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Zolol [24]
3 years ago
5

A circle is entered on the point (-1,5) and contains the point (7,11). What is the area of this circle?

Mathematics
1 answer:
bezimeni [28]3 years ago
8 0

The answer is 100.

<u>Step-by-step explanation</u>:

<u>Given</u>:

A circle is centered on the point(-1,5) and contains the point(7,11)

<u>To find</u>:

Area of a circle.

<u>Formula</u>:

(x – a)2 + (y – b)2 = r2

<u>Solution</u>:

D(A,B)=√ (xa − xb)2 + (ya − yb)2

D(A,B)=√ (7 + 1 )2 + (11− 5)2

D(A,B)=√ (8 )2 + (6)2

D(A,B)=√ 100

D(A,B)=10

Substituting in the above equation

(x + 1 )2 + (y – 5)2 = 100

                                                                                     

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We are given the number of hurricanes that occurred in each year in a certain region.

8 9 8 7 9 15 5 6 8 4 12 7 8 2

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The range of the data set is found by

Range = Maximum value - minimum value

The maximum value in the data set is 15

The minimum value in the data set is 2

Range = 15 - 2

Range = 13

Variance:

To find the variance, first compute the mean of the data set.

Mean = Sum/n

Mean = (8+9+8+7+9+15+5+6+8+4+12+7+8+2)/14

Mean = 108/14

Mean = 7.714

The variance is given by

σ² = (x - mean)²/(n - 1)

σ² = (8 - 7.714)² + (9 - 7.714)²+ (8 - 7.714)² + (7 - 7.714)² + (9 - 7.714)² + (15 - 7.714)² + (5 - 7.714)² + (6 - 7.714)² + (8 - 7.714)² + (4 - 7.714)² + (12 - 7.714)² + (7 - 7.714)² + (8 - 7.714)² + (2 - 7.714)²/(14 - 1)

σ² = 10.22

Standard deviation:

The standard deviation of the data set is given by

σ² = √σ

σ² = √10.22

σ² = 3.20

Since this data is time-series therefore, the measures of variation do not reveal anything about the pattern of hurricanes over time.

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