The drawing below (not to scale) shows a running track. The ends are semicircles. The distance between the two inner parallel straight lines is 60 meters, and they are each 100 meters long. The track is 10 meters wide/

4200 m²

Step-by-step explanation:

The drawing below (not to scale) shows a running track. The ends are semicircles. The distance between the two inner parallel straight lines is 60 meters, and they are each 100 meters long. The track is 10 meters wide. Find the area of the track. Shaded part

Solution:

The big semicircle has a diameter = 60 m + 10 m + 10 m = 80 m

The radius of the big semicircle = 80 m / 2 = 40 m

The area of the two big semicircles at both end of the big track = 2 * (1/2 πr²) = πr² = π(40)² = 5027 m²

The big track has semicircles at both ends and a rectangle. The length of the rectangle = 100 m, the width of the rectangle = diameter of big semicircle = 80 m

Area of big rectangle = length * width = 100 m * 80 m = 8000 m²

Area of big track = 8000 m² + 5027 m² = 13027 m²

The small semicircle has a diameter = 60 m

The radius of the small semicircle = 60 m / 2 = 30 m

The area of the two small semicircles at both end of the small track = 2 * (1/2 πr²) = πr² = π(30)² = 2827 m²

The small track has semicircles at both ends and a rectangle. The length of the rectangle = 100 m, the width of the rectangle = diameter of small semicircle = 60 m

Area of small rectangle = length * width = 100 m * 60 m = 6000 m²

Area of small track = 6000 m² + 2827 m² = 8827 m²

The area of track (shaded part) = Area of big track - Area of small track = 13027 m² - 8827 m² = 4200 m²

practice. practice. practice.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1