Mathematics, 06.10.2019 04:30 slbutler2005

The equation x^2+y^2-4x+2y=b describes a circle. determine the y-coordinate of the center of the circle.
the radius of the circle is 7 units. what is the value of b in the equation?

Answers: 2

Show answers

Answers

X² + y² - 4 x + 2 y = b
x² - 4 x + 4 + y² + 2 y + 1 = b + 4 + 1
( x - 2 )² + ( y + 1 )² = b + 5
y - coordinate of the center of the circle is: y = - 1
b + 5 = r
b + 5 = 7
b = 7 - 5
b = 2

Answer from: cedricevans41p4j3kx

Step-by-step explanation:

The equation is given as:

x^2+y^2-4x+2y=b

Upon solving this equation, we have

x^2-4x+4+y^2+2y+1=b+4+1

which can be written as:

(x-2)^2+(y+1)^2=b+5 (1)

Thus, the y- coordinate of the center of the circle is y=-1 .

Now, comparing the equation (1) with the equation of circle, we have

(x-a)^2+(y-c)^2=r^2

where r is the radius of the circle and (a,c) is the center.

Thus, on comparing, we have

⇒ b+5=r^2

Also, it is given that the radius of the circle is 7 units, thus putting r=7 in above equation, we get

⇒ b+5=(7)^2

⇒ b+5=49

⇒ b=44 units

Thus, the value of b is 44 units in the given equation.

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.

Answer from: Quest

it is true

step-by-step explanation:

all the combinations add up i used calculator

Another question on Mathematics

Mathematics, 21.06.2019 13:00

Dee used 2 1/3 cups of sugar for a cake recipe. if the amount of sugar the container holds is 3 times the amount she used, does the container hold more than, less than, or equal to 3 cups of sugar? explain.

Answers: 2

Answer

Mathematics, 21.06.2019 18:30

What is the prime factorization of 230

Answers: 1

Answer

Mathematics, 21.06.2019 18:30

10% of 1,900,000. show me how you got the answer

Answers: 2

Answer

Mathematics, 21.06.2019 21:00

Rewrite the following quadratic functions in intercept or factored form. show your work. f(t) = 20t^2 + 14t - 12