Answer:
Eq: (x+a/2)²+(y+1)²=(a²-8)/4
Center: O(-a/2, -1)
Radius: r=0.5×sqrt(a²-8)
Mandatory: a>2×sqrt(2)
Step-by-step explanation:
The circle with center in O(xo,yo) and radius r has the equation:
(x-xo)²+(y-yo)²=r²
We have:
x²+y²+ax+2y+3=0
But: x²+ax=x²+2(a/2)x+a²/4-a²/4= (x+a/2)²-a²/4
And
y²+2y+3=y²+2y+1+2=(y+1)²+2
Replacing, we get:
(x+a/2)²-a²/4+(y+1)²+2=0
(x+a/2)²+(y+1)²=a²/4-2=(a²-8)/4
By visual inspection we note that:
- center of circle: O(-a/2, -1)
- radius: r=sqrt((a²-8)/4)=0.5×sqrt(a²-8). This means a²>8 or a>2×sqrt(2)
From the identity:
the inverse of f is g such that f(g(x))=x,
we must find g(x), such that
![\frac{1}{cos[g(x)]}=x](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7Bcos%5Bg%28x%29%5D%7D%3Dx%20)
thus,
![cos[g(x)]= \frac{1}{x}](https://tex.z-dn.net/?f=cos%5Bg%28x%29%5D%3D%20%5Cfrac%7B1%7D%7Bx%7D%20)
Answer: b. g(x)=cos^-1(1/x)
5 = what percent of 23
5 = x% of 23
5 = (x/100)*23
5 = 23x/100
5*100 = 23x
23x = 5*100
x = 5*100/23
x = 21.739
5 is ≈ 21.739% of 23
The equation of an ellipse is x²/a² + y²/b² =1
a being the distance between the center & x intercept =7
b being the distance between the center & y intercept =5
Hence the equation of this ellipse is:
x²/49 + y²/25 =1
Answer:
The equation
c x 2 > k
l x 3 ?> c > k
g = 30 = c + l + k
this equation is the same as...
Cecile read twice as many books as Kami.
Laura read 3 times as many books as Kami, but possibly less than Cecile.
Gigi read 30 books. 30 books is the same as all 3 girls combined.
To find out how many books each girl read, you need to find 3 unequal numbers that add up to 30. These numbers are substituted, only because they can be anything at all, and I want to prevent confusions.
hope this helps!
