1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
BlackZzzverrR [31]
3 years ago
13

an athletic facility is building an indoor track. the track is composed of a rectangle and two semicircles, as shown. a) write a

formula fir the perimeter of the indoor track. b) solve the formula for x. c) the perimeter of the track is 660 feet, and r is 50 feet. find x. round your answer to the nearest foot.

Mathematics
1 answer:
stepan [7]3 years ago
6 0

Answer:

(a) P = 2x + 2r + 2πr

(b) x = ½(P - 2r - 2πr)

(c) x = 123 feet

Step-by-step explanation:

See Attachment for sketch of the track

Solving for (a): Perimeter of the track

This is calculated by adding the perimeter of the rectangle to the 2 semicircles as follows.

P = Perimeter of Rectangle + Perimeter of 2 Semicircles

P = 2(x + r) + 2 * πr

[Where r is the radius of both semicircles]

Open bracket

P = 2x + 2r + 2πr

Solving for (b): Formula for x

P = 2x + 2r + 2πr

Make x the subject of formula

2x = P - 2r - 2πr

Divide both sides by 2

x = ½(P - 2r - 2πr)

Solving for (c): the value of x when r = 50 and P = 660

Substitute the given values in the formula in (b) above

x = ½(P - 2r - 2πr)

x = ½(660 - 2 * 50 - 2π * 50)

x = ½(660 - 100 - 100π)

x = ½(560 - 100π)

Take π as 3.14

x = ½(560 - 100 * 3.14)

x = ½(560 - 314)

x = ½ * 246

x = 123 feet

You might be interested in
Team A is located on the south bank of a river. Teams B and C are located on the north bank. The angle formed from Team C to Tea
creativ13 [48]
The correct answer is 58.5
6 0
3 years ago
a surveyor measures the distance to the two landmarks as shown in the diagram what is the distance d. between the landmarks​
Inessa [10]
<h3>The distance between two landmarks is 123 meters</h3>

<em><u>Solution:</u></em>

We have to find the distance between two landmarks

<em><u>Use the law of cosines</u></em>

The third side of a triangle can be found when we know two sides and the angle between them

c^2 = a^2 + b^2 - 2ab\ cos c

Here, angle between 90 meters and 130 meters is 65 degrees

From figure,

a = 90

b = 130

c = d

Therefore,

d^2 = 90^2 + 130^2 - 2(90)(130)\ cos 65\\\\d^2 = 8100 + 16900 - 23400\ cos\ 65\\\\d^2 = 25000 - 23400 \times 0.4226\\\\d^2 = 25000 - 9889.267\\\\d^2 = 15110.73\\\\d = 122.92\\\\d \approx 123

Thus, the distance between two landmarks is 123 meters

8 0
3 years ago
-1/3+(-7/4) in simplist form
Airida [17]

Answer:

your answer will be -\frac{25}{12}

Step-by-step explanation:

hope this helps have a nice day :)

8 0
2 years ago
Read 2 more answers
Manufacture of a certain component requires three different machining operations. Machining time for each operation has a normal
tigry1 [53]

Answer:

0.0314 = 3.14% probability that it takes at most 1 hour of machining time to produce a randomly selected component

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Sum of normal variables:

When normal variables are added, the mean is the sum of the means while the standard deviation is the square root of the sum of the variances.

The mean values are 20, 15, and 30 min, respectively:

This means that \mu = 20 + 15 + 30 = 65

The standard deviations are 1, 2, and 1.5 min, respectively.

This means that \sigma = \sqrt{1^2 + 2^2 + 1.5^2} = 2.6926

What is the probability that it takes at most 1 hour of machining time to produce a randomly selected component?

Mean and standard deviation are in minutes, so this is the pvalue of Z when X = 60.

Z = \frac{X - \mu}{\sigma}

Z = \frac{60 - 65}{2.6926}

Z = -1.86

Z = -1.86 has a pvalue of 0.0314

0.0314 = 3.14% probability that it takes at most 1 hour of machining time to produce a randomly selected component

7 0
2 years ago
Geometry: Solve for X
nevsk [136]
6) x= 2, angle = 90 degrees obviously
7) Im not sure on this one
8) x = 5
9) x = 1

3 0
3 years ago
Read 2 more answers
Other questions:
  • A woman is twice as old as her daughter. Twenty years ago, she was four times as old as he daughter. How old are they now? (i do
    5·1 answer
  • What is 5,382,619 rounded to the nearest 1,000
    14·1 answer
  • Can you show how to solve this question? Thomas and Sharlina work on weekends and holidays doing odd jobs around the neighborhoo
    11·1 answer
  • Andy got a 32%discound on all his purchases at his favorite shop. If he saved 64$ on the total bill, the bill amount with out th
    15·1 answer
  • Help I'll give brainlist for anyone who can write and solve the hardest math problem!,,
    10·1 answer
  • Out of the 30 days in April, 3/5 of the days were sunny and clear. The rest of the days were either cloudy or contained some rai
    9·1 answer
  • Whats the answer for -2x+11+6x ?
    9·1 answer
  • What is the sum of y and 7
    6·1 answer
  • What will be the answer?
    11·1 answer
  • Solución del problema
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!