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3 years ago

A circle is centered at the point (5, -4) and passes through the point (-3, 2).

Mathematics

1 answer:

Sedbober [7]3 years ago

8 0

Answer:

The equation of the circle is (x + -5)² + (y + 4)² = 100

Step-by-step explanation:

* Lets revise the standard form of the equation of the circle

- If the center of the circle is point (h , k) and the length of its radius is r,

then the equation of the circle is (x - h)² + (y - k)² = r² in standard form

* Now lets solve the problem

- The center of the circle is point (5 , -4)

∴ h = 5 and k = -4

∴ The equation of the circle is (x - 5)² + (y - -4)² = r²

∴ The equation of the circle is (x - 5)² + (y + 4)² = r²

- The circle passes through the point (-3 , 2)

- To find r substitute the x-coordinate and the y-coordinate of the

point in the equation of the circle

∵ Point (-3 , 2) is on the circle

∴ x = -3 and y = 2

∴ (-3 - 5)² + (2 + 4)² = r² ⇒ simplify it

∴ (-8)² + (6)² = r² ⇒ solve power 2

∴ 64 + 36 = r² ⇒ add the like terms

∴ 100 = r²

∵ The equation of the circle is (x - 5)² + (y + 4)² = r²

∴ The equation of the circle is (x - 5)² + (y + 4)² = 100

- To complete the form

∴ The equation of the circle is (x + -5)² + (y + 4)² = 100

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garri49 [273]

Answer:

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3 years ago

Wayne Gretsky scored a Poisson mean six number of points per game. sixty percent of these were goals and forty percent were assi

BartSMP [9]

Answer:

a) The mean for the total revenue he earns per game is of 13.2K while the standard deviation is of 3.63K.

b) 0.05 = 5% probability that he has four goals and two assists in one game

Step-by-step explanation:

In hockey, a point is counted for each goal or assist of the player.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval. The standard deviation is the square root of the mean.

(a) Find the mean and standard deviation for the total revenue he earns per game.

60% of six are goals, which means that 60% of the time he earned 3K.

40% of six are goals, which means that 40% of the time he earned 1K.

The mean is:

$\mu = 6*0.6*3 + 6*0.4*1 = 13.2$

The standard deviation is:

$\sigma = \sqrt{\mu} = \sqrt{13.2} = 3.63$

The mean for the total revenue he earns per game is of 13.2K while the standard deviation is of 3.63K.

(b) What is the probability that he has four goals and two assists in one game

Goals and assists are independent of each other, which means that we find the probability P(A) of scoring four goals, the probability P(B) of getting two assists, and multiply them.

Probability of four goals:

60% of 6 are goals, which means that:

$\mu = 6*0.6 = 3.6$

The probability of scoring four goals is:

$P(A) = P(X = 4) = \frac{e^{-3.6}*(3.6)^{4}}{(4)!} = 0.19122$

Probability of two assists:

40% of 2 are assists, which means that:

$\mu = 6*0.4 = 2.4$

The probability of getting two assists is:

$P(B) = P(X = 2) = \frac{e^{-2.4}*(2.4)^{2}}{(2)!} = 0.26127$

Probability of four goals and two assists:

$P(A \cap B) = P(A)*P(B) = 0.19122*0.26127 = 0.05$

0.05 = 5% probability that he has four goals and two assists in one game

5 0

3 years ago

Dude this should be so easy but this is going in one ear and out the other how do I do this send help

kipiarov [429]

Answer:

0.5 hours

Explanation:

Given:

speed: 17 miles/hour

distance: 8 miles

Formula:

time taken = distance ÷ speed

Solve:

time taken = 8 ÷ 17 = 0.4706 ≈ 0.5 hours (rounded to nearest tenth)

6 0

2 years ago

In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving that lines

ohaa [14]

Answer:

See the proof.

Step-by-step explanation:

Statement   Reason

1.∠1 and ∠2 are supplementary angles --- Given

2. m∠1 + m∠2 = 180° --- Linear pair, they are supplementary

3. m∠1 and m∠3 are supplementary angles -- m∠1 + m∠3= 180

(Supplementary angles add upto 180 degrees)

4. m∠1 and m∠3 ------ Exterior sides in opposite rays

5. m∠1 + m∠2 = m∠1 + m∠3 ------ Transitive property

6. m∠2 = m∠3 -------------- Subtraction property

7. l || m ------------- If two lines are cut by transversal the alternative interior

angles are the same, then the lines are paralle.

Thank you.

4 0

3 years ago

3. The matrices show the enrollment of boys and girls on the basketball, lacrosse, and soccer teams in two towns. Town A Town B

bazaltina [42]

(a). The element a₂₁ is the number of boys enrolled in Lacrosse.

(b). The address is a₁₂.

(c). [196 174]
[136 169]
[214 242]

(d). The matrix represents the number of boys and girls from towns A and B enrolled in different sports classes.

(e). 1.125 A = [108 90 ]
[72 99 ]
[117 135]

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3 years ago