The function g(x) represents f(x)=9 cos (x-pi/2)+3 after translating pi/6 units left and 4 units up. which equation represents g
1 answer:
Answer:
g(x)= 9 cos (x - ) +7
Step-by-step explanation:
What is given is f(x) = g cos (x - pi/2) + 3
Note that the standard form of cosine function is a cos (bx + c) + d
a= amplitude
-c/b = phase shift
d = vertical shift
After moving pi/6 to the left --
x = pi/2 - pi/6 = pi/3
once moving pi/6 left, it is at pi/3
moving 4 units up just means adding 4 + 3, and that equals 7, that would be the vertical shift once applied.
So the equation that represents g(x) is C. 9 cos (x - pi/3) + 7
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Answer:
The time that elapses before the players collide is 4.59 secs
Step-by-step explanation:
The distance between the two players is 41 meters. Hence, they would have total distance of 41 meters by the time they collide.
We can write that
S₁ + S₂ = 41 m
Where S₁ is the distance covered by Player 1 before collision
and S₂ is the distance covered by Player 2 before collision
From one of the equations of kinematics for linear motion,
+
Where is distance
is the initial velocity
is acceleration
and is time
Since the players collide at the same time, then time spent by player 1 before collision equals time spent by player 2 before collision
That is, t₁ = t₂ = t
Where t₁ is the time spent by player 1
and t₂ is the time spent by player 2
For player 1
= S₁
= 0 m/s ( The player starts at rest)
= 2.2 m/s²
Then,
S₁ = +
S₁ =
For player 2
= S₂
= 0 m/s ( The player starts at rest)
= 1.7 m/s²
Then,
S₂ = +
S₂ =
Since the time spent by both players is equal, We can write that
=
Then,
From, S₁ + S₂ = 41 m
S₂ = 41 - S₁
Then,
This is the distance covered by the first player. We can then put this value into to determine how much time elapses before the players collide.
Hence, the time that elapses before the players collide is 4.59 secs