paper work
Project
In
Mathematics
Submitted by: Michelle Quitalig Section: IV-Gold
Submitted to: Mrs. Diño
Problem:
1. A satellite dish in storage has parabolic cross sections and is resting on its vertex.A point on the rim is 4 feet high and is 6 feet horizontally from the vertex. How high is a point which is 3 feet horizontally from the vertex?
2. Jack Pott dives off the high diving board. His distance from the surface of the water varies quadratically with the number of seconds that have passed since he left the board. His distance at time 1, 2 and 3 seconds since he left the board are 24, 18, 2 meters above the water respectively. How high is the diving board?
3. A ball is thrown into the air. Its height above the ground, h (measured in feet), at any given time after the ball is thrown, t (measured in seconds), can be modelled using the quadratic function h(t) = -16t2 + 16t + 32. From what height above the ground was the ball thrown?
Solutions:
1. C = 0 Using point (-6, 4 ) and (6, 4) 4 = a (-6)^2 + (-6)b + c 4 = 36 a -6b + c 4 = 36 a + 6b + c 8 = 72 a a = 1/9 Solving for b ; 4 = 36 (1/9) + 6b 4 = 4 + 6b B = 0 The equation of the parabola is y = 1/9 x^2 Y = 1/9 (3)^2 Y = 1/9(9) = 1
The point which is 3 feet horizontally from the vertex is 1 foot high.
2. -3a - b = 6 let this be equation 4 Using equation 2 and equation 3 to eliminate c 4a + 2b + c = 18 -9a - 3b + c = - 2 -5a - b = 16 let this be equation 5 Solving for a and b using equation 4 and equation 5 -3a –b = 6 +5a +b = -16
2a = -10 a = -5 substituting a = -5 in equation 4
-3(-5) – b = 6
15 – b = 6 b = 15 – 6 b = 9 substituting a = -5 b = 9 in equation 1 to solve for c
-5 + 9 + c = 24
In
Mathematics
Submitted by: Michelle Quitalig Section: IV-Gold
Submitted to: Mrs. Diño
Problem:
1. A satellite dish in storage has parabolic cross sections and is resting on its vertex.A point on the rim is 4 feet high and is 6 feet horizontally from the vertex. How high is a point which is 3 feet horizontally from the vertex?
2. Jack Pott dives off the high diving board. His distance from the surface of the water varies quadratically with the number of seconds that have passed since he left the board. His distance at time 1, 2 and 3 seconds since he left the board are 24, 18, 2 meters above the water respectively. How high is the diving board?
3. A ball is thrown into the air. Its height above the ground, h (measured in feet), at any given time after the ball is thrown, t (measured in seconds), can be modelled using the quadratic function h(t) = -16t2 + 16t + 32. From what height above the ground was the ball thrown?
Solutions:
1. C = 0 Using point (-6, 4 ) and (6, 4) 4 = a (-6)^2 + (-6)b + c 4 = 36 a -6b + c 4 = 36 a + 6b + c 8 = 72 a a = 1/9 Solving for b ; 4 = 36 (1/9) + 6b 4 = 4 + 6b B = 0 The equation of the parabola is y = 1/9 x^2 Y = 1/9 (3)^2 Y = 1/9(9) = 1
The point which is 3 feet horizontally from the vertex is 1 foot high.
2. -3a - b = 6 let this be equation 4 Using equation 2 and equation 3 to eliminate c 4a + 2b + c = 18 -9a - 3b + c = - 2 -5a - b = 16 let this be equation 5 Solving for a and b using equation 4 and equation 5 -3a –b = 6 +5a +b = -16
2a = -10 a = -5 substituting a = -5 in equation 4
-3(-5) – b = 6
15 – b = 6 b = 15 – 6 b = 9 substituting a = -5 b = 9 in equation 1 to solve for c
-5 + 9 + c = 24