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likoan [24]
3 years ago
14

Write the equation for the hyperbola with foci (–12, 6), (6, 6) and vertices (–10, 6), (4, 6).

Mathematics
1 answer:
fomenos3 years ago
7 0

Answer:

\frac{(x--3)^2}{49} -\frac{(y-6)^2}{32}=1

Step-by-step explanation:

The standard equation of a horizontal hyperbola with center (h,k) is

\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1

The given hyperbola has vertices at (–10, 6) and (4, 6).

The length of its major axis is 2a=|4--10|.

\implies 2a=|14|

\implies 2a=14

\implies a=7

The center is the midpoint of the vertices (–10, 6) and (4, 6).

The center is (\frac{-10+4}{2},\frac{6+6}{2}=(-3,6)

We need to use the relation a^2+b^2=c^2 to find b^2.

The c-value is the distance from the center (-3,6) to one of the foci (6,6)

c=|6--3|=9

\implies 7^2+b^2=9^2

\implies b^2=9^2-7^2

\implies b^2=81-49

\implies b^2=32

We substitute these values into the standard equation of the hyperbola to obtain:

\frac{(x--3)^2}{7^2} - \frac{(y-6)^2}{32}=1

\frac{(x+3)^2}{49} -\frac{(y-6)^2}{32}=1

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8 0
3 years ago
All the edges of a regular square pyramid have length 8 . What is the:
user100 [1]

Answer:

vol=BX1/3 h

=64* 1/3 square root of 32

Step-by-step explanation:

5 0
3 years ago
Use the grouping method to factor x^3+x^2+3x+3
maks197457 [2]

Answer:

(x^2 + 3)(x + 1).

Step-by-step explanation:

x^3 + x^2 + 3x + 3

= x^2(x + 1) + 3(x + 1)

= (x^2 + 3)(x + 1).

7 0
2 years ago
The measure of an angle is 5 times as great as the measure of it's complement. Find the measure of the angle
horrorfan [7]
15 is the mesure of the angle
4 0
3 years ago
Read 2 more answers
What is the solution to the inequality below?
Svetlanka [38]

Answer:

B. x < -8 or x > 8

Step-by-step explanation:

You can use process of elimination to solve this problem by going through every solution and testing them out, but let's jump right to B.

Process:

You know that since the inequality states that x^2 has to be greater than 64, x  has to be more than 8, or less than -8.

This is because 8^2 = 64, and -8^2 = 64, and the inequality requires the answer to be more than 64.

Looking at B., you can see that if x is < -8, the square of, for example, -9, would be 81. This is greater than 64, so this works!

Now, B. also has an alternative. The 'or' is a major clue to which is the correct answer, since the square root of any number can be positive or negative. (-8^2 = 8^2)

The 'or' states that x must be greater than 8. So, for example, if we take the square of 10, we get 100, and that is also greater than 64.

We've proven that this solution is accurate for both parts, so it is definitely the one we want!

Hope this helps!

4 0
3 years ago
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