MATH SOLVE

2 months ago

Q:
# PLEASE HELP!!1. calculate the length of the track2. how many laps do you need to travel 1609 meters (about 1 mile)?3. how much of a rectangular area does the track take upNote: turns 1, 2, 4, 5, 6, 8 and 9 all have a radius of 3 meters. Turns 3 and 7 each have a radius of 2.25 meters

Accepted Solution

A:

#1) 163.81 m

#2) About 9.8 laps.

#3) 1314 square meters

Explanation

#1) We first add all of the horizontal and vertical sections:

30+8+6+6+12+30+20 = 112 m

Now we find the distance around each curve. The distance around a circle is the circumference; the formula for circumference is

C=πd.

We will use 3.14 for π for each curve:

Curve 5: The radius is 3, so the diameter is 2*3 = 6. This is 1/4 of a curve, so we multiply the circumference by 1/4:

1/4(3.14)(6) = 4.71

Curve 4: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 3: This is 1/2 of a curve, so we will multiply the circumference by 1/2. The radius is 2.25, so the diameter is 2*2.25 = 4.5:

1/2(3.14)(4.5) = 7.065

Curve 2: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 1: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 9: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 8: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 7: This is another 1/2 curve with a radius of 2.25, so the distance around is 7.065, just as curve 3.

Curve 6: This is 1/2 of a curve with a radius of 3, so the distance around is 1/2(3.14)(2*3) = 9.42

The total distance around the curved parts is:

4.71+4.71+7.065+4.71+4.71+4.71+4.71+7.065+9.42 = 51.81

Together this gives us 112+51.81 = 163.81.

#2) To find the number of laps it takes to go 1609 meters, divide:

1609/163.81 = 9.8

#3) To find the rectangular area, we first need the total distance across and the total distance vertically.

Horizontally, we have a radius of 3, a horizontal distance of 30, and another radius of 3:

3+30+3 = 36

(looking at the right hand side)

Vertically, we have a radius of 3, vertical distance of 8, radius of 3, radius of 2.25, radius of 2.25, radius of 3, vertical distance of 12, and radius of 3:

3+8+3+2.25+2.25+3+12+3 = 36.5

The area is then 36(36.5) = 1314 m²

#2) About 9.8 laps.

#3) 1314 square meters

Explanation

#1) We first add all of the horizontal and vertical sections:

30+8+6+6+12+30+20 = 112 m

Now we find the distance around each curve. The distance around a circle is the circumference; the formula for circumference is

C=πd.

We will use 3.14 for π for each curve:

Curve 5: The radius is 3, so the diameter is 2*3 = 6. This is 1/4 of a curve, so we multiply the circumference by 1/4:

1/4(3.14)(6) = 4.71

Curve 4: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 3: This is 1/2 of a curve, so we will multiply the circumference by 1/2. The radius is 2.25, so the diameter is 2*2.25 = 4.5:

1/2(3.14)(4.5) = 7.065

Curve 2: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 1: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 9: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 8: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 7: This is another 1/2 curve with a radius of 2.25, so the distance around is 7.065, just as curve 3.

Curve 6: This is 1/2 of a curve with a radius of 3, so the distance around is 1/2(3.14)(2*3) = 9.42

The total distance around the curved parts is:

4.71+4.71+7.065+4.71+4.71+4.71+4.71+7.065+9.42 = 51.81

Together this gives us 112+51.81 = 163.81.

#2) To find the number of laps it takes to go 1609 meters, divide:

1609/163.81 = 9.8

#3) To find the rectangular area, we first need the total distance across and the total distance vertically.

Horizontally, we have a radius of 3, a horizontal distance of 30, and another radius of 3:

3+30+3 = 36

(looking at the right hand side)

Vertically, we have a radius of 3, vertical distance of 8, radius of 3, radius of 2.25, radius of 2.25, radius of 3, vertical distance of 12, and radius of 3:

3+8+3+2.25+2.25+3+12+3 = 36.5

The area is then 36(36.5) = 1314 m²