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.
The answer to the question is √3(−n+36)
Answer:
my answer is A. you only need substitute n from 1 to 4
Answer:
8:1
Step-by-step explanation:
the actual table's height in inches is 4*12 = 48 inches.
48/6 = 8
so the ratio is 8:1.
3)The original rational number was 17/12.
4)The age of Ruby and Reshma are 20 and 28 years respectively.
Explanation:
3)Let the numerator be x.
So denominator will be (x - 5)
If we add 5 to numberator then it will be (x + 5)
New number is (x + 5)/(x - 5)=11/6
Solve for X by cross multiplying
6(x + 5)=11(x - 5)
6x + 30=11x - 55
5x=85
x=17
So original rational number was 17/12.
4)The ages of Ruby and Reshma are in the ratio 5:7
So, let the present ages of Ruby and Reshma be 5x and 7x respectively.
Also, it is given that four years from now the ratio of their ages will be 3:4
So, the equation - 5x + 4 / 7x + 3 = 3/4
⇒4(5x+4)=3(7x+4)
⇒20x+16=21x+12
⇒21x−20x=16−12
⇒x=4
⇒5x=20 and 7x=28
The age of Ruby and Reshma are 20 and 28 years respectively.
