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Topic: Pre calculus (Conic Sections: Hyperbola)

1.)

A ship 5 km north of island I(1) , wishes to go to point X east of I(1). Since the advanced navigational system of the ship malfunctioned, they have to rely on a back-up system that uses radio signals from I(1) and another island, I(2). The captain is informed that they will reach X if they maintained the current difference in their distances from I(1) and I(2). If I(2) is 12 km east of I(1). How far is X from I(1).

2.) Anna lives 10 km west of Jose. One quiet evening, Anna suddenly hears a loud explosion. If Jose hears the explosion exactly 22 6/7 seconds later, find the collection of all possible locations of the explosion source. Assume that sound travels at a speed of 350 m s^-1.

3.) The foci of a hyperbola are (-5,-3) and (9,-3). For any point on the hyperbola, the absolute value of the difference of its of its distances from the foci is 10. Find the standard equation of the hyperbola.

the image of (6, 9) under a dilation is (4, 6). the scale factor is

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1                     1

1                     2

1                     3

1                     4

2                   1

2                   2

2                   3

2                   4   = not 1, and 4

3                   1

3                   2

3                   3

3                   4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation:

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true