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LORAN is a long range hyperbolic navigation system. Suppose two LORAN transmitters are located at the coordinates (−60,0) and (6

USPshnik [31]

LORAN follows an hyperbolic path.

The equation of the hyperbola is: $\mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}$

The coordinates are given as:

$\mathbf{(x,y) = (-60,0)\ (60,0)}$

The center of the hyperbola is

$\mathbf{(h,k) = (0,0)}$

The distance from the center to the focal points is given as:

$\mathbf{c = 60}$

Square both sides

$\mathbf{c^2 = 3600}$

The distance from the receiver to the transmitters is given as:

$\mathbf{2a = 100}$

Divide both sides by 2

$\mathbf{a = 50}$

Square both sides

$\mathbf{a^2 = 2500}$

We have:

$\mathbf{b^2 = c^2 - a^2}$

This gives

$\mathbf{b^2 = 3600 - 2500}$

$\mathbf{b^2 = 1100}$

The equation of an hyperbola is:

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

So, we have:

$\mathbf{\frac{(x - 0)^2}{2500} + \frac{(y - 0)^2}{1100} = 1}$

$\mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}$

Hence, the equation of the hyperbola is: $\mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}$

Read more about hyperbolas at:

brainly.com/question/15697124

7 0

3 years ago

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Jenna is driving 400 miles to visit her grandmother. She managesto travel the first 100 miles of her trip in two hours. Is she c

dalvyx [7]

Answer:

Jenna will complete remaining distance in 6 hours.

Step-by-step explanation:

Since we know that $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$ . Let us find the rate at which Jenna traveled 100 miles.

$\text{Speed}=\frac{100\text{ miles}}{2\text{ hours}}$

$\text{Speed}=50\frac{\text{ miles}}{\text{ hours}}$

Remaining distance is 400-100=300.

Now let us find the time Jenna will take to travel 300 miles.

$\text{Time}=\frac{300}{50}$

$\text{Time}=6$

Therefore, Jenna took 6 hours to complete remaining distance.

4 0

3 years ago

121 as a fration simplifid

PSYCHO15rus [73]

Answer:

-1/1

Step-by-step explanation:

Is the another way to simplified, there's no other way besides that and 121.

4 0

3 years ago

Read 2 more answers

Fifty-five and one-half percent of shareholders in a fast food chain are under 40. If 91,00 shareholders, how many are 40 and ov

Setler [38]

0.555x91,000=50,505 are under 40
91,000-50,505=40,495 are over 40

3 0

3 years ago

The graph of y=-3x+4 is:

Mariulka [41]

y=-3x+4

this is a line with slope -3 and y intercept of 4

the line is all the points that are the solutions to the equation

D.a line that shows the set of all solutions to the equation

4 0

3 years ago