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3 years ago

Find an equation of the circle that has center (-2, 6) and passes through (-6, 1).

Mathematics

1 answer:

Darya [45]3 years ago

8 0

Answer:

(x+2)^2 + (y-6)^2 = 41

Step-by-step explanation:

The equation for a circle is (x-h)^2+(y-k)^2=r^2

So first, it is known that the circle's center is at (-2,6), Therefore, this can be filled in:

(x+2)^2+(y-6)^2=r^2

Next, we need to find the radius, and one of the points is already known, being (-6, 1)

With this, find the distance between these two points by doing the Pythagorean Theorem, a^2+b^2=c^2. The a^2 would be the x value changed and the b^2 would be the y value changed between the two numbers. Note that this is interchangeable.

To find a:

-2 to -6 = change of 4

To find b:

6 to 1 = change of 5

Next, write out the equation for this:

4^2+5^2=c^2

16+25=c^2

41=c^2

c = √41

The radius would be √41, so the equation can now be completed. Since c will be brought to the second power, this will cancel out the square root.

(x+2)^2 + (y-6)^2 = 41

Hope that helps.

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Answer:

-4 1/4 When you subtract -3 3/8 from 7/8 you will get this answer.

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3 years ago

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3 years ago

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dsp73

Answer:

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Step-by-step explanation:

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3 years ago

Consider two competing firms in a declining industry that cannot support both firms profitably. Each firm has three possible cho

yaroslaw [1]

Answer:

a) attached below

b) ( T,T )

c) The Pure-strategy Nash equilibria are : ( N,E ) and ( E,N )

d) The mixed-strategy Nash equilibrium for Firm 1 = ( 1/3 , 0, 2/3 )

while the mixed -strategy Nash equilibrium for Firm 2 = ( 1/3 , 0, 2/3 )

Step-by-step explanation:

A) write down the game in matrix form

let: E = exit at the industry immediately

T = exit at the end of the quarter

N = exit at the end of the next quarter

matrix is attached below

B) weakly dominated strategies is ( T,T )

C) Find the pure-strategy Nash equilibria

The Pure-strategy Nash equilibria are : ( N,E ) and ( E,N )

D ) Find the unique mixed-strategy Nash equilibrium

The mixed-strategy Nash equilibrium for Firm 1 = ( 1/3 , 0, 2/3 )

while the mixed -strategy Nash equilibrium for Firm 2 = ( 1/3 , 0, 2/3 ) since T is weakly dominated then the mixed strategy will be NE

Assume that P is the probability of firm 1 exiting immediately ( E )

and q is the probability of firm 1 staying till next term ( N ) ∴ q = 1 - P.

hence the expected utility of firm 2 choosing E = 0 while the expected utility of choosing N = 4p - 2q .

The expected utilities of E and N to firm 2 =

0 = 4p - 2q = 4p - 2 ( 1-p) = 6p -2 which means : p = 1/3 , q = 2/3

4 0

2 years ago

A jar contains 8 red marbles numbered 1 to 8 and 7 blue marbles numbered 1 to 7. A marble is drawn at random from the jar. Find

Shkiper50 [21]

Answer:

Therefore the probability that the marble is blue or even numbered is $\frac{11}{15}$

Step-by-step explanation:

Probability: The ratio of favorable outcomes to the total outcomes.

It is denoted by P.

$Probability= \frac{\textrm{favorable outcomes}}{\textrm{Total outcomes}}$

Given that a jar contains 8 red marbles and 7 blue marbles.

Total number of marbles = (8+7) = 15

Let A = Event of getting a blue marble

B= Event of getting of even marble.

Even number blue marbles are 2, 4,6

Even number red marbles are 2, 4,6,8

The number of even marbles are =(3+4)=7

The probability of getting a blue marble is P(A)

$=\frac{\textrm{Total number of blue marbles}}{\textrm{Total number of blue marbles}}$

$=\frac{7}{15}$

The probability of getting a even marble is P(B)

$=\frac{\textrm{The number of even number marbles}}{\textrm{Total number of marbles}}$

$=\frac{7}{15}$

The probability of getting a even numbered blue marble P(A∩B)

$=\frac{3}{16}$

P(blue marble or even- numbered)

=P(A∪B)

=P(A)+P(B)-P(A∩B)

$=\frac{7}{15} +\frac{7}{15}-\frac{3}{15}$

$=\frac{11}{15}$

Therefore the probability that the marble is blue or even numbered is $\frac{11}{15}$

3 0

3 years ago