Suppose that two people standing 6 miles apart both see the burst from a fireworks display. after a period of time, the first person standing at point a hears the burst. four seconds later, the second person standing at point b hears the burst. if the person at point b is due west of the person at point a and if the display is known to occur due north of the person at point a, where did the fireworks display occur? note that sound travels at 1100 feet per second.

the fireworks display north of the person at point a

Step-by-step explanation:

The figure attached show a general description of the problem.

For this case the best way to solve the problem is use the general equation for an hyperbola given by:

We assume that the longer axis for the hyperbola is on the y axis.

On this case the total distance traveled by the sound is 1100 and we can find the value of a like this:

Since both people are apart 6 miles we can find the value of c like this:

c= 6 miles and we can convert this into ft like this:

And we can find the value of b like this:

And then our equation is given by:

And for this case we want to find the value of x when y = 6ft=31680 ft[/tex], and solving for x we got:

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

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