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.
Area of base is Circumference x 
or A = 25 x
A = 78.53981
Volume = Area of Base x Height or V = 78.53981 x 8
V = 628.32 Units
The volume of the cylinder is 628.32 units
Answer:
either a. or c. I hope it helps
Step-by-step explanation:
because half of 64 is 32
Answer:
The answer is B. 5/8 quarts
Step-by-step explanation:
1 ounce is equal to .03125 quarts so to find the amount of quarts, you multiply 20 times .03125 to get .625 or 5/8.
Answer:
x = 4/7
Step-by-step explanation:
x^3 = 64/ 343 // - 64/ 343
x^3 - ( 64/ 343 ) = 0
x^3 - 64 / 343 = 0
1*x^3 = 64/ 343 // : 1
x^3 = 64/ 343
x^3 = 64/ 343 // ^ 1/3
x = 4/ 7
