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SOVA2 [1]
2 years ago
11

What is the center of the circle?

Mathematics
1 answer:
Arada [10]2 years ago
3 0

Answer:

Step-by-step explanation:

This is not a question we need to at least know it’s equation.

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2 years ago
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kherson [118]

Step-by-step explanation:

The equation of a circle can be the expanded form of

\large \text{$(x-a)^2+(y-b)^2=r^2$}(x−a)

2

+(y−b)

2

=r

2

where rr is the radius of the circle, (a,\ b)(a, b) is the center of the circle, and (x,\ y)(x, y) is a point on the circle.

Here, the equation of the circle is,

\begin{gathered}\begin{aligned}&x^2+y^2+10x-4y-20&=&\ \ 0\\ \\ \Longrightarrow\ \ &x^2+y^2+10x-4y+25+4-49&=&\ \ 0\\ \\ \Longrightarrow\ \ &x^2+y^2+10x-4y+25+4&=&\ \ 49\\ \\ \Longrightarrow\ \ &x^2+10x+25+y^2-4y+4&=&\ \ 49\\ \\ \Longrightarrow\ \ &(x+5)^2+(y-2)^2&=&\ \ 7^2\end{aligned}\end{gathered}

⟹

⟹

⟹

⟹

x

2

+y

2

+10x−4y−20

x

2

+y

2

+10x−4y+25+4−49

x

2

+y

2

+10x−4y+25+4

x

2

+10x+25+y

2

−4y+4

(x+5)

2

+(y−2)

2

=

=

=

=

=

0

0

49

49

7

2

From this, we get two things:

\begin{gathered}\begin{aligned}1.&\ \ \textsf{Center of the circle is $(-5,\ 2)$.}\\ \\ 2.&\ \ \textsf{Radius of the circle is $\bold{7}$ units. }\end{aligned}\end{gathered}

1.

2.

Center of the circle is (−5, 2).

Radius of the circle is 7 units.

Hence the radius is 7 units.

4 0
2 years ago
Hezekiel runs 1000 m at a rateof 3 minutes per km. how long does he take to run 500 m​
lana66690 [7]

Step-by-step explanation:

1 km = 1000 m

(hence the term "kilo" which means 1000).

so. he runs 1000 m at the rate of 3 minutes per km, that means 3 minutes per 1000 m.

now, we can see the solution already with our eyes.

but let's do it formally :

the rate or ratio between time and distance must be the same for the same speed.

so,

3 min / 1000 m = x min / 500 m

500 m × 3 min / 1000 m = x min

1/2 × 3 min = x min

3/2 = 1.5 min = x min

so, it takes him 1.5 minutes (90 seconds) to run 500 m.

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