6 units, so the square was 36 square units.
The pieces are 1, 2, and 3 units, so the squares are 1,4,and 9, for a total of 14 square units.
The value per square unit is $10872/36 square units=$302/square unit.
36-14=22 square units were lost, which would have a value of $302/square unit*22square units= $6644.
2006-06-26 07:52:32 · answer #2 · answered by manda 4 · 0⤊ 0⤋
I think no loss occurs if you do calculations to the third decimal place but if it is done with less decimal places, there may be a loss or profit may occur due to rounding off of the figures.
2006-06-26 07:10:36 · answer #3 · answered by james 1 · 0⤊ 0⤋
too much loss
2006-06-26 06:57:57 · answer #4 · answered by who am i ? 1 · 0⤊ 0⤋
loss is wort $7852
2006-06-26 07:02:28 · answer #5 · answered by monu 1 · 0⤊ 0⤋
dont know........
2006-06-26 06:57:40 · answer #6 · answered by kris 2 · 0⤊ 0⤋