matt is standing on top of a cliff 305 feet above a lake. The measurement of the angle of depression to a boat on a lake is 42 d
egrees. how far is the boat from matt
1 answer:
Answer:
So, the distance from boat to matt is 455.81535feet
Step-by-step explanation:
We are given height of a cliff is 305 feet
and the measurement of the angle of depression to a boat on a lake is 42 degrees
so, we can draw diagram
Let's assume
distance from boat to matt is x
We can use trig
now, we can solve for x
So, the distance from boat to matt is 455.81535feet
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Answer:
a)
b)
c)
Step-by-step explanation:
1) Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
2) Part a
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability on this way:
3) Part b
From the central limit theorem we know that the distribution for the sample mean is given by:
And using a calculator, excel or the normal standard table we have that:
4) Part c
And using a calculator, excel or the normal standard table we have that:
Answer:
Part A)
A reasonable domain to plot the growth function is:
Part B)
The <em>y-</em>intercept represents that when the biologist started her study, the radius of the algae was five millimeters.
Part C)
The average rate of change from <em>d</em> = 4 to <em>d</em> = 11 was about 0.11. This means that from the 4th day to the 11th, the radius of the algae grew, on average, at a rate of 0.11 mm per day.
Step-by-step explanation:
The radius of the algae f(d) in millimeters after <em>d</em> days is given by the function:
Part A)
We know that the radius of the algae was approximately 6.34 mm when the biologist concluded her study. To find the reasonable domain, we can substitute 6.34 for f(d) and solve for <em>d</em>. Therefore:
Divide both sides by five:
Take the log of both sides with base 1.02:
Using the Change of Base Property, evaluate for <em>d: </em>
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So, the biologist concluded her study after 12 days.
Therefore, a reasonable domain to plot the growth function is:
Part 2)
The <em>y-</em>intercept of the function is when <em>d</em> = 0. Find the <em>y-</em>intercept:
Since <em>d</em> represent the amount of days after the study had begun, the <em>y-</em>intercept represents the radius of the algae on the initial day.
So, when the biologist started her study, the radius of the algae was five millimeters.
Part 3)
To find the average rate of change for a nonlinear function, we find the slope between the two endpoints on the interval.
We want to find the average rate of change of f(d) from <em>d</em> = 4 to <em>d</em> = 11.
Find the endpoints:
And find the slope between them:
Since f(d) measures millimeters and <em>d</em> measures days, this tells us that, on average, the radius of the algae grew by about 0.11 mm per day from the 4th day to the 11th day.