A fountain is made up of two semicircles and a quarter circle. Find the perimeter of the fountain. Round your answer to the near
est tenth. The perimeter of the fountain is about a feet.
1 answer:
complete question:
A fountain is made up of two semicircles and a quarter circle. The diameter of the semicircles is 10 ft. Find the perimeter of the fountain. Round your answer to the nearest tenth. The picture is represented below.
Answer:
The perimeter of the fountain = 47.1 ft
Step-by-step explanation:
The fountain has 2 semi circle from a smaller circle with the diameter represented as 10 ft and a quarter circle from a bigger circle with the radius equals to 10 ft.
The perimeter is the distance around the fountain.The perimeter is the circumference in circular perspective. Therefore,
perimeter for a full circle = 2πr
Half circle = 2πr/2 = πr
For 2 half circle = πr + πr = 2πr
For 2 half circle = 2πr
r = 10/2 = 5
perimeter for 2 half circle = 2 × 5 × 3.14 = 31.4 ft
Perimeter for the quarter circle
r = 10 ft
Quarter circle perimeter = 1/4 × 2πr = πr/2
Quarter circle perimeter = (3.14 × 10)/2
Quarter circle perimeter = (31.4)/2
Quarter circle perimeter = 15.7 ft
The perimeter of the fountain = 15.7 ft + 31.4 ft = 47.1 ft
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Answer:
- f(x) = 34.59 +3.74x
- 0.96
- very strong
- 8.93
Step-by-step explanation:
1. The selection of answers offers a choice of positive or negative slope, a slope of about 4 or about 35, and y-intercepts from the same set of values.
If you consider a couple of points (at the ends of the domain is usually a good choice), you see the slope is about 4 and the y-intercept is around 30.
For example, the points (5, 50) and (15, 91) have a slope of (91-50)/(15-5) = 4.1 so will give rise to the equation ...
y -50 = 4.1(x -5)
Filling in x=0 gives y = 50 -20.5 = 29.5
So, the nearest of the offered choices is ...
f(x) = 34.59 +3.74x
Please note that no calculator is involved. We simply estimated the parameters of the regression line based on a couple of the data points. This estimate is sufficient to allow us to find the correct answer choice.
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2. If we look at a few other data points, we see that they have a generally upward trend that matches the above equation pretty well. That suggests a very high value of correlation, so the appropriate choices would be 0.93 or 0.96. Of course, the correlation is positive, matching the sign of the slope of the regression line. (Since the data points do not fall exactly on a line, the correlation is not 1.00. My assessment is they fall close enough to the line to rate a correlation of .96 instead of .93.)
At this point, the output of your calculator can confirm that the correlation coefficient is closer to 0.96. Mine says r = 0.9624.
r = 0.96
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3. We have already determined by examining the data points that the correlation is "very strong." The correlation coefficient of 0.96 confirms this.
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4. Using the equation of part 1, we can find the number of study hours:
68 = 34.59 +3.74x
(68 -34.59)/3.74 = x ≈ 8.933
We expect a score of 68 is associated with about 8.93 study hours.
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Please note that we have used very little calculation to determine the answers to this question. The only requirement is a general understanding of what linear regression and correlation coefficients mean.
