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:
2
Step-by-step explanation:
10-8
<span>The
<u>correct answer</u> is:
350 ml.
Explanation<span>:
Let x be the amount in the fifth container.
The mean is found by adding all of the amounts together and dividing by the number of containers (in this problem, 5). We know that the total from the other 4 containers is 2750; add this to x, our unknown number. Then we divide by 5 to arrive at our answer of 620.
Algebraically,
</span></span>
<span><span>
To solve, multiply both sides by 5:
</span></span>
<span><span>
Subtract 2750 from both sides:
2750+x-2750=3100-2750
x=350.
There are 350 ml in the fifth container.</span></span>
The answer would be 6, 0.5
Answer:
SA = 664 square inches
Step-by-step explanation:
Surface area is the area of all the sides added together. A prism has six sides.
Take the dimensions and change them so each of the numbers are multiplied with the others.
14 * 10 * 8
14 * 10 = 140
14 * 8 = 112
10 * 8 = 80
Multiply each answer by 2 because there are two sides that have the same dimensions.
14 * 10 = 140 * 2 = 280
14 * 8 = 112 * 2 = 224
10 * 8 = 80 * 2 = 160
Add the areas together.
280 + 224 + 160 = 664
SA = 664 square inches
