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svp [43]
1 year ago
14

The general form of the equation of a circle is x2 + y2 + 42x + 38y − 47 = 0. The equation of this circle in standard form is (x

- 21)^2 + (y - 19)^2 = 127 (x + 21)^2 + (y + 19)^2 = 849 (x + 21)^2 + (y + 19)^2 = 851 (x - 19)^2 + (y - 21)^2 = 2,209 . The center of the circle is at the point (-19, -21) (-21, -19) (19, 21) (21, 19) , and its radius is 127^(1/2) 849^(1/2) 851^(1/2) 47 units. The general form of the equation of a circle that has the same radius as the above circle is x^2 + y^2 + 60x + 14y + 98 = 0 x^2 + y^2 + 44x - 44y + 117 = 0 x^2 + y^2 - 38x + 42y + 74 = 0 x^2 + y^2 - 50x - 30y + 1 = 0 .
Mathematics
1 answer:
DaniilM [7]1 year ago
5 0
We have the following equation:
 x2 + y2 + 42x + 38y - 47 = 0
 We rewrite the equation:
 x2 + 42x + y2 + 38y - 47 = 0
 x2 + 42x + y2 + 38y = 47
 Rewriting we have:
 x2 + 42x + (42/2) ^ 2 + y2 + 38y + (38/2) ^ 2 = 47 + (42/2) ^ 2 + (38/2) ^ 2
 x2 + 42x + 441 + y2 + 38y + 361 = 47 + 441 + 361
 Rewriting we have:
 (x + 21) ^ 2 + (y + 19) ^ 2 = 849
 The center of the circle is:
 (x, y) = (-21, -19)
 The radio is:
 r = root (849)
 r = (849) ^ 2

 A circle of the same radius is given by:
 x ^ 2 + y ^ 2 - 50x - 30y + 1 = 0
 Let's check:
 x ^ 2 - 50x + y ^ 2 - 30y + 1 = 0
 x ^ 2 - 50x + y ^ 2 - 30y = - 1
 x ^ 2 - 50x + (-50/2) ^ 2 + y ^ 2 - 30y + (-30/2) ^ 2 = - 1 + (-30/2) ^ 2 + (-50/2) ^ 2
 x ^ 2 - 50x + (-50/2) ^ 2 + y ^ 2 - 30y + (-30/2) ^ 2 = - 1 + 225 + 625
 (x-25) ^ 2 + (y-15) ^ 2 = 849
 Answer:
 
(x + 21) ^ 2 + (y + 19) ^ 2 = 849
 
(x, y) = (-21, -19)
 
r = (849) ^ 2
 
x ^ 2 + y ^ 2 - 50x - 30y + 1 = 0
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A website reports that 70% of its users are from outside a certain country, and 60% of its users logon the website every day. Su
JulijaS [17]

Answer:

The value is P (I |  L  )  =     0.63

The probability has increased

Step-by-step explanation:

From the question we are told that

   The percentage that are from outside the country is  P(O) =  0.70

    The  percentage that logs on everyday is  P(L) =  0.60

    The  percentage that logs on everyday that are from the inside the country is     P(L  |  I) =  0.80

Generally using Bayes' Rule the probability that a person is from the country given that he logs on the website every day is mathematically represented as

     P (I |  L  )  =  \frac{P(I)* P(L|I)}{ P(O) *P(L|O) + P(I) *P(L|I) }

Where  P(I) is the percentage that are from inside that country which is mathematically represented as

       P(I) =  1 -  P(O)

      P(I) =  1 -  0.70

      P(I) =  0.30

And P(L| O) is  percentage that logs on everyday that are from the outside  the country which is evaluated as

      P(L| O)  =  1-  P(L| I)

       P(L| O)  =  1-  0.80

       P(L| O)  = 0.20

P (I |  L  )  =  \frac{ 0.3* 0.80 }{ 0.7 *0.20 + 0.3 * 0.8 }    

P (I |  L  )  =     0.63

Given that the percentage that are from inside that country is  P(I) =  0.30

and that the probability that a person is from the country given that he logs on the website every day is  P (I |  L  )  =     0.63

We see that the additional information increased the probability

5 0
1 year ago
The hypotenuse of a 45°-45°-90° triangle measures 10 StartRoot 5 EndRoot in. A right triangle is shown. The hypotenuse has a len
suter [353]

Answer:

5\sqrt{10}\ units

5 StartRoot 10 EndRoot

Step-by-step explanation:

we know that

The legs of a 45°-45°-90° triangle are congruent

Let

x ---->  the length of one leg of the triangle

Applying the Pythagorean Theorem

c^2=a^2+b^2

where

c is the hypotenuse

a and b are the legs

we have

c=10\sqrt{5}\ units

a=b=x\ units

substitute

(10\sqrt{5})^2=x^2+x^2

500=2x^2\\x^2=250\\x=\sqrt{250}\ units

Simplify

x=5\sqrt{10}\ units

5 StartRoot 10 EndRoot

4 0
2 years ago
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Which problem can be represented by the equation 12z + 2= 98
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Where are the problems?

8 0
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In △XYZ, m∠Z = 34, x = 61 cm, and z = 42 cm. Find m∠X. Round your answer to the nearest tenth of a degree.
Elza [17]
M∠X = 54.3°.

Using the Law of Sines, we have:
\frac{\sin{Z}}{z}=\frac{\sin{X}}{x}
\\
\\\frac{\sin{34}}{42}=\frac{\sin{X}}{61}

Cross multiplying gives us
61(sin 34) = 42(sin X)

Divide both sides by 42:
(61(sin 34))/42 = (42(sin X))/42
(61(sin 34))/42 = sin X

Take the inverse sine of both sides:
sin⁻¹((61(sin 34))/42) = sin⁻¹(sin X)
54.3 = X
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In a golf tournament, Sam played 4 rounds and was within 2 strokes of par for all 4 rounds of the tournament. If par is 72 on th
In-s [12.5K]

Given:

|x-4(72)|=2

To find:

The highest and lowest scores Sam could have made in the tournament.

Solution:

We have,

|x-4(72)|=2

|x-288|=2

It can be written as

x-288=\pm 2

Add 288 on both sides.

x=288\pm 2

x=288-2 and x=288+2

x=286 and x=290

Therefore, the highest and lowest scores Sam could have made in the tournament are 290 and 286 respectively.

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