A student working on a report about mathematicians decides to find the 98% confidence interval for the difference in mean age at
1 answer:
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Answer:
a) Figure attached
b) For this case we just need to see what is the value of the function when x tnd to infinity. As we can see in our original function if x goes to infinity out function tend to 1000 and thats our limiting size.
c)
And if we find the derivate when t=1 we got this:
And if we replace t=10 we got:
d)
And then:
Step-by-step explanation:
Assuming this complete problem: "A lake is stocked with 500 fish, and the population increases according to the logistic curve p(t) = 10000 / 1 + 19e^-t/5 where t is measured in months. (a) Use a graphing utility to graph the function. (b) What is the limiting size of the fish population? (c) At what rates is the fish population changing at the end of 1 month and at the end of 10 months? (d) After how many months is the population increasing most rapidly?"
Solution to the problem
We have the following function
(a) Use a graphing utility to graph the function.
If we use desmos we got the figure attached.
(b) What is the limiting size of the fish population?
For this case we just need to see what is the value of the function when x tnd to infinity. As we can see in our original function if x goes to infinity out function tend to 1000 and thats our limiting size.
(c) At what rates is the fish population changing at the end of 1 month and at the end of 10 months?
For this case we need to calculate the derivate of the function. And we need to use the derivate of a quotient and we got this:
And if we simplify we got this:
And if we simplify we got:
And if we find the derivate when t=1 we got this:
And if we replace t=10 we got:
(d) After how many months is the population increasing most rapidly?
For this case we need to find the second derivate, set equal to 0 and then solve for t. The second derivate is given by:
And if we set equal to 0 we got:
And then:
Answer:
An equation of the line that passes through the point (6, − 2) and is perpendicular to the line will be:
Step-by-step explanation:
We know that the slope-intercept form of the line equation is
y=mx+b
where m is the slope and b is the y-intercept.
Given the line
6x+y=2
Simplifying the equation to write into the slope-intercept form
y = -6x+2
So, the slope = -6
As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line.
Thus, the slope of the perpendicular line will be: -1/-6 = 1/6
Therefore, an equation of the line that passes through the point (6, − 2) and is perpendicular to the line will be
substituting the values m = 1/6 and the point (6, -2)
subtract 2 from both sides
Therefore, an equation of the line that passes through the point (6, − 2) and is perpendicular to the line will be:
I hope this helps you
