25x² + 9y² + 72y - 81 = 0
25x² + 9y² + 72y - 81 + 81 = 0 + 81
25x² + 9y² + 72y = 81
25x² + 9(y² + 8y + 16) = 81 + 9(16)
25x² + 9(y² + 4y + 4y + 16) = 81 + 144
25x² + 9(y(y) + 4(y) + 4(y) + 4(4)) = 225
25x² + 9(y(y + 4) + 4(y + 4)) = 225
25x² + 9(y + 4)(y + 4) = 225
<u>25x²</u> + <u>9(y + 4)²</u> = <u>225</u>
225 225 225
<u> x²</u> + <u>9(y + 4)²</u> = 1
25 25
The conic section is an ellipse.
Answer:
θ = 5π/6 rad and 11π/6 rad
Step-by-step explanation:
Given the expression cotθ+√3=0
Subtract √3 from both sides
cotθ+√3-√3=0-√3
cotθ = -√3
Since cotθ = 1/tanθ
1/tanθ = -√3
Reciprocate both sides:
tanθ = -1/√3
θ = tan^-1(-1/√3)
θ = -30°
Since the angle is negative, and tanθ is negative in the second and fourth quadrant.
In the second quadrant;
θ = 180-30
θ = 150°
Since 180° = πrad
150° = 150π/180
150° = 5π/6 rad
In the fourth quadrant;
θ = 360-30
θ = 330°
Since 180° = πrad
330° = 330π/180
330° = 11π/6 rad
Hence the solutions are 5π/6 rad and 11π/6 rad.
IDK if i have to explain again but
A. (-infinity, infinity)
B. (-infinity, -3]
C. (-infinity, -4)u(-4, 0)u(0, infinity)
those u's are the logic symbol
2. domain: [-6, -1)u(-1, 3]u [3, -infinity)
range: (-infinity, 4]
3a. 8x^2 + 17
3b. 32x^2 + 80x + 53
3c. I cant see the multiplication symbol
Answer:
(-3,4)
(-1,4)
(-3,7)
Step-by-step explanation:
(1,1) → (1-4, 1+3) → (-3,4)
(3,1) → (3-4, 1+3) → (-1,4)
(1,4) → (1-4, 4+3) → (-3,7)
(-5,9) because -6—1=-6+1 which equals -5 and 7—2=7+2 which equals 9
