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
vladimir1956 [14]
3 years ago
10

A crawling tractor sprinkler is located as pictured below, 100 feet South of a sidewalk. Once the water is turned on, the sprink

ler waters a circular disc of radius 20 feet and moves North along the hose at the rate of 1/2 inch/second. The hose is perpendicular to the 10 ft. wide sidewalk. Assume there is grass on both sides of the sidewalk.
a) Impose a coordinate system. Describe the initial coordinates of the sprinkler and find equations of the lines forming and find equations of the lines forming the north and south boundaries of the sidewalk.

b) When will the water first strike the sidewalk?

c) When will the water from the sprinkler fall completely north of the sidewalk?

d) Find the total amount of time water from the sprinkler falls on the sidewalk.

e) Find the area of grass watered after one hour.

Mathematics
1 answer:
deff fn [24]3 years ago
5 0

Answer:

  a) see below

  b) 32 minutes after turn-on

  c) 52 minutes after turn-on

  d) 20 minutes

  e) 6856.6 ft²

Step-by-step explanation:

a) We have elected to put the origin at the point where the hose crosses the south edge of the sidewalk. Units are feet. Then the sprinkler starts at (0, -100). After 1 hour, 3600 seconds, the sprinkler is 1800 inches, or 150 ft north of where it started, so stops at (0, 50).

The lines forming the sidewalk boundaries are y=0 and y=10.

__

b) Water will first strike the sidewalk when the sprinkler is 20 feet south of it, or 80 feet north of where it started. The sprinkler travels that distance in ...

  (80 ft)(12 in/ft)/(1/2 in/s)(1 min/(60 s)) = 32 min . . . time to start sprinkling sidewalk

__

c) The sprinkler has to travel to a point 130 ft north of its starting position for the water to fall north of the sidewalk. That distance is traveled in ...

  (130 ft)(2/5 min/ft) = 52 min . . . time until end of sprinkling sidewalk

Note that we have combined the scale factors in the expression of part b into one scale factor of (2/5 min/ft).

__

d) The difference of times in parts b and c is the time water falls on the sidewalk: 20 minutes.

__

e) In one hour, the sprinkler travels a distance of ...

  (60 min)(5/2 ft/min) = 150 ft

Of that distance, 10 feet is sidewalk. So, the sprinkler covers an area of grass that is a 140 ft by 40 ft rectangle and a circle of 20 ft radius. The total area of that is ...

  A = LW + πr² = (140 ft)(40 ft) +π(20 ft)² = (14+π)(400) ft² ≈ 6856.6 ft²

The area of grass watered in 1 hour is about 6856.6 ft².

You might be interested in
A sphere has a surface area of about 999 square millimeters. What is the radius, in millimeters, of the sphere
motikmotik

Given that, a sphere has a surface area of about 999 square millimeters.

Formula to find the surface area of sphere is,

S= 4πr² Where r = radius of the sphere and S= surface area.

Given S= 999 square millimeters.

So, we can write:

4πr² = 999

4 * 3.14 * r² = 999 Since, π = 3.14

12.56 *r² = 999

r^2=\frac{999}{12.56} Divide each sides by 12.56.

r² = 79.53821656

r = √79.53821656 Taking square root to each sides of equation.

r = 8.918420071

So, r = 8.918 Rounded to nearest thousandth.

So, radius of the sphere is 8.918 millimeters.

Hope this helps you!

5 0
3 years ago
What is the result of the calculation of 89.332 + 1.1 without adjusting for the correct number of significant figures?
Orlov [11]
The answer is 90.432.
7 0
3 years ago
Simplify 30 – 5(15 - 10). A. -55B. 125C.20D.5
Harrizon [31]

Simplify : 30 – 5(15 - 10).

Apply BODMAS :

B- Brackets

O-Of

D-Division

M-Multiplication

A-Adition

S-Subtraction

\begin{gathered} 30-5(15-10) \\ 30-5(5) \\ 30-25 \\ 5 \end{gathered}

Answer : D) 5

6 0
1 year ago
Find the volume of a cylinder with height 12 cm and diameter 7 cm.
Svet_ta [14]
<span>461.81 cm^3 .................................</span>
3 0
3 years ago
Someonee helppp pleaseee
lyudmila [28]
7,874 inches is the answer
Hope this helps!!!


5 0
2 years ago
Read 2 more answers
Other questions:
  • The sides of a triangle are of lengths 13, 14, 1nd 15. the altitude of the triangle meet at point h. if ad is the altitude to th
    8·1 answer
  • The <br> 180<br> falls between which two whole numbers?
    5·2 answers
  • If f(2)=pi+7 then f^-1(pi+7)=?
    10·2 answers
  • A coin is to be tossed as many times as necessary to turn up one head. Thus the elements c of the sample space C are H, TH, TTH,
    13·1 answer
  • what is 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 12 + 10 + 1 + 8 + 6 + 5 + 8 + 1 + 16 + 84 + 6 + 10 + 10 + 10 + 10
    7·2 answers
  • 1000 divided by _____________= 100
    15·2 answers
  • Suppose a line has slope -2/3 and passes through the point (1, 8). which other point must also be on the graph?
    9·1 answer
  • Alice bought a (k) kg of pork and (i) kg of chicken. how many kg of meat did alice buy??
    8·1 answer
  • 39.54 divided by 3 please.
    10·2 answers
  • What would step 3 look like after you have added the two equations?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!