Select the ordered pairs that represents a solution to the functions below. F(x)= - x^2 +5.F(x)=x^2+5.
1 answer:
Answer:
(0,5)
Step-by-step explanation:
(1) y = -x² + 5
(2) y = x² + 5
2y =10 Added (1) and (2)
(3) y = 5 Divided each side by 2
5 = x² + 5 Substituted (3)into (2)
0 = x² Subtracted 5 from each side
x = 0 Took the square root of each side
The only ordered pair that represents a solution to both functions is (0, 5).
The graph of the second function is an upward-opening parabola (y = x²) translated up five units.
The graph of the first function is a downward-opening parabola (y = -x²) translated up five units.
The two graphs meet at their common vertex, (0, 5).
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Draw a diagram to illustrate the problem as shown below.
When the smaller gear rotates through a revolution, it sweeps an arc length of
2π(4) = 8π inches.
Part 1
The same arc length is swept by the larger gear. The central angle of the larger gear, x, is
7x = 8π
x = (8π)/7 radians = (8π)/7 * (180/π) = 205.7°
Answer: 205.7° (nearest tenth)
Part 2
When the larger gear makes one rotation, it sweeps an arc length of
2π(7) = 14π inches.
If the central angle for the smaller gear is y radians, then
4y = 14π
y = 3.5π radians = (3.5π)/2π revolutions = 1.75 revolutions
Answer:
The smaller gear makes 1.75 rotations
When the smaller gear rotates through a revolution, it sweeps an arc length of
2π(4) = 8π inches.
Part 1
The same arc length is swept by the larger gear. The central angle of the larger gear, x, is
7x = 8π
x = (8π)/7 radians = (8π)/7 * (180/π) = 205.7°
Answer: 205.7° (nearest tenth)
Part 2
When the larger gear makes one rotation, it sweeps an arc length of
2π(7) = 14π inches.
If the central angle for the smaller gear is y radians, then
4y = 14π
y = 3.5π radians = (3.5π)/2π revolutions = 1.75 revolutions
Answer:
The smaller gear makes 1.75 rotations