Mathematics, 10.01.2020 14:31 taesthetic11

Write the equation of a circle with center (4, -5) and radius = square root of 13

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Answer from: asra44

Hello!

The answer is:

The equation of the given circle is:

$(x-4)^{2}+(y+5)^{2}=13$

Why?

The equation of a circle is given by the following equation:

$(x-h)^{2} +(y-k)^{2}=r^{2}$

We are given the center point (4,-5) and the radius.

So,

Where:

$h=x=4\\k=y=-5\\r=\sqrt{13}$

Then, substituting into the circle equation, we have:

$(x-4)^{2} +(y-(-5))^{2}=(\sqrt{13})^{2}$

Hence, the simplified equation of the circle is:

$(x-4)^{2}+(y+5)^{2}=13$

Have a nice day!

Answer from: kluke7170

The required equation in standard form is (x-4)^2+(y+5)^2=13

Step-by-step explanation:

The equation of a circle with center (h,k) an radius, r units is given by the formula;

(x-h)^2+(y-k)^2=r^2

The given circle has center (4,-5) and radius $r=\sqrt{13}$ .

We substitute these values into the formula to obtain;

$(x-4)^2+(y--5)^2=(\sqrt{13})^2$

We simplify to get;

(x-4)^2+(y+5)^2=13

Answer from: Quest

he spend 5.1 minutes chatting with his friends

step-by-step explanation:

2/5+1/2=9/10

6/1-9/10=5 1/10

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

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Write the equation of a circle with center (4, -5) and radius = square root of 13...