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Eva8 [605]
3 years ago
8

An army base in the desert is located at the origin, O of an x-y coordinate system. A soldier at point P needs to determine his

coordinates with respect to the army base, but he does not have a link to a global positioning system. He is, however, in radio contact with several small towns in the vicinity. Two of the towns are town A and town B. Town A is 32 miles due south of the army base; town B is 18 miles north of the base. At an agreed-upon instant, both towns send out identifying radio signals. The soldier receives the signal from B slightly before the signal from A, so he knows that he is closer to B than to A. Furthermore, by measuring the time difference between receiving the two signals, the soldier is able to compute that he is 40 miles closer to town B than to town A. Explain why the point P must lie on a certain hyperbola.
Mathematics
1 answer:
Nutka1998 [239]3 years ago
8 0

Answer/step-by-step explanation

The soldier at point P lie on a parabola because he determined his position and distances from towns A and B through measurement of the difference in timing (phase) of radio signals received from the two towns.

This analysis of the signal time difference gives the difference in distance of the soldier at P, from the towns.

This process is known as hyperbolic navigation.

These distances of point P from towns A and B is estimated by the soldier at point P, by measuring the delay localizes the receiver to a hyperbolic line on a chart.

Two hyperbolic lines will be drawn by taking timing measurements from the

towns A and B .

Point P will be at the intersection of the lines.

These distances of point P(The soldier's positions) from town A and town B were determined using the timing of the signals received from the two towns, due to the fact that point P was on a certain hyperbola.

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GI and JL are parallel lines.<br><br> Which angles are supplementary angles?
solmaris [256]

Answer:

The answer is A.

Step-by-step explanation:

A supplementary angles are angles that when adding both sides will sum up to 180 Degrees.

<JKH and <LKH will be the correct answer because they add up tp 180 degrees.

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6 0
3 years ago
What is the value of 54-4a^2+3b^3 when a=-2 and b=4
max2010maxim [7]

2015-12-14T20:17:50+00:00If you would like to know what is the value of <span>54 - 4 * a^2 + 3 * b^3 </span>when a = -2 and b = 4, you can calculate this using the following steps:

54 - 4 * a^2 + 3 * b^3 = 54 - 4 * (-2)^2 + 3 * 4^3 = 54 - 4 * 4 + 3 * 64 = 54 - 16 + 192 = 230

If you would like to know what is the value of 54 - 4 * a^2 - 3 * b^3 when a = -2 and b = 4, you can calculate this using the following steps:

54 - 4 * a^2 - 3 * b^3 = <span>54 - 4 * (-2)^2 - 3 * 4^3 = 54 - 4 * 4 - 3 * 64 = 54 - 16 - 192 = -154</span>
8 0
3 years ago
Read 2 more answers
Which graph represents the solution to the system of inequalities below?
Reika [66]

Answer:

The correct option is;

B

Step-by-step explanation:

The given system of inequalities are;

5·x - 4·y > 4...(1)

x + y < 2...(2)

Representing both inequalities as a function of "y", gives;

For, 5·x - 4·y > 4...(1), we have;

-4·y > 4 - 5·x

y < 4/(-4) - 5·x/(-4)

∴ y < 5·x/4 - 1

For x + y < 2...(2), we have;

y < 2 - x

Therefore, y is less than the values given by the equation of the straight line equalities, and the feasible region is given by the common region under both dashed lines representing both inequalities as shown in the attached diagram created using Microsoft Excel

The correct option is therefore, B.

3 0
3 years ago
Equations and inequalities!<br> solve for w <br> 11=253-w
Annette [7]

Answer:

w = 242

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

  • 11=-w + 253
  • -w + 253 = 11

Step 2: Subtract 253 from both sides.

  • -w + 253 - 253 = 11 - 253
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Step 3: Divide both sides by -1.

  • \frac{-w}{-1}=\frac{-242}{-1}
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Step 4: Check if solution is correct.

  • 11 = 253 - (242)
  • 11 = 253 - 242
  • 11 = 11

Therefore, w = 242.

Have a lovely rest of your day/night.

8 0
2 years ago
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