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HACTEHA [7]
2 years ago
9

The center of circle q has coordinates (-2, 1). if circle q passes through r (6, 7), what is the length of its diameter?

Mathematics
1 answer:
Oksana_A [137]2 years ago
7 0
<h2>Diameter of a Circle</h2>

There are multiple strategies we can use to find the diameter of a circle. For this question, we must calculate the length of the radius first and multiply by 2 to find the diameter.

<h2>Solving the Question</h2>

We're given the centre and a point on the circumference: (-2,1),(6,7).

Find the distance between them using the distance equation:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Plug in the given points:

d=\sqrt{(-2-x_1)^2+(1-y_1)^2}\\d=\sqrt{(-2-6)^2+(1-7)^2}\\d=\sqrt{(-8)^2+(-6)^2}\\d=\sqrt{64+36}\\d=\sqrt{100}\\d=10

Therefore, the radius of the circle is 10 units.

Multiply the radius by 2 to find the length of the diameter:

10 × 2

= 20

Therefore, the length of the diameter is 20 units.

<h2>Answer</h2>

20 units

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A store selling newspapers orders only n = 4 of a certain newspaper because the manager does not get many calls for that publica
umka2103 [35]

Answer:

a) The expected value is 2.680642

b) The minimun number of newspapers the manager should order is 6.

Step-by-step explanation:

a) Lets call X the demanded amount of newspapers demanded, and Y the amount of newspapers sold. Note that 4 newspapers are sold when at least four newspaper are demanded, but it can be <em>more</em> than that.

X is a random variable of Poisson distribution with mean \mu = 3 , and Y is a random variable with range {0, 1, 2, 3, 4}, with the following values

  • PY(k) = PX(k) = ε^(-3)*(3^k)/k! for k in {0,1,2,3}
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we obtain:

PY(0) = ε^(-3) = 0.04978..

PY(1) = ε^(-3)*3^1/1! = 3*ε^(-3) = 0.14936

PY(2) = ε^(-3)*3^2/2! = 4.5*ε^(-3) = 0.22404

PY(3) = ε^(-3)*3^3/3! = 4.5*ε^(-3) = 0.22404

PY(4) = 1- (ε^(-3)*(1+3+4.5+4.5)) = 0.352768

E(Y) = 0*PY(0)+1*PY(1)+2*PY(2)+3*PY(3)+4*PY(4) =  0.14936 + 2*0.22404 + 3*0.22404+4*0.352768 = 2.680642

The store is <em>expected</em> to sell 2.680642 newspapers

b) The minimun number can be obtained by applying the cummulative distribution function of X until it reaches a value higher than 0.95. If we order that many newspapers, the probability to have a number of requests not higher than that value is more 0.95, therefore the probability to have more than that amount will be less than 0.05

we know that FX(3) = PX(0)+PX(1)+PX(2)+PX(3) = 0.04978+0.14936+0.22404+0.22404 = 0.647231

FX(4) = FX(3) + PX(4) = 0.647231+ε^(-3)*3^4/4! = 0.815262

FX(5) = 0.815262+ε^(-3)*3^5/5! = 0.91608

FX(6) = 0.91608+ε^(-3)*3^6/6! = 0.966489

So, if we ask for 6 newspapers, the probability of receiving at least 6 calls is 0.966489, and the probability to receive more calls than available newspapers will be less than 0.05.

I hope this helped you!

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Use vieta's theorem to solve the problems.
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Using Vieta's Theorem, it is found that c = 72.

<h3>What is the Vieta Theorem?</h3>
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y = ax^2 + bx + c

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The Theorem states that:

p + q = -\frac{b}{a}

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In this problem, the polynomial is:

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Since the difference of the solutions is 1, we have that:

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Now, from the second equation:

pq = \frac{c}{a}

72 = c

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To learn more about Vieta's Theorem, you can take a look at brainly.com/question/23509978

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