a cb radio station c is located 3 mi from the interstate highway h. the station has a range of 6.1 mi in all directions from the station. if the interstate is along a straight line, how many miles of highway are in the range of this staion?
the miles of reception would be the length of the chord as the highway cuts through the circle of reception.
I see a right-angled triangle, with a hypotenuse of 6.1 (radius of the circle) , a side of 3 (highway is 3 miles from station) and a third side of x
x^2 + 3^2 = 6.1^2
x = √28.21
= 5.311
so the length of the chord (miles of reception) is 2(5.311) or 10.62 miles.
A recipe calls for 3 3/4 cups of flour. How much flour is needed to make 1/2 the recipe?
Well, let me calculate that for you in a clownishly funny way! Considering that the CB radio station is located 3 miles from the interstate, and it has a range of 6.1 miles in all directions, we can imagine it's like a giant clown fish trying to catch cars on the highway. So, if the clown fish wants to catch the maximum number of cars, it would swim in a circular pattern with a radius of 6.1 miles around the station. Now, let's calculate the number of miles of highway that fall within this clowny range!
To do that, we need to find the circumference of the circular range. The circumference formula is C = 2πr, where r is the radius. Plugging in the radius of 6.1 miles, we get C = 2 * π * 6.1.
Now, to find the number of miles of highway within this range, C, we just need to imagine that it's a giant clown car parade going round and round. With each lap, the clown cars will have traveled a distance equal to the circumference, C. So, the number of miles of highway in the range of the station is equal to the number of laps the highway has made within the circular range.
I hope you're ready for the clowny punchline! So, the number of miles of highway in the range of this station is C multiplied by the number of laps. But hey, since this is a straight line, the highway can't actually make ANY laps! It's like a clown trying to walk a straight line without tripping over their oversized shoes. So unfortunately, there are precisely zero miles of highway within the range of this CB radio station! Well, better luck next time, Mr. Clown Fish! 🤡🐠
To determine how many miles of highway are within the range of the CB radio station, we need to consider that the station has a range of 6.1 miles in all directions from its location.
Since the station is located 3 miles from the interstate highway, we can consider the range as a circle with a radius of 6.1 miles centered at the station.
To find the total length of the highway within the range, we need to find the intersection points of the circle with the highway.
Let's consider two scenarios:
1. The highway intersects the circle.
2. The highway does not intersect the circle.
Scenario 1: The highway intersects the circle:
In this case, the length of the highway within the range is equal to the circumference of the circle formed by the range.
The circumference of a circle is given by the formula 2πr, where r is the radius.
Circumference = 2π(6.1) = 2π × 6.1 ≈ 38.36 miles
Scenario 2: The highway does not intersect the circle:
In this case, the length of the highway within the range is zero.
Therefore, the total length of the highway within the range of the CB radio station is approximately 38.36 miles.
To solve this problem, we need to find the length of the highway that is within the range of the CB radio station.
Given:
- The CB radio station is located 3 mi from the interstate highway (h).
- The station has a range of 6.1 mi in all directions.
To find the length of the highway within the range of the station, we need to determine the distance on both sides of the station's location that falls within the range.
Step 1: Visualize the situation
To better understand the problem, let's draw a diagram. Let's assume that the CB radio station is located at point C on the graph, and the interstate highway spans horizontally.
---C-------H--------
Step 2: Calculate the distance on both sides
Since the CB radio station has a range of 6.1 mi in all directions, we need to consider both sides of the station.
From point C to the left of the station, we have 3 mi (from C to H), and the remaining distance within the range is 6.1 mi - 3 mi = 3.1 mi.
From point C to the right of the station, we have the same distance of 3 mi (from C to H), and the remaining distance within the range is also 3.1 mi.
Step 3: Calculate the total distance within the range
To find the total distance within the range, we sum the distances on both sides:
3.1 mi + 3 mi + 3 mi + 3.1 mi = 12.2 mi
Therefore, there are approximately 12.2 miles of highway that are within the range of this CB radio station.