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grandymaker [24]
3 years ago
13

A circle with center at (12,−1) passes through (0,−1). Find the circumference and area of the circle in terms of p.

Mathematics
1 answer:
madreJ [45]3 years ago
6 0

Answer:

C = 75.36

A = 452.16

Step-by-step explanation:

Find the radius r by finding the distance between (12,-1) and (0,-1) using the distance formula.

d = \sqrt{(12-0)^2 + (-1--1)^2} =\sqrt{(12)^2 + (0^2} =\sqrt{144+0} =\sqrt{144}=12

The radius is 12.

So the circumference of the circle is C = 2\pi r = 2\pi 12 = 24\pi = 75.36

So the area of the circle is A = \pi r^2\\A = \pi 12^2\\A = 144\pi\\A = 452.16

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A club with five members will randomly select the president and vice president. Each possible pair will be assigned an equal por
Tju [1.3M]

Answer:

C. 20

Step-by-step explanation:

The order in which the members are selected is important. The first one selected is the president and the second is the vice president.

So we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

P_{(n,x)} = \frac{n!}{(n-x)!}

In this problem:

2 people are going to be chosen from a set of 5. So

P_{(5,2)} = \frac{5!}{(5-2)!} = 20

So the correct answer is:

C. 20

3 0
3 years ago
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Mashutka [201]

Answer:

The altitude will begin at angle D and go in a straight line downwards.

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7 0
2 years ago
Find the value of the variable.
nalin [4]

Answer:

The variable, y is 11°

Step-by-step explanation:

The given parameters are;

in triangle ΔABC;          {}              in triangle ΔFGH;

Segment \overline {AB} = 14         {}               Segment \overline {FG} = 14

Segment \overline {BC} = 27         {}              Segment \overline {GH} = 19

Segment \overline {AC} = 19         {}               Segment \overline {FH} = 2·y + 5

∡A = 32°                       {}                ∡G = 32°

∡A = ∠BAC which is the angle formed by segments \overline {AB} = 14 and \overline {AC} = 19

Therefore, segment \overline {BC} = 27, is the segment opposite to ∡A = 32°

Similarly, ∡G = ∠FGH which is the angle formed by segments \overline {FG} = 14 and \overline {GH} = 19

Therefore, segment \overline {FH} = 2·y + 5, is the segment opposite to ∡A = 32° and triangle ΔABC ≅ ΔFGH by Side-Angle-Side congruency rule which gives;

\overline {FH} ≅ \overline {BC} by Congruent Parts of Congruent Triangles are Congruent (CPCTC)

∴ \overline {FH} = \overline {BC} = 27° y definition of congruency

\overline {FH} = 2·y + 5 = 27° by transitive property

∴ 2·y + 5 = 27°

2·y = 27° - 5° = 22°

y = 22°/2 = 11°

The variable, y = 11°

8 0
2 years ago
A website offers a coupon such that each customer has a
sweet-ann [11.9K]

Answer:

62.29%

Step-by-step explanation:

The probability of Aya being offered a coupon on at least one of the six days she visits the website is 100% minus the probability that she is not offered a coupon on any of the six days, which is described by a binomial probability with zero successes in six trials with a probability of succes p = 0.15.

P = 1 - (\frac{6!}{(6-0)!0!}* p^0*(1-p)^{6-0})\\P = 1 - (1* 1*(1-0.15)^{6})\\P=0.6229=62.29\%

The probability that Aya will be offered a coupon on at least one of the days she visits the website is 62.29%.

8 0
3 years ago
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Someone please help me with this problem
Greeley [361]

Answer:

corresponding

Step-by-step explanation:

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