Answer:
(a) 3118=61*t
(b) The amount of time the roller coaster is in motion is 51.11 seconds.
Step-by-step explanation:
Speed is a magnitude that expresses the relationship between the space traveled by an object, the time used for it and its direction. In other words, speed is associated with the change in position of a body over time and can be expressed as:

Then the distance traveled can be expressed as:
distance=speed*time
(a) If x represents the total time that the roller coaster is in motion for each ride, the average speed is 61 feet per second and the distance is 3118 feet then the expression to represent the situation is:
<u><em>3118=61*x</em></u>
(b) To calculate the amount of time the roller coaster is moving, you simply need to solve the expression found in (a). Dividing 61 to both sides:

51.11 seconds=x
<u><em>
The amount of time the roller coaster is in motion is 51.11 seconds.</em></u>
Common difference: 6
First term: 7
Second term: 13
Third term: 19
Fourth term: 25
Fifth term: 31
I hope this is correct and helps!
Answer:
Step-by-step explanation:
V≈24543.69
Let the required point be (a,b)
The distance of (a,b) from (7,-2) is
= 
But this distance needs to be betweem 50 & 60
So

Squaring all sides
2500 < (a-7)² + (b+2)² < 3600
Let a = 7
So we have
2500 < (b+2)² <3600
b+2 < 60 or b+2 > -60 => b <58 or b > -62
Also
b+2 >50 or b + 2 < -50 => b >48 or B < -52
Let us take one value of b < 58 say b = 50
So now we have the point as (7, 50)
The other point is (7,-2)
Distance between them
= 
This is between 50 & 60
Hence one point which has a distance between 50 & 60 from the point (7,-2) is (7, 50)