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3 years ago

The circle below is centered at the point (3,1) and has a radius of length 2. What is its equation?

Mathematics

2 answers:

Orlov [11]3 years ago

6 0

Answer:

The correct option is B.

Step-by-step explanation:

The standard form of the circle is

$(x-h)^2+(y-k)^2=r^2$

Where, (h,k) is the center of the circle and r is the radius of the circle.

It is given that the center of the circle is (3,1) and the radius of the circle is 2.

The equation of the circle is

$(x-3)^2+(y-1)^2=2^2$

This equation is represents by option B, therefore option B is correct.

Paul [167]3 years ago

3 0

It is letter B.
Equation of a circle is in the form:
(x-h)^2 + (y-k)^2 = r^2
where (h,k) is the center of the circle with radius r.

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3 years ago

Miguel is a golfer, and he plays on the same course each week. The following table shows the probability distribution for his sc

aivan3 [116]

1) 4.55

2) Short hit

Step-by-step explanation:

The table containing the score and the relative probability of each score is:

Score 3 4 5 6 7

Probability 0.15 0.40 0.25 0.15 0.05

Here we call

X = Miguel's score on the Water Hole

The expected value of a certain variable X is given by:

$E(X)=\sum x_i p_i$

where

$x_i$ are all the possible values that the variable X can take

$p_i$ is the probability that $X=x_i$

Therefore in this problem, the expected value of MIguel's score is given by:

$E(X)=3\cdot 0.15 + 4\cdot 0.40 + 5\cdot 0.25 + 6\cdot 0.15 + 7\cdot 0.05=4.55$

In this problem, we call:

X = Miguel's score on the Water Hole

Here we have that:

- If the long hit is successfull, the expected value of X is

$E(X)=4.2$

- Instead, if the long hit fails, the expected value of X is

$E(X)=5.4$

Here we also know that the probability of a successfull long hit is

$p(L)=0.4$

Which means that the probabilty of an unsuccessfull long hit is

$p(L^c)=1-p(L)=1-0.4=0.6$

Therefore, the expected value of X if Miguel chooses the long hit approach is:

$E(X)=p(L)\cdot 4.2 + p(L^C)\cdot 5.4 = 0.4\cdot 4.2 + 0.6\cdot 5.4 =4.92$

In part 1) of the problem, we saw that the expected value for the short hit was instead

$E(X)=4.55$

Since the expected value for X is lower (=better) for the short hit approach, we can say that the short hit approach is better.

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2 years ago

What is the perimeter of ΔABC?

Serggg [28]

Answer:

Choice D: Perimeter = 5 + $\sqrt{65}$ + $\sqrt{34}$ units

Step-by-step explanation:

point B(9, 2) , point C(4, 5), point A (1,1)

Perimeter = D( A, C) + D (A, B) + D (B, C)

where D (A, C) = distance between A and C

so...

D(A, C) = root ( (4 - 1)^2 + (5 - 1)^2) = 5 from a 3-4-5 right triangle.

D(A, B) = root( (9- 1)^2 + (2 -1)^2) = root( 64 + 1) = root(65)

D(B, C) = root( (9 -4)^2 + (2 -5)^2) = root (25 + 9) = root(34)

Perimeter = 5 + root(65) + root(34)

Perimeter = 5 + $\sqrt{65}$ + $\sqrt{34}$ units

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3 years ago