The starting weight of the radioactive isotope = 96 grams
Weight after one hour is half of the starting weight. So the weight of the radioactive isotope after 1 hour = 48 grams
After 2 hours the weight is half as compared to the weight after previous hour. So weight after 2 hours = 24 grams.
This means, after every hour the weight is being halved. The half life of radioactive isotope is one hour.
Since after every hour, the weight is being halved, the weight of the isotope can be modeled by an exponential equation.
So,
Initial Weight = W₁ = 96
Change factor = 1/2 = 0.5
The general equation of the sequence will be:
Here t represents the number of hours. Using various values of t we can find the weight of the radioactive isotope at that time.
We can plot the sequence using the above equation. The graph is attached below.
Answer:
the answer is A. 10/8 cubic in.
Step-by-step explanation:
V = LWH
length is 2 (1/3 in)
width is 3 (1/3 in)
height is 5 (1/3 in)
V = 2/3 in * 3/3 in * 5/3 in.
V = 10/9 cubic in.
If signs are different you subtract. So 2.5- -1.25 equals 1.25 and keep the sign of the biggest number
Tan(angle) = opposite/adjacent
tan(x) = 90/51
x = arctan(90/51)
x = 60.461217740442
which rounds to 60 when rounding to the nearest whole number
Answer: 60
A) zeroes
P(n) = -250 n^2 + 2500n - 5250
Extract common factor:
P(n)= -250 (n^2 - 10n + 21)
Factor (find two numbers that sum -10 and its product is 21)
P(n) = -250(n - 3)(n - 7)
Zeroes ==> n - 3 = 0 or n -7 = 0
Then n = 3 and n = 7 are the zeros.
They rerpesent that if the promoter sells tickets at 3 or 7 dollars the profit is zero.
B) Maximum profit
Completion of squares
n^2 - 10n + 21 = n^2 - 10n + 25 - 4 = (n^2 - 10n+ 25) - 4 = (n - 5)^2 - 4
P(n) = - 250[(n-5)^2 -4] = -250(n-5)^2 + 1000
Maximum ==> - 250 (n - 5)^2 = 0 ==> n = 5 and P(5) = 1000
Maximum profit =1000 at n = 5
C) Axis of symmetry
Vertex = (h,k) when the equation is in the form A(n-h)^2 + k
Comparing A(n-h)^2 + k with - 250(n - 5)^2 + 1000
Vertex = (5, 1000) and the symmetry axis is n = 5.