Solved: Pythagorean Theorem An airplane is approaching Los

Determine which quadrant contains each of the following points. (2, -4)

Determine which quadrant contains each of the following points. (-4, -2)

Determine which quadrant contains each of the following points. (1, \1'3)

Determine which quadrant contains each of the following points. (-v3, 1)

Graph each of the following lines. y x

Graph each of the following lines. y -x

Graph each of the following lines. Y -x

Graph each of the following lines. y = -2x

In what two quadrants do all the points have negative x-coordinates?

In what two quadrants do all the points have negative y-coordinates?

For points (x, y) in quadrant I, the ratio x/y is always positive because x and y are always positive. In what other quadrant is the ratio x/y always positive?

For points (x, y) in quadrant II, the ratio x/y is always negative because x is negative and y is positive in quadrant II. In what other quadrant is the ratio x/y always negative?

Graph each of the following parabolas:Y = x 2 - 4

Graph each of the following parabolas:y = (x 2)2

Graph each of the following parabolas:y (x + 2)2 + 4

Graph each of the following parabolas:y = -(x + 2)2 + 4 4

Use your graphing calculator to graph y ax2 for a = /0' t, 1,5, and 10. Copy all five graphs onto a single coordinate system and label each one. What happens to the shape of the parabola as the value of a gets close to zero? What happens to the shape of the parabola when the value of a gets large?

Use your graphing calculator to graph y = ax2 for a = t, 1, and 5, then again for a -t, -1, and -5. Copy all six graphs onto a single coordinate system and label each one. Explain how a negative value of a affects the parabola.

Use your graphing calculator to graph y (x - hi for h = -3,0, and 3. Copy all three graphs onto a single coordinate system, and label each one. What happens to the position of the parabola when h < O? What if h > O?

Use your graphing calculator to graph y = x 2 + k for k -3,0, and 3. Copy all three graphs onto a single coordinate system, and label each one. What happens to the position of the parabola when k < O? What if k > O?

Human Cannonball A human cannonball is shot from a cannon at the county fair. He reaches a height of 60 feet before landing in a net 160 feet from the cannon. Sketch the graph of his path, and then find the equation of the graph. Verify that your equation is correct using your graphing calculator.

Human Cannonball Referring to Problem 21, find the height, reached by the human cannonball after he has traveled 30 feet horizontally, and after he has traveled 150 feet horizontally. Verify that your answers are correct using your graphing calculator.

Find the distance between the following points:(3,7), (6, 3)

Find the distance between the following points:(4,7), (8, 1)

Find the distance between the following points:(0, 12), (5, 0)

Find the distance between the following points:(-3,0), (0,4)

Find the distance between the following points: 1, -2), (-10,5)

Find the distance between the following points:8), (-1,6)

Find the distance from the origin out to the point (3, -4).

Find the distance from the origin out to the point (12, -5).

Find x so the distance between (x,2) and (1, 5) is Vl3.

Find Y so the distance between (7, y) and (3, 3) is 5.

Pythagorean Theorem An airplane is approaching Los Angeles International Airport at an altitude of 2,640 feet. If the horizontal distance from the plane to the runway is 1.2 miles, use the Pythagorean Theorem to find the diagonal distance from the plane to the runway (Figure 23). (5,280 feet equals 1 mile.) l.2mi Figure 23 horne Figure 24

Softball Diamond In softball, the distance from home plate to first base is 60 feet, L_ as is the distance from first base to second base. If the lines joining home plate to first base and first base to second base form a right angle, how far does a catcher standing on home plate have to throw the ball so that it reaches the shortstop standing on second base (Figure 24)?

Softball and Rectangular Coordinates If a coordinate system is superimposed on the softball diamond in Problem 34 with the x-axis along the line from home plate to first base and the y-axis on the line from home plate to third base, what would be the coordinates of home plate, first base, second base, and third base?

Softball and Rectangular Coordinates If a coordinate system is superimposed on the softball diamond in Problem 34 with the origin on home plate and the positive x-axis 'along the line joining home plate to second base, what would be the coordinates of first base and third base?

Verify that each point lies on the graph of the unit circle. (0, -1)

Verify that each point lies on the graph of the unit circle. (-1,0)

Verify that each point lies on the graph of the unit circle. (, ';)

Verify that each point lies on the graph of the unit circle. (~,-t)

Graph each of the following circles. x 2 + y2 = 25

Graph each of the following circles. x2 + y2 = 36

Graph the circle x 2 + y2 = 1 with your graphing calculator. Use the feature on your calculator that allows you to evaluate a function from the graph to find the coordinates of all points on the circle that have the given x-coordinate. Write your answers as ordered pairs and round to four places past the decimal point when necessary.x -

Graph the circle x 2 + y2 = 1 with your graphing calculator. Use the feature on your calculator that allows you to evaluate a function from the graph to find the coordinates of all points on the circle that have the given x-coordinate. Write your answers as ordered pairs and round to four places past the decimal point when necessary.x =

Graph the circle x 2 + y2 = 1 with your graphing calculator. Use the feature on your calculator that allows you to evaluate a function from the graph to find the coordinates of all points on the circle that have the given x-coordinate. Write your answers as ordered pairs and round to four places past the decimal point when necessary.x=

Graph the circle x 2 + y2 = 1 with your graphing calculator. Use the feature on your calculator that allows you to evaluate a function from the graph to find the coordinates of all points on the circle that have the given x-coordinate. Write your answers as ordered pairs and round to four places past the decimal point when necessary.x

Graph the circle x 2 + y2 = 1 with your graphing calculator. Use the feature on your calculator that allows you to evaluate a function from the graph to find the coordinates of all points on the circle that have the given x-coordinate. Write your answers as ordered pairs and round to four places past the decimal point when necessary.x

Graph the circle x 2 + y2 = 1 with your graphing calculator. Use the feature on your calculator that allows you to evaluate a function from the graph to find the coordinates of all points on the circle that have the given x-coordinate. Write your answers as ordered pairs and round to four places past the decimal point when necessary.=

Use the graph of Problem 41 to name the points at which the line x + y = 5 will intersect the circle x 2 + y2 25.

Use the graph of Problem 42 to name the points at which the line x - y = 6 will intersect the circle x 2 + y2 36.

At what points will the line y = x intersect the unit circle x 2 + y2 = I?

At what points will the line y - x intersect the unit circle x 2 + y2 = I?

Use the diagram in Figure 22 to help find the complement ofeach of the following angles.45

Use the diagram in Figure 22 to help find the complement ofeach of the following angles.30

Use the diagram in Figure 22 to help find the complement ofeach of the following angles.60

Use the diagram in Figure 22 to help find the complement ofeach of the following angles.0

Use the diagram in Figure 22 to help find the supplement of each of the following angles.120

Use the diagram in Figure 22 to help find the supplement of each of the following angles.150

Use the diagram in Figure 22 to help find the supplement of each of the following angles.90

Use the diagram in Figure 22 to help find the supplement of each of the following angles.45

Use the diagram in Figure 22 to help you name an angle between 0 and 360 that is coterminal with each of the following angles.-60

Use the diagram in Figure 22 to help you name an angle between 0 and 360 that is coterminal with each of the following angles.135

Use the diagram in Figure 22 to help you name an angle between 0 and 360 that is coterminal with each of the following angles.2lO

Use the diagram in Figure 22 to help you name an angle between 0 and 360 that is coterminal with each of the following angles.300

Draw each of the following angles in standard position, and find one positive angle and one negative angle that is coterminal with the given angle.300

Draw each of the following angles in standard position, and find one positive angle and one negative angle that is coterminal with the given angle.225 0

Draw each of the following angles in standard position, and find one positive angle and one negative angle that is coterminal with the given angle.-150

Draw each of the following angles in standard position, and find one positive angle and one negative angle that is coterminal with the given angle.-330

Draw each of the following angles in standard position and then do the following: a. Name a point on the terminal side of the angle. b. Find the distance from the origin to that point. c. Name another angle that is coterminal with the angle you have drawn.135

Draw each of the following angles in standard position and then do the following: a. Name a point on the terminal side of the angle. b. Find the distance from the origin to that point. c. Name another angle that is coterminal with the angle you have drawn.45

Draw each of the following angles in standard position and then do the following: a. Name a point on the terminal side of the angle. b. Find the distance from the origin to that point. c. Name another angle that is coterminal with the angle you have drawn.2250

Draw each of the following angles in standard position and then do the following: a. Name a point on the terminal side of the angle. b. Find the distance from the origin to that point. c. Name another angle that is coterminal with the angle you have drawn.315

Draw each of the following angles in standard position and then do the following: a. Name a point on the terminal side of the angle. b. Find the distance from the origin to that point. c. Name another angle that is coterminal with the angle you have drawn.90

Draw each of the following angles in standard position and then do the following: a. Name a point on the terminal side of the angle. b. Find the distance from the origin to that point. c. Name another angle that is coterminal with the angle you have drawn.360

Draw each of the following angles in standard position and then do the following: a. Name a point on the terminal side of the angle. b. Find the distance from the origin to that point. c. Name another angle that is coterminal with the angle you have drawn.450

Draw each of the following angles in standard position and then do the following: a. Name a point on the terminal side of the angle. b. Find the distance from the origin to that point. c. Name another angle that is coterminal with the angle you have drawn.-900

Find all angles that are coterminal with the given angle.30

Find all angles that are coterminal with the given angle.150

Find all angles that are coterminal with the given angle.1350

Find all angles that are coterminal with the given angle.-45

Find all angles that are coterminal with the given angle.90

Find all angles that are coterminal with the given angle.270

Draw 30 in standard position. Then find a if the point (a, 1) is on the terminal side of 30.

Draw 60 in standard position. Then find b if the point (2, b) is on the terminal [ side of 60.

Draw an angle in standard position whose terminal side contains the point (3, -2). Find the distance from the origin to this point.

Draw an angle in standard position whose terminal side contains the point c (2, -3). Find the distance from the origin to this point.

For problems 87 and 88, use the converse of the Pythagorean Theorem, which states 2 that if c a2 + b2, then the triangle must be a right triangle.Plot the poiuts (0, 0), (5, 0), and (5, 12) and show that, when connected, they are the vertices of a right triangle.

For problems 87 and 88, use the converse of the Pythagorean Theorem, which states 2 that if c a2 + b2, then the triangle must be a right triangle.Plot the points (0, 2), (-3,2), and (-3, -2) and show that they form the vertices of a right triangle.

Descartes and Pascal In the introduction to this section we mentioued two French philosophers, Descartes and Pascal. Many people see the philosophies of the two men as being opposites. Why is this?

Pascal's Triangle Pascal has a triangular array of numbers named after him, Pascal's triangle. What part does Pascal's triangle play in the expansion of (a + b)n, where n is a positive integer?