Answer:
graph of cosine function
Explanation:
<u>f(x) = sin(x)</u>
The curve of the sine function crosses the y-axis at the origin, heads up to y = 1 at x = π/2 and down to y = -1 at x = 3π/2.
Domain: (-∞, ∞)
Range: [-1, 1]
<u>f(x) = cos(x)</u>
The curve of the cosine function crosses the y-axis at (0, 1) which is its maximum, heads down to y = -1 at x = π then heads up again.
Domain: (-∞, ∞)
Range: [-1, 1]
Given information:
If the wheel starts when time t = 0 seconds, and they begin their journey at the top of the wheel (the maximum point), the most appropriate graph to model their ride is the graph of the cosine function since it is at its highest point when x = 0.
Answer:
The distance is 55.636 billion miles, or 528.2 AU.
Explanation:
Since the distance from the Sun to Neptune is 2.7818 billion miles, the distance from the Sun to Planet Nine would be 20 times that, which is:
or 55.636 billion miles.
Since 1 astronomical unit (AU) is 93 million miles, that distance is also:
The canoe is moving at 14.1 m/s to the right after the collision.
Explanation:
According to the law of conservation of momentum, in absence of external forces the total momentum of the system must be conserved before and after the collision. So we can write:
where:
is the mass of the canoe
is the initial velocity of canoe (we take right as positive direction, and since the canoe is moving to the left, its velocity is negative)
is the final velocity of the canoe
is the mass of the raft
is the initial velocity of the raft
is the final velocity of the raft
Re-arranging the equation and substituting the values, we find: the final velocity of the canoe:
So, the canoe is moving at 14.1 m/s to the right after the collision.
Learn more about momentum:
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