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:
Step-by-step explanation:
p and h are number of plumbers and helpers, respectively.
Twenty workers earn a total of $2600
p+h = 20
h = 20-p
160p + 100h = 2600
160p + 100(20-p) = 2600
60p = 600
p = 10
h = 20-p = 10
Ten plumbers and ten helpers.
Multiply 5.2 x 30 and you get 156 miles
Answer:
= 40/3 = 13 1/3
Step-by-step explanation:
8/1 ÷ 3/5 = 8/1 x 5/3
8 x 5 = 40
1 x 3 = 3
= 40/3 = 13 1/3
In mathematics, 'is' would be the equal sign. And 'of' would be the multiplcation sign. The missing number would be any variable.
56 is 28% of a number would be translated algebraically to:
Solving for x, we get:
Divide 28 on both sides
Multiply 100 on both sides
56 is 28% of 200
