Randy wants to run half a marathon. Half a marathon is 13.1 miles. if she wants to run the race in 2 hours what rate(in minutes
2 answers:
Answer:
Step-by-step explanation:
Randy wants to run half a marathon that is 13.1 miles long.
She wants to run the race in 2 hours.
1 hour = 60 minutes
2 hours = 60 × 2 = 120 minutes
speed rate (minutes per mile) =
=
= 9.16 minutes per mile
She should run each mile in 9.16 minutes.
At the 10 mile mark, Randy realizes that her total running time is 90 minutes.
whereas she was prepared to complete 10 miles in (9.16 × 10) = 91.6 minutes.
So Randy has been faster than her intended pace.
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Answer:
233.48s
3.84 min
Step-by-step explanation:
In order to solve this problem, we can start by drawing what the situation looks like. See attached picture.
We can model this situation by making use of a trigonometric function. Trigonometric functions have the following shape:
where:
A= amplitude =-20m because the model starts at the lowest point of the trajectory.
f= the function to use, in this case we'll use cos, since it starts at the lowest point of the trajectory.
t= time
angular speed.
in this case:
where T is the period, in this case 6 min or
so:
and
= phase angle
C= vertical shift
in this case our vertical shift will be:
2m+20m=22m
in this case the phase angle is 0 because we are starting at the lowest point of the trajectory. So the equation for the ferris wheel will be:
Once we got this equation, we can figure out on what times the passenger will be higher than 13 m, so we build the following inequality:
so we can solve this inequality, we can start by turning it into an equation we can solve for t:
and solve it:
and we can take the inverse of cos to get:
which yields two possible answers: (see attached picture)
so
or
so we can solve the two equations. Let's start with the first one:
t=63.25s
and the second one:
t=296.73s
so now we can build our possible intervals we can use to test the inequality:
[0, 63.25] for a test value of 1
[63.25,296.73] for a test value of 70
[296.73, 360] for a test value of 300
let's test the first interval:
[0, 63.25] for a test value of 1
2>13 this is false
let's now test the second interval:
[63.25,296.73] for a test value of 70
15.16>13 this is true
and finally the third interval:
[296.73, 360] for a test value of 300
12>13 this is false.
We only got one true outcome which belonged to the second interval:
[63.25,296.73]
so the total time spent above a height of 13m will be:
196.73-63.25=233.48s
which is the same as:
see attached picture for the graph of the situation. The shaded region represents the region where the passenger will be higher than 13 m.
