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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Step-by-step explanation:
I'm struggling with that to sowy T T
Answer:
37.68 Inches cubed (A)
Step-by-step explanation:
The formula for a cylinder is:
πr^2(h)
First, let's find the radius, which is:
4/2 = 2
Now, we can plug in the values:
3.14(2)^2(3)
Do exponents first:
3.14(4)(3)
Multiply left to right:
12.56(3)
Again:
37.68 Inches
So, the answer is:
37.68 Inches cubed (Or A)
Hope this helps!
To solve for x, you need to isolate/get the variable "x" by itself in the equation:
3x - 3(x + 1) = 3 Distribute/multiply -3 into (x + 1)
3x + (-3)x + (-3)1 = 3
3x - 3x + 1 = 3
1 = 3
Your answer is no solution because the variable "x" is canceled out and 1 ≠ 3
Answer:
Find the LCD of the first two, then the LCD of that and the third one.
Step-by-step explanation:
You can do it by finding the LCD of two of the denominators, then the LCD of that and the third denominator.
Or, you can factor each of the denominators and find their LCM by multiplying the unique factors to their highest powers.
___
<u>Example:</u>
1/21 + 1/35 + 1/45
The LCD of 1/21 and 1/35 is (21·35)/5 = 105. The LCD of 1/105 and 1/45 is ...
(105·45)/15 = 315
__
Using factoring ...
- 21 = 3·7
- 35 = 5·7
- 45 = 3²·5
LCD = 3²·5·7 = 315
