Look at the black points on the graph. Fill in the
2 answers:
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Answer:
FH ~ 10.02
Step-by-step explanation:
1. Approach
One should first find the circumference of the given circle. Then one should find how large the fraction of the circumference one is supposed to find is. Finally, one should multiply the fraction of the circumference one is supposed to find by the total circumference.
2. Circumference of the circle
The formula for circumference is;
π
Substitute in the given values;
It is given that the radius is, hence
2 (7) π
14π
3. Find the fraction of the circumference one is supposed to find
It is given that the angles over the measure of the total degrees of angles in a circle are equal to the arc surrounding the angles of the circumference. Essentially;
Substitute in the given information and solve;
arc =
arc =
arc ~ 10.02
Answer:
A) The expression for the number of bacteria is .
B) After 5 hours there will be 19593 bacteria.
C) After 5.55 hours the population of bacteria will reach 30000.
Step-by-step explanation:
A) Here we have a problem with differential equations. Recall that we can interpret the rate of change of a magnitude as its derivative. So, as the rate change proportionally to the size of the population, we have
where stands for the population of bacteria.
Writing as
, we get
.
Notice that this is a separable equation, so
.
Then, integrating in both sides of the equality:
.
We have,
.
Now, taking exponential
.
The next step is to find the value for the constant . We do this using the initial condition
. Recall that this is the initial population of bacteria. So,
.
Hence, the expression becomes
.
Now, we find the value for . We are going to use that
. Notice that
.
Then,
.
Taking logarithm
, so
.
So, , and approximating to the fourth decimal place we can take
. Hence,
.
B) To find the number of bacteria after 5 hours, we only need to evaluate the expression we have obtained in the previous exercise:
.
C) In this case we want to do the reverse operation: we want to find the value of t such that
.
This expression is equivalent to
.
Now, taking logarithm we have
.
Finally,
.
So, after 5.55 hours the population of bacteria will reach 30000.