Center = (-8, 4) = (h, k)
Since the transverse axis is parallel to the x axis, this hyperbola opens left/right
The length of the transverse axis = 4 units... so a = 2
And b = 12/2 = 6
So....the equation is
( x + h)^2 (y - k)^2
_________ - ________ = 1
a^2 b^2
( x + 8)^2 ( y - 4)^2
___________ - _________ = 1
4 36
Here's the graph : https://www.desmos.com/calculator/zuuet2usbm
[ 9 This goes in the first box
7 ]
The inverse is
1 [ 2 - 1 = 1 [ 2 - 1 This goes in the second box
___________ -3 - 4 ] - ______ -3 -4]
(2)(-4) - (1)(3) 11
-1 [ 2 - 1 [ 9 = -1 [ 11
__ -3 -4 ] 7 ] _______ -55] This goes in the third box
11 11
[ -1
5 ] This goes in the last box
The points ( 1, 2) , ( 4, 3) and (7, 4) are on the graph of f(x)
The inverse reverses these....so.....the points ( 2, 1) , ( 3, 4) and (4, 7) are on the inverse
f-1(3) = 4
So
f-1 ( f-1 (3)) = f-1(4) = 7
Heureka had an ingenious solution, here :
https://web2.0calc.com/questions/let-denote-the-circular-region-bounded-by-x-2-y-2
x^3 + 2x^2 - 5x - 6 =
Write this as
[ x^3 + x^2 ] + [ x^2 - 5x - 6 ] =
x^2 ( x + 1) + (x + 1) ( x - 6) =
(x + 1) ( x^2 + x - 6) =
( x + 1) ( x + 3) ( x - 2)
-1 [ 1 -1 - 2 5 - 6 ]
-1 2 0 -5
______________________
1 - 2 0 5 -11
-2 [ 1 - 1 -2 5 - 6 ]
-2 6 -8 6
_____________________
1 -3 4 -3 0
-3 [ 1 -1 -2 5 -6 ]
-3 12 -30 75
1 -4 10 -25 69
We get alternating signs on the bottom row......thus -3 is the lower bound
See the graph, here : https://www.desmos.com/calculator/sxca8cg7bf
The graph of the function crosses through the x-axis at 2 and behaves in a cubic fashion. The graph of the function touches and bounces off of the x-axis at −5 and crosses straight through the x-axis at 0.
To convert .07 (repeating) to a fraction
Let x = .07 (repeating)
Multiply both sides by 100
100x = 7.07 (repeating)
100x - x = 7.07(repeating) - .07(repeating)
99x = 7
x = 7/99
.07 - .07 (repeating) =
7/100 - 7/99 =
7(99) - 7(100)
___________ =
100 * 99
7 (99 - 100)
__________ =
9900
7 (-1)
______ =
-7
_____
See here : https://web2.0calc.com/questions/please-help-i-really-don-t-know
The length of the major axis = 2a = 420
So a = 210
The length of the minor axis = 2b = 180
So b = 90
And c = sqrt ( 210^2 -90^2 ) = sqrt (36000) ≈ 189.736 ft
And the distance between Angela and Zach = 2c = 2 ( 189.736) ≈ 379.4 ft
