X 2 +y 2 +4x−2y=−1space, x, start superscript, 2, end superscript, plus, y, start superscript, 2, end superscript, plus, 4, x, m
stepan [7]
The radius is 2.
We will rewrite this equation in center-radius form,
(x-h)²+(y-k²)=r²
where (h, k) is the center of the circle and r is the radius.
In order to do this, we will need to complete the square. We will first rewrite this with the x terms grouped together and the y terms grouped together:
x²+4x+y²-2y = -1
To complete the square for the x terms, we divide the coefficient b (as in bx) by 2:
4/2 = 2
Now we square this:
2²=4
We will add this to both sides of the equation (in order to maintain balance, we must add it to both sides):
x²+4x+4+y²-2y=-1+4
x²+4x+4+y²-2y=3
We have completed the square for the x terms. When we divided b by 2, that gave us the number we need, 2:
(x+2)²+y²-2y=3
Now we will do the same thing for the y terms. The b for our y terms is -2:
-2/2 = -1
(-1)²=1
So we will add 1 to both sides, and use -1 in the finalized form:
(x+2)²+y²-2y+1=3+1
(x+2)²+(y-1)²=4
We can see that the center would be located at (-2, 1) and the radius is √4=2.
Answer:
A
Step-by-step explanation:
Answer:
b=4 makes the equation a perfect square.
Step-by-step explanation:
As long as you factorize out the equation, you'll get a result of (x+2)^2. This multiplied using foil gives you, x^2 + 2x + 4. Making it a perfect square. You could also have -2 = b which makes a perfect square, but that's not in the options.
Answer:
see explanation
Step-by-step explanation:
The area (A) of the sector of a circle is
A = area of circle × fraction of circle
= πr² ×
diameter = 12.4 ⇒ r = 6.2, thus
A = π × 6.2² ×
= π × 38.44 ×
= ≈ 20.13 m² ( to 2 dec. places )
If the question is 3^(2/3),
The answer is the cube root of 9.