The equation of the hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0) is 
<h3>How to determine the equation of the hyperbola?</h3>
The given parameters are:
- Directrices at x = ±2
- Foci at (5, 0) and (−5, 0)
The foci of a hyperbola are represented as:
Foci = (k ± c, h)
The center is:
Center = (h,k)
And the directrix is:
Directrix, x = h ± a²/c
By comparison, we have:
k ± c = ±5
h = 0
h ± a²/c = ±2
Substitute h = 0 in h ± a²/c = ±2
0 ± a²/c = ±2
This gives
a²/c = 2
Multiply both sides by c
a² = 2c
k ± c = ±5 means that:
k ± c = 0 ± 5
By comparison, we have:
k = 0 and c = 5
Substitute c = 5 in a² = 2c
a² = 2 * 5
a² = 10
Next, we calculate b using:
b² = c² - a²
This gives
b² = 5² - 10
Evaluate
b² = 15
The hyperbola is represented as:
So, we have:
Evaluate
Hence, the equation of the hyperbola is
Read more about hyperbola at:
brainly.com/question/3405939
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Answer:
Step-by-step explanation:
sin(7y)=cos(5y+14)=sin(90-(5y+14))=sin(76-5y)
7y=76-5y
12y=76
y=76/12=19/3
or
sin(7y)=cos (5y+14)=sin (90+(5y+14))=sin (5y+104)
7y=5y+104
2y=104
y=52
I dont have time to do all of these right now my apolgies but Ill explain how to do it.
The 3 angles of a triangle add up to 180.
So let me show you how to do 1.
.
.
.
1. 58 degrees
92, 30, ?
If we add together the first two angles,
92+30= 122
Knowing the total addition of all three angles would ne 180, we can subtract 122 from it to get the third angle.
180-122= 58
So we now know the last angle is 58 degrees because
92+30+58=180
Answer:
102 feet of fencing.
Step-by-step explanation:
Since this is asking to <u> enclose </u> the yard, it is a perimeter question.
22.5 x 2 = 45
28.5 x 2 = 57
45 + 57 = 102
102 is your answer.
Hope this helps.
The first one is 2x-3y/2
The second one is 1/x+2
The third one is (2x-5y)/(2x+5y)
The fourth one is x^2/z^2
