A running track consists of two straight sections with semi-circular ends. If the straight sections measure 100 metres and one compete lap on the inside of the track measures 1/2 k, what is the distance x between the two straights?
well, add up the distances. You have two straight sections of 100m and a circle of diameter x, so
2*100 + πx = 500
x = 300/π
Ah, the running track, the perfect place to burn calories while simultaneously questioning your life choices. But fear not, I shall help you solve this mathematical conundrum!
So, let's break this down. We know that one complete lap on the inside of the track measures 1/2 kilometer. Since one lap consists of two straight sections and two semi-circular bends, we need to find the distance between the two straight sections.
The straight sections of the track measure 100 meters each. Since there are two of them, the total distance covered by the straight sections is 200 meters.
Now, we need to find the distance covered by the semi-circular ends. We know that the total lap is 1/2 kilometer, which is equal to 500 meters. Since the straight sections accounted for 200 meters, the distance covered by the semi-circular ends is 500 - 200 = 300 meters.
The semi-circular ends each cover the same distance because they're, well, semi-circular. So each semi-circular end covers 300 / 2 = 150 meters.
Now, to find the distance between the two straights, we need to add the lengths of the semi-circular ends. Therefore, x = 150 meters.
So, the distance between the two straight sections of the running track is a clown-worthy 150 meters!
To find the distance x between the two straights, we need to determine the length of the curved semicircular ends of the running track.
Given that one complete lap on the inside of the track measures 1/2 k, we can calculate the length of the curved section.
The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
Since the curved section is a semicircle, the circumference is half of the full circle.
Let's assume the radius of the semicircular ends is "r". Therefore, the curved section's length will be (1/2)(2πr) = πr.
For one complete lap inside the track to be equal to 1/2 k, the distance covered by the two straight sections and the curved sections must be 1/2 k.
So we can write the equation:
2 × (100 meters) + 2 × (πr) = 1/2 k
We know that 1 kilometer equals 1000 meters, so 1/2 k is equal to 1/2 × 1000 = 500 meters.
Substituting this value into the equation, we have:
2 × 100 + 2 × πr = 500
Simplifying the equation:
200 + 2πr = 500
2πr = 300
Dividing both sides of the equation by 2π:
r = 150 / π
Now, we need to find the distance x between the two straights, which is twice the length of the curved section:
x = 2 × πr
x = 2 × π × (150 / π)
x = 300 meters
Therefore, the distance x between the two straights is 300 meters.
To find the distance between the two straight sections of the running track, we need to first calculate the length of one complete lap on the inside of the track.
One complete lap on the inside of the track consists of two straight sections and two semi-circular ends. The length of the straight sections is given as 100 meters each.
The length of a semi-circle is calculated using the formula C = πd, where C is the circumference and d is the diameter. Since we know the length of the straight sections, we can find the diameter of the semi-circular ends.
The circumference of a semi-circle is half of that of a full circle, so we need to divide the circumference by 2.
Given that the length of one complete lap on the inside of the track is 1/2 k, we can write the equation:
100 + 100 + (πd)/2 + (πd)/2 = 1/2 k
Simplifying the equation, we have:
200 + πd = 1/2 k
Now, we need to know the value of k to solve for d.
Once we know the value of d, we can find the distance x between the two straight sections by subtracting the diameter from the total length of one complete lap on the inside of the track:
x = 1/2 k - d