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zlopas [31]
3 years ago
11

What is the center and radius of the circle with equation (x - 2)^2 + (y - 5)^2 = 100?

Mathematics
2 answers:
ololo11 [35]3 years ago
5 0
Answer: 
Center = (2,5)
Radius = 10
Choice A

To find this answer, first write the equation 
(x-2)^2 + (y-5)^2 = 100
into 
(x-2)^2 + (y-5)^2 = 10^2

Note how the second equation is in the form
(x-h)^2 + (y-k)^2 = r^2

We see that (h,k) = (2,5) is the center
and r = 10 is the radius
777dan777 [17]3 years ago
5 0

Answer:

A) Center ( 2 , 5 ) ; radius = 10 .

Step-by-step explanation:

Given  :  (x - 2)² + (y - 5)² = 100.

To find : What is the center and radius of the circle with equation.

Solution : We have given  (x - 2)² + (y - 5)² = 100.

Standard form of circle :  (x - h)² + (y - k)² = r².

Where, center = ( h ,k )  , r = radius .

On comparing  (x - 2)² + (y - 5)² = 100 with  (x - h)² + (y - k)² = r².

We can write (x - 2)² + (y - 5)² = 10².

h = 2 , k  = 5 , r = 10 .

Center ( 2 , 5 ) ; radius = 10 .

Therefore, A) Center ( 2 , 5 ) ; radius = 10 .

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2 years ago
Find the 12th term of the geometric sequence 5, -25, 125, ...5,−25,125,...
katovenus [111]

Answer:

  • a_{12}=-244140625

Step-by-step explanation:

Considering the geometric sequence

5,-25,\:125,\:...

a_1=5

As the common ratio 'r' between consecutive terms is constant.

\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}

r=\frac{-25}{5}=-5

r=\frac{125}{-25}=-5

The general term of a geometric sequence is given by the formula:  

a_n=a_1\cdot \:r^{n-1}

where a_1 is the initial term and r the common ratio.

Putting n = 12 , r = -5 and a_1=5 in the general term of a geometric sequence to determine the 12th term of the sequence.

a_n=a_1\cdot \:r^{n-1}

a_n=5\left(-5\right)^{n-1}

a_{12}=5\left(-5\right)^{12-1}

      =5\left(-5^{11}\right)

\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a

       =-5\cdot \:5^{11}

\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}

        =-5^{1+11}     ∵ 5\cdot \:5^{11}=\:5^{1+11}

        =-244140625

Therefore,

  • a_{12}=-244140625
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Step-by-step explanation:

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<u>Step-by-step explanation:</u>

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