Answer: Initially, he had 27 sweets.
Step-by-step explanation: The most logical approach is to work backwards from what remained after the third day to the start of the first day.
On the third day, he consumed one-third of his sweets and was left with 8. If we let the total sweets on day three be denoted as a, then one-third of a equals what he ate and the two-thirds left equals 8, giving us:
8/a = 2/3
By cross-multiplying, we find:
8 x 3 = 2a
Therefore, 24 = 2a
This leads to a = 12.
Let the sweets on day two be represented as b. If he consumed one-third of b and was left with 12, we have the same structure; hence:
12/b = 2/3
Cross-multiplying gives:
12 x 3 = 2b
So, 36 = 2b, leading to b = 18.
Denote the number of sweets on day one as x. If one-third of x was eaten and 18 remained, we can set up the equation:
18/x = 2/3
Again, cross-multiplying results in:
18 x 3 = 2x
Which simplifies to 54 = 2x, yielding x = 27.
Thus, Tim received 27 sweets at the start.
A.) P(t) = P0e^(kt)
P(20/60) = 40 e^(20k/60)
80 = 40 e^(k/3)
e^(k/3) = 80/40 = 2
k/3 = ln(2)
k = 3ln(2)
b.) P(8) = 40(2)^24 = 40(16777216) = 671088640 cells
d.) Rate of change = e^(8k) = e^(8(3ln(2))) = e^(24ln(2)) = e^(16.6355) = 16777216 cells/hour
e.) P(t) = 40(2)^(3t); t in hours
1,000,000 = 40(8)^t
25,000 = 8^t
ln(25,000) = t ln(8)
t = ln(25,000)/ln(8) = 4.87 hours
Answer:
The ratio comparing the volume of a cone to that of a cylinder is 
Step-by-step explanation:
According to the provided information
The formula for the volume of a cone is described as
The expression for the volume of a cylinder can be given as
Thus, the ratio we seek to find is
This is achievable since both the height and base
radius remain identical
1,107 cc
The scanning consists of 10 intervals:
[0,1.5), [1.5,3), [3,4.5), [4.5,6), [6,7.5), [7.5,9), [9,10.5), [10.5,12), [12,13.5), [13.5,15)
To estimate the volume using the Midpoint Rule, n should be set to 10.
Given that we will use n=5, we will split the range [0,15] into five intervals of lengths 3 each:
[0,3], [3,6], [6,9], [9,12], [12,15] and calculate their midpoints:
1.5, 4.5, 7.5, 10.5, and 13.5.
Next, we will determine the volume V from the five cylinders, where each has a height h=3 and the base area A corresponds to the calculated midpoints' intervals:
Cylinder 1
Midpoint=1.5, corresponding to the 2nd interval
A = 18, V= height * area of the base = 18*3 = 54 cc
Cylinder 2
Midpoint=4.5, corresponding to the 4th interval
A = 78, V= height * area of the base = 78*3 = 234 cc
Cylinder 3
Midpoint=7.5, corresponding to the 6th interval
A = 106, V= height * area of the base = 106*3 = 318 cc
Cylinder 4
Midpoint=10.5, corresponding to the 8th interval
A = 129, V= height * area of the base = 129*3 = 387 cc
Cylinder 5
Midpoint=13.5, corresponding to the 10th interval
A = 38, V= height * area of the base = 38*3 = 114 cc
Thus, the estimated volume is
54 + 234 + 318 + 387 + 114 = 1,107
