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
Temka [501]
2 years ago
7

Problem: A piece of farmland is a watering plot of land in a circular pattern. A sewer line needs to be installed from a new hou

sing project to a processing plant The city does not want the sewer line to cross the farm land. Can a direct line be installed?
● Let 1 unit = 100 feet.
● The entry to the sewer plant is at (2,3)
● The sewage exit from the housing project is at (12,6)
● The sprinkler system extends 200 ft and the center of the land is at (8,3)
Questions: (1) Will the sewer line cross the farmland? If so then at what points?
(2) If the farmer wants to maximize the farming area and does not want to cross the sewer line, what is the longest sprinkler system that could be installed?

Mathematics
1 answer:
Musya8 [376]2 years ago
3 0

The entry and exit points of (2, 3), and (12, 6), and 200 ft. extension of the sprinkler system gives;

(1) The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)

(2) The longest installable sprinkler system is approximately 172.4 feet

<h3>How can the points where the line crosses the farmland be found?</h3>

1. The slope of the sewer line is found as follows;

  • m = (6 - 3)/(12 - 2) = 3/10 = 0.3

The equation of the sewer line can be expressed in point and slope form as follows;

  • (y - 3) = 0.3×(x - 2)

y = 0.3•x - 0.6 + 3

y = 0.3•x + 2.4

The equation of the circumference of the sprinkler can be expressed as follows;

  • (x - 8)² + (y - 3)² = 2²

Therefore;

(x - 8)² + (0.3•x + 2.4 - 3)² = 2²

Solving gives;

x= 6.53, or x = 8.48

y = 0.3×6.53 + 2.4 = 4.36

y = 0.3×8.48 + 2.4 = 4.9

Therefore;

  • The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)

2. When the farmland does not cross the sewer line, we have;

sewer line is tangent to circumference of farmland

Slope of radial line from center of the land is therefore;

m1 = -1/0.3

Equation of the radial line to the point the sewer line is tangent to the circumference is therefore;

y - 3 = (-1/0.3)×(x - 8)

Which gives;

y = (-1/0.3)×(x - 8) + 3

The x-coordinate is therefore;

0.3•x + 2.4 = (-1/0.3)×(x - 8) + 3

  • x ≈ 7.5

  • y = 0.3 × 7.5 + 2.4 ≈ 4.65

The longest sprinkler system is therefore;

d = √((7.5 - 8)² + (4.65 - 3)²) ≈ 1.724

Which gives;

  • The longest sprinkler system is 1.724 × 100 ft. ≈ 172.4 ft.

Learn more about the equation of a circle here:

brainly.com/question/10368742

#SPJ1

You might be interested in
What equation best represents the following sentence?
nikdorinn [45]

Answer: n + 2 = 2n

Step-by-step explanation:

sum = add

number and two = n, 2

twice the number = 2 x n

4 0
3 years ago
Please help I don't understand
aniked [119]

Answer:

The expression can be written as:

5(2) + 6(3) + 2(4).

if I'm wrong, please tell me

5 0
2 years ago
Hey What is -5t &gt; 10
yanalaym [24]

Answer: 10 (ten) is an even number

following 9 and preceding 11

Step-by-step explanation:

3 0
3 years ago
Pls answer and explain how you got it - i will mark brainliest<br> (just answer #28)
Akimi4 [234]

Answer:

5 x^2 y^ (-3) z = ?

Step-by-step explanation:

We know the volume of a rectangular prism is given by

V = l*w*h

V = 2x^2 * y^-2 * ?

We are given the volume

V =10x^4 y^-5 z

Set  the two equal

10x^4 y^-5 z = 2x^2 * y^-2 * ?

Divide each side by 2x^2 y^-2

10x^4 y^-5 z /2x^2 y^-2 = 2x^2 * y^-2 * ?/2x^2 * y^-2

10x^4 y^-5 z/ 2x^2 y^-2 = ?

Simplifying

10/2  * x^4/x^2  y^-5/ y^-2  z = ?

We know that a^b/ a^c = a^(b-c)

5 x^ (4-2) y^(-5 - -2) z = ?

5 x^2 y^ (-5 +2) z = ?

5 x^2 y^ (-3) z = ?

4 0
3 years ago
Read 2 more answers
In the figure below, BD and EC are diameters of circle P.
Zinaida [17]

Answer: 333 degrees

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • How far away can a boy ride on a bicycle if he rides away at 10 kilometers per hour and returns at 9 kilometers per hour? The en
    11·1 answer
  • Twice a number increased by three times the number?
    10·2 answers
  • How to put the answer in a mixed number? (35^3/8)
    14·1 answer
  • Helpppp me plz any help would work :)
    15·2 answers
  • What is the polynomial is factored form please help
    8·1 answer
  • Determine whether the statement is true or false. If it is false, rewrite it as a true statement. Data at the ratio level cannot
    12·1 answer
  • Which of the following is an accurate description of the scatterplot?
    13·2 answers
  • Lulah is buying beach balls for her beach party. each package contains 6 beach balls
    10·1 answer
  • What previously accepted explanation did Dr. Goldman and Dr. Nottebohm challenge with their work regarding neurons of female son
    8·1 answer
  • What is the value of the expression -38-16-(-23)?<br> O-31<br> O-45<br> O-54<br> O-77
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!