/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 69 A sprinkler on a golf green spra... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 69

A sprinkler on a golf green sprays water over a distance of 15 meters and rotates through an angle of \(140^{\circ} .\) Draw a diagram that shows the region that the sprinkler can irrigate. Find the area of the region.

Short Answer

Expert verified
To find the region the sprinkler can irrigate, calculate the area of a circular sector with a radius of 15m and subtended angle of \(140^{\circ}\). Convert the degrees into radians before substituting into the formula for the area of the circular sector. The calculation should yield the area in square meters (m虏).

Step by step solution

01

Understanding the problem

The first step is to understand the concept of a circular sector and how its area is calculated. The region watered by the sprinkler would form a circular sector with the sprinkler as the center. The region's area can be calculated using the formula for the area of a circular sector: \(Area = 0.5R^2胃\), where \(R\) is the radius and \(胃\) is the angle. Here, \(R = 15m\) and \(胃 = 140^{\circ}\), but note that \(胃\) must be in radian. To convert from degrees to radians, use the relation \(1 rad = \frac{180}{蟺} degree\).
02

Convert degrees to radian

Convert the angle from degrees to radian using these relations. Find \(胃\) in radian. \(胃 = 140 脳 \frac{蟺}{180} rad.\)
03

Calculate the Area

Substitute the values of \(R\) and \(胃\) into the formula for the area of a circular sector. Solve to obtain the area. \(Area = 0.5 脳 (15m)^2 脳 140 脳 \frac{蟺}{180} rad.\)
04

Simplify the Result

Simplify the result obtained in the previous step to find the area that the sprinkler can irrigate, ensuring your units are correctly represented.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Determine whether the statement is true or false. Justify your answer. To find the reference angle for an angle \(\theta\) (given in degrees), find the integer \(n\) such that \(0 \leq 360^{\circ} n-\theta \leq 360^{\circ} .\) The difference \(360^{\circ} n-\theta\) is the reference angle.

Write a short paper explaining to a classmate how to evaluate the six trigonometric functions of any angle \(\theta\) in standard position. Include an explanation of reference angles and how to use them, the signs of the functions in each of the four quadrants, and the trigonometric values of common angles. Be sure to include figures or diagrams in your paper.

Converting to \(\mathrm{D}^{\circ} \mathrm{M}^{\prime} \mathrm{S}^{\prime \prime}\) Form \(\quad\) Convert each angle measure to degrees, minutes, and seconds without using a calculator. Then check your answers using a calculator. (a) \(240.6^{\circ}\) (b) \(-145.8^{\circ}\)

Prove each identity. (a) \(\arcsin (-x)=-\arcsin x\) (b) \(\arctan (-x)=-\arctan x\) (c) \(\arctan x+\arctan \frac{1}{x}=\frac{\pi}{2}, \quad x>0\) (d) \(\arcsin x+\arccos x=\frac{\pi}{2}\) (e) \(\arcsin x=\arctan \frac{x}{\sqrt{1-x^{2}}}\)

The circular blade on a saw rotates at 5000 revolutions per minute. (a) Find the angular speed of the blade in radians per minute. (b) The blade has a diameter of \(7 \frac{1}{4}\) inches. Find the linear speed of a blade tip.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.