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.
3a + b = 54
Substitute b for 9
3a + 9 = 54
Subtract 9 to both sides
3a = 45
Divide 3 to both sides
a = 15
Hey there!
I believe your answer would be a transformation, and not a translation.
A transformation is an operation that moves, flips, or otherwise changes a figure to create a new figure.
Hope this helps!
Have a wonderful day! :)
105/7=15
so you will have to read 15 pages per day
Answer:
1330.5 cm³
Step-by-step explanation:
The volume of a cylinder is: V = πr²h
Substitute the values for those variables.
V = π(5.5)²(14)
V = π(30.25)(14)
V = 1330.5
