LORAN follows an hyperbolic path.
The equation of the hyperbola is: 
The coordinates are given as:

The center of the hyperbola is

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

Square both sides

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

Divide both sides by 2

Square both sides

We have:

This gives

The equation of an hyperbola is:

So, we have:


Hence, the equation of the hyperbola is: 
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We see that in these 3 terms, 6 is a common factor. So, let's factor out a 6:

We can set this equal to 0 and factor by using the quadratic formula which is:

So, let's do just that:

Note that the 6 goes away if you divide both sides by 6. In this case, a = 1, b = -1, and c = -2. Let's plug that into the quadratic equation:


So, we can write this as:

Notice that the 6 comes back because it was only temporarily mad. And that the roots have opposite signs in the parentheses because to find the roots, you need to set each parentheses equal to 0 and solve for n. With that in mind, your final answer is 6(n-1)(n+2). Hope I could help you!
Answer:
"A value that is substituted in for the variable in a function in order to generate an output value" is gonna be known as an input.
"A group of two numbers written in the form (x, y) where the x value represents a horizontal position and the y value represents a vertical position" is known as an ordered pair.
"A value generated by a function when an input value is substituted into the function and evaluated" is known as an output.
I hope I have helped with this problem. Have a good day.
The situation that is defined by the linear equation P = 40 + 22t is "The initial amount is 40 and the rate of change is 22".
<h3>What is a linear equation?</h3>
Given:
P = 40 + 22t
where,
- P = total price
- 40 = initial amount
- 22 = rate of change
- t = number of rate of change
So,
if t = 3
P = 40 + 22t
= 40 + 22(3)
= 40 + 66
P = 106
Therefore, the initial amount is 40 and the rate of change is 22 describes the linear equation P = 40 + 22t
Learn more about linear equation:
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76.6% so rounded up would be 77% as an a fraction 46/60