Center (3, -2) Radius = 3
1 answer:
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Answer:
Height of mound = 794 ft
Step-by-step explanation:
To illustrate the angle of elevation and distance, i have drawn it and attached below.
Now, from my diagram;
h = the height of the mound
At his first point of his trip to the foot of the mound, the angle of elevation is 40°, while the horizontal distance to the foot of the mound is "X"
So, by triangle definition,
tan(40°) = h/x
And so;
h = x tan40
h = 0.8391x - - - - (eq 1)
At his second point of the trip to the foot of the mound, Joe is now,
"(x - 450) ft" from the foot of the mound.
Thus, his angle of elevation is 40 + 18 = 58°.
So, by triangle definition,
tan(58°) = h/(x - 450)
h = (x - 450)•(tan(58°))
h = 1.6003(x - 450)
h = 1.6003x - 720.135 - - - - -(eq2)
To get the height(h) of the mound, let's equate (eq1) to (eq2).
0.8391x = 1.6003x - 720.135
1.6003x - 0.8391x = 720.135
0.7612x = 720.135
x = 720.135/0.7612
x = 946.0523 ft
Let's put this value for x in eq (1);
h = 0.8391 x 946.0523 = 793.83 ft ≈ 794ft
Step-by-step explanation:
4. So, total time traveled is calculated by adding travel times in both directions.
From Detroit to Chicago, Charlie flew 300 miles at 150 miles per hour speed. That means that he traveled:
t1 = s / v1
t1 = 300 miles / 150 miles per hour
t1 = 2 hours
Now, let's do the same for the opposite direction. Since it's the same distance, he again flew 300 miles, but the speed this time was 100 miles per hour:
t2 = s / v2
t2 = 300 miles / 100 miles per hour
t2 = 3 hours
So, total time he traveled was t1 + t2 = 2 hours + 3 hours = 5 hours.
For the trip distance we need to add distances in both directions. We already said that the distance is the same, so the total trip distance is 300 miles + 300 miles = 600 miles.
Displacement shows how far are the ending and the starting point. Since Charlie started from Detroit, flew to Chicago, and then came back to Detroit, his ending point is the same as the starting, so the displacement is 0.
We can calculate average speed by dividing total distance with the total travel time. We already found that the total trip distance was 600 miles, and the total travel time was 5 hours. That means that:
v(average) = s(total) / t (total)
v(average) = 600 miles / 5 hours
v (average) = 120 miles per hour
As for the average velocity, we calculate it by dividing displacement by total travel time. Since the displacement was 0, average velocity will also be 0.
5. From the left graph we see that the object went from 0 to 2 meters (it moved 2 meters) in 1 second. That means that its speed was:
v1 = s1 / t1
v1 = 2 meters / 1 second
v1 = 2m/s
From there, it went from 2 to 4 meters (it moved 2 meters) in the next 4 seconds. That means that its speed, during that interval, was:
v2 = s2 / t2
v2 = 2 meters / 4 seconds
v2 = 0.5 m/s
So, our graph will show, for the first second, velocity of 2m/s, and for the next four seconds, the velocity of 0.5 m/s.
6. Again, when calculating speed, we use the equation:
v = s / t
In this case, the distance (s) is 325 miles and the time (t) is 5 hours. So, the speed will be:
v = 325 miles / 5 hours
v = 65 mph
7. Now, we have the same distance (s) of 325 miles ant the speed (v) of 70 mph. We want know how long will the drive take:
t = s / v
t = 325 miles / 70 mph
t = 4.64 hours.
