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
Answer:
For the problem we have:
Sam had 14 people at the party.
The party lasted for 4 hours.
He paid $2 for each person's skate rental and 3 for each person's entry ticket.
Suppose we want to know how much Sam spent on the party.
But we do not know if the $2 of the skate rental are per hour or per two hours, or in total, for example, if the amount is per hour, then the total amount for each skate is $2*4 = $8, so in the case that the rental depends on the time, we can not solve this problem because we do not have enough information.
If the $2 are fixed (do not depend on the time that the party lasted) then the fact that the party lasted for 4 hours does not matter.
We can calculate as 14 persons* ($2 + $3) each = 14*$5 = $70, then you can see that in this case the 4 hours data is not necessary
80 tickets have been given out
50*.4=20
50*.6=30
30*2=60
60+20=80
20 5/81 in its simplest form is 20 5/81.
20 5/81 originally looks like this ⇒ 1625/81
((20 * 81)+5)/81 = (1620+5)/81 = 1625/81 * this is an improper fraction because the numerator is greater than the denominator. Improper fractions must be converted to proper fractions. It will then become a mixed fraction.
<u> 0020 5/81</u>
81 | 1625
<u>162 </u> * 81 x 2
05
An equivalent expression would be s+15
You simplify the expression.
So yea the answer is s+15
