Answer:
1) 2 lbs
2) 0.17 lbs
3) 9.5 lbs
Step-by-step explanation:
Amount of sugar Ella has = 0.5 lbs
Let the amount of water she adds to make the solution = x lbs
So total amount of the mixture would be = (x + 0.5) lbs
Case 1: 20% syrup
20% syrup means the sugar percentage in the mixture should be 20% of the entire mixture. So, 0.5 should be 20% of (x + 0.5). In equation form this can be written as:
0.5 = 20% of (x + 0.5)
0.5 = 0.2(x + 0.5)
Dividing both sides by 0.2, we get:
2.5 = x + 0.5
x = 2 lbs
This means, 2 lbs of water should be added to make 20% syrup solution. So, total syrup she would have will be 2.5 lbs.
Case 2: 75% syrup
75% syrup means the sugar percentage in the mixture should be 75% of the entire mixture. So, 0.5 should be 75% of (x + 0.5). In equation form this can be written as:
0.5 = 75% of (x + 0.5)
0.5 = 0.75(x + 0.5)
Dividing both sides by 0.75, we get:
0.67 = x + 0.5
x = 0.17 lbs
This means, 0.17 lbs of water should be added to make 75% syrup solution. So, total syrup she would have will be 0.67 lbs.
Case 3: 5% syrup
5% syrup means the sugar percentage in the mixture should be 5% of the entire mixture. So, 0.5 should be 5% of (x + 0.5). In equation form this can be written as:
0.5 = 5% of (x + 0.5)
0.5 = 0.05(x + 0.5)
Dividing both sides by 0.05, we get:
10 = x + 0.5
x = 9.5 lbs
This means, 9.5 lbs of water should be added to make 5% syrup solution. So, total syrup she would have will be 10 lbs.
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, can be calculated as follows:![z^n = \rho^n [\cos n\theta + i \sin n\theta ]](https://tex.z-dn.net/?f=z%5En%20%3D%20%5Crho%5En%20%5B%5Ccos%20n%5Ctheta%20%2B%20i%20%5Csin%20n%5Ctheta%20%5D)
is equal to![z^3 = \rho^3 [\cos 3 \theta + i \sin 3 \theta ] = (5^3) [\cos (3 \cdot 330^{\circ}) + i \sin (3 \cdot 330^{\circ}) ]](https://tex.z-dn.net/?f=z%5E3%20%3D%20%5Crho%5E3%20%5B%5Ccos%203%20%5Ctheta%20%2B%20i%20%5Csin%203%20%5Ctheta%20%5D%20%3D%20%285%5E3%29%20%5B%5Ccos%20%283%20%5Ccdot%20330%5E%7B%5Ccirc%7D%29%20%2B%20i%20%5Csin%20%283%20%5Ccdot%20330%5E%7B%5Ccirc%7D%29%20%5D)
(1)
, (1) becomes![z^3 = 125 [\cos 270^{\circ} + i \sin 270^{\circ} ]](https://tex.z-dn.net/?f=z%5E3%20%3D%20125%20%5B%5Ccos%20270%5E%7B%5Ccirc%7D%20%2B%20i%20%5Csin%20270%5E%7B%5Ccirc%7D%20%5D)