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
#SPJ1
11. 8/7
14. 13/10
17. 11/14
a < -9
Rearrange:
Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :
5*a+18-(-27)<0
Step by step solution :
Step 1 :
Pulling out like terms :
1.1 Pull out like factors :
5a + 45 = 5 • (a + 9)
Equation at the end of step 1 :
Step 2 :
2.1 Divide both sides by 5
Solve Basic Inequality :
2.2 Subtract 9 from both sides
a < -9
No, the given sequence is not an arithmetic sequence.
What is Arithmetic Sequence ?
An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.
In the above question,
The sequence is 3,5/2,3/2,-3/2,...
Take the 2nd term and minus the 1st term.
Now take the 3rd term and minus the 2nd term.
We can clearly notice that the differences are not same. Hence there is no common difference and therefore it's not an arithmetic sequence
To read about arithmetic sequence click here :
brainly.com/question/27079755
#SPJ4
Answer:
$6
Step-by-step explanation:
divide 19.50 by 3.25
