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:
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9514 1404 393
Explanation:
Both sides of the equation are squared.
I like this better without fractions, so would multiply by 16 at this point (or earlier).
x^2 -40x +144 = 0
(x -36)(x -4) = 0
x = 4 or 36 . . . . . . x = 4 is extraneous
The solution is x = 36.
Answer:
yes 5 is right
Step-by-step explanation:
<u><em>Answer:</em></u>
Nelson burned the most calories per hour
<u><em>Explanation:</em></u>
To solve this question, we will get the amount calories burned by each in one hour and then compare the two values
To do this, we will divide the total amount of calories burned by the total time
<u>1- For Sabra:</u>
We are given that she burnt 845 calories in 
(which is equivalent to 3.25) hours
<u>Therefore:</u>
Calories burnt in an hour = 
calories/hour
<u>2- For Nelson:</u>
We are given that he burnt 1435 calories in 
(which is equivalent to 4.875) hours
<u>Therefore:</u>
Calories burnt in an hour = 
calories/hour
<u>3- Comparing the two values:</u>
From the above calculations, <u>we can deduce that</u> Nelson burned the most calories per hour
Hope this helps :)
Answer:
1 whole
Step-by-step explanation:
