Answer:
If you have a quantity X of a substance, with a decay constant r, then the equation that tells you the amount of substance that you have, at a time t, is:
C(t) = X*e^(-r*t)
Now, we know that:
We have 2000g of substance A, and it has a decay constant of 0.03 (i assume that is in 1/year because the question asks in years)
And we have 3000 grams of substance B, with a decay constant of 0.05.
Then the equations for both of them will be:
Ca = 2000g*e^(-0.03*t)
Cb = 3000g*e^(-0.05*t)
Where t is in years.
We want to find the value of t such that Ca = Cb.
So we need to solve:
2000g*e^(-0.03*t) = 3000g*e^(-0.05*t)
e^(-0.03*t) = (3/2)e^(-0.05*t)
e^(-0.03*t)/e^(-0.05*t) = 3/2
e^(t*(0.05 - 0.03)) = 3/2
e^(t*0.02) = 3/2
Now we can apply Ln(x) to both sides, and get:
Ln(e^(t*0.02)) = Ln(3/2)
t*0.02 = Ln(3/2)
t = Ln(3/2)/0.02 = 20.3
Then after 20.3 years, both substances will have the same mass.
Answer: 166 laptops
Step-by-step explanation:
From the question, each laptop costs $1350;
Number of laptops = $225000/1350
= 166.667
1) this is simply solving it, so if you divide 16 by 3, you end up getting 5 1/3
2) 3 1/2, by multiplying 7 by 1/2
3) 224, by multiplying 14 by 16
4) 54 mph, by dividing 324 by 6
5) blue, because only the 1/4 ribbon color would be collected after 3/4 mile
6) 7/8 - 3/8 equals 4/8, or 1/2 when simplified
I think it would be 35 combinations but I may be wrong
8 - 11 = -3. The square root of 25/121 = (the square root of 25) / (the square root of 121) = 5/11 . -3 x 5/11 = -3/1 x 5/11 = (-3 x 5) / (1 x 11) = (-15)/11 = -15/11.
