What is 792 divided by 44

An equation of a hyperbola is given.

siniylev [52]

Answer:

a)

The vertices are $\left(3,\:0\right),\:\left(-3,\:0\right)$ .

The foci are $\left(3\sqrt{5},\:0\right),\:\left(-3\sqrt{5},\:0\right)$ .

The asymptotes are $y=2x,\:y=-2x$ .

b) The length of the transverse axis is 6.

c) See below.

Step-by-step explanation:

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$ is the standard equation for a right-left facing hyperbola with center $\left(h,\:k\right)$ .

a)

The vertices $\:\left(h+a,\:k\right),\:\left(h-a,\:k\right)$ are the two bending points of the hyperbola with center $\:\left(h,\:k\right)$ and semi-axis a, b.

Therefore,

$\frac{x^2}{9}-\frac{y^2}{36}=1$ , is a right-left Hyperbola with $\:\left(h,\:k\right)=\left(0,\:0\right),\:a=3,\:b=6$ and vertices $\left(3,\:0\right),\:\left(-3,\:0\right)$ .

For a right-left facing hyperbola, the Foci (focus points) are defined as $\left(h+c,\:k\right),\:\left(h-c,\:k\right)$ where $c=\sqrt{a^2+b^2}$ is the distance from the center $\left(h,\:k\right)$ to a focus.

Therefore,

$\frac{x^2}{9}-\frac{y^2}{36}=1$ , is a right-left Hyperbola with $\:\left(h,\:k\right)=\left(0,\:0\right),\:a=3,\:b=6$ $c=\sqrt{3^2+6^2}= 3\sqrt{5}$ and foci $\left(3\sqrt{5},\:0\right),\:\left(-3\sqrt{5},\:0\right)$

The asymptotes are the lines the hyperbola tends to at $\pm \infty$ . For right-left hyperbola the asymptotes are: $y=\pm \frac{b}{a}\left(x-h\right)+k$

Therefore,

$\frac{x^2}{9}-\frac{y^2}{36}=1$ , is a right-left Hyperbola with $\:\left(h,\:k\right)=\left(0,\:0\right),\:a=3,\:b=6$ and asymptotes

$y=\frac{6}{3}\left(x-0\right)+0,\:\quad \:y=-\frac{6}{3}\left(x-0\right)+0\\y=2x,\:\quad \:y=-2x$

b) The length of the transverse axis is given by $2a$ . Therefore, the lenght is 6.

c) See below.

4 0

3 years ago

Marcia can make 5 candles in an hour. Kevin can make only 4 candles in an hour, but he already has 7 completed candles. Explain

RUDIKE [14]

M(h)=5h
that is marcia's number of candles where she makes 5 candles per hour (h)

kevin makes 4 but already did 7 so
k(h)=4h+7

when will they have same numbre of candles?
when will m(h)=k(h)
set equal

5h=4h+7
minus 4h from both sides
1h=7

answer is 7 hours

system of equation is
m=5h
k=4h+7
find what value of h makes m=k true

answer is 7 hours

7 0

4 years ago

Tell whether x and y are proportional when y/x=3

mars1129 [50]

Answer:

y is directly proportional to x

Step-by-step explanation:

if y/x = 3

then, y = 3x.

5 0

3 years ago

What is the angle measure of a each interior angle of a regular decagon

Mama L [17]

Answer:

idk

Step-by-step explanation:

idk

3 0

3 years ago

Expand and simplify<br> (x+2)(x-6)

svetlana [45]

Do the rainbow method
x^2 - 6x + 2x - 12
Now simplify
x^2 - 4x - 12
The answer is x^2-4x-12

6 0

3 years ago

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