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3 years ago

Find the center and the radius of the circle with the equation: x^2 +2x + y^2-2y-14 =0

Mathematics

2 answers:

maw [93]3 years ago

6 0

X²+2x+y²-2y=14
adding 1+1 both sides

x²+2x+1+y²-2y+1=14+1+1

(x+1)² +(y-1)² = 4²

x=-1 y= 1 r = 4

hope it helps !!

FrozenT [24]3 years ago

5 0

We need to convert the equation of the circle to standard form only then we can find the radius and the center of the circle.

$x^{2} +2x+ y^{2}-2y-14=0 \\ \\ 
x^{2} +2x+ y^{2}-2y=14 \\ \\ 
x^{2} +2(x)(1)+ y^{2}-2(y)(1)=14 \\ \\ 
 x^{2} +2x+1 + (y^{2}-2y+1)=14+1+1 \\ \\ 
(x+1)^{2}+(y-1)^{2} =16 
$

From this equation we can write:

Center of the circle is (-1,1) and the radius of the circle is 4.

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snow_tiger [21]

Answer:

Step-by-step explanation:

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3 years ago

A computer uses 1/200 second of a secount to finish a math problem . How many math questions can the computer solve in 2 minutes

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3 years ago

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Alexeev081 [22]

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2 years ago

Apply green’s theorem to evaluate the integral 3ydx 2xdy

Ne4ueva [31]

The value of the integral 3ydx+2xdy using Green's theorem be - xy

The value of $\int\limits_c 3ydx+2xdy$ be -xy

<h3>What is Green's theorem?</h3>

Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D bounded by C.

If M and N are functions of (x, y) defined on an open region containing D and having continuous partial derivatives there, then

$\int\limits_c Mdx+Ndy$ = $\int\int\〖(N_{x}-M_{y}) \;dxdy$

Using green's theorem, we have

$\int\limits_c Mdx+Ndy$ = $\int\int\〖(N_{x}-M_{y}) \;dxdy$ ............................... (1)

Here $N_{x}$ = differentiation of function N w.r.t. x

$M_{y}$ = differentiation of function M w.r.t. y

Given function is: 3ydx + 2xdy

On comparing with equation (1), we get

M = 3y, N = 2x

Now, $N_{x}$ = $\Luge\frac{dN}{dx}$

= $\frac{d}{dx} (2x)$

= 2

and, $M_{y}$ = $\Huge\frac{dM}{dy}$

= $\frac{d}{dy} (3y)$

= 3

Now using Green's theorem

= $\int\int\〖(2 -3) dx dy$

= $\int\int\ -dxdy$

= $-\int\ x dy$

= $-xy$

The value of $\int\limits_c 3ydx+2xdy$ be -xy.

Learn more about Green's theorem here:

brainly.com/question/14125421

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2 years ago

How many gallons of a 50% antifreeze solution must be mixed with 80 gallons of 30% antifreeze to get a mixture that is 40% a

Bas_tet [7]

I don't know what the "six-step method" is, but I do know how to solve the problem:

Let x = number of gallons of 50% solution

amount of antifreeze in 50% solution = 0.50x
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Then, 0.50x + 8 = 0.40x + 32

0.10x = 24

x = 240 gal

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2 years ago