The center of an ice rink is located at (0, 0) on a coordinate system measured in meters. Susan is skating along a path that can
be modeled by the equation y = 6x – x2 – 5. Luke starts at (10, –21) and skates along a path that can be modeled by a quadratic function with a vertex at (8, –9). If the rink is a circle with a radius of 35 meters, which statement best interprets the solution(s) of a system of equations modeling the paths of the skaters?
A. The skaters’ paths intersect once, but that point is outside the rink.
B. The skaters’ paths intersect once, and that point is inside the rink.
C. The skaters’ paths intersect twice, but only one of those points is inside the rink.
D. The skaters’ paths intersect twice, and both points are inside the rink.
A. The skaters’ paths intersect once, but that point is outside the rink.
B. The skaters’ paths intersect once, and that point is inside the rink.
C. The skaters’ paths intersect twice, but only one of those points is inside the rink.
D. The skaters’ paths intersect twice, and both points are inside the rink.
2 answers:
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Response:
A 120 cm long pipe produces resonance at wavelengths of 480 cm, 160 cm, and 96 cm, but fails to resonate with any wavelengths longer than those. Consequently, this pipe is classified as:
A. closed at both ends
B. open at one end and closed on the other
C. open at both ends.
D. we cannot determine since we lack information about the sound frequency.
The correct answer is:
B. open at one end and closed at the other.
Explanation in steps:
The given data states that the pipe has a length of
= 120 cmwith wavelengths = 480 cm
= 160 cm and = 96 cm
Note:
For a pipe open at both ends, the fundamental wavelength is 2L.
For a pipe closed at one end and open at the other, the fundamental wavelength is 4L.
- From this information,
- It appears that this pipe is open at one end and closed at the other.
In the case of a pipe with one open end and one closed end:[
Odd multiples of one-quarter wavelength must fit within the length L.
⇒
⇒
⇒⇒ ⇒ ⇒
⇒Thus, it confirms that the pipe is open at one end and closed at the other.