/*! 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 65 A ship sails north for 2 miles a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 65

A ship sails north for 2 miles and then west for 5 miles. How far is the ship from its starting point?

Short Answer

Expert verified
The ship is approximately \(\sqrt{29}\) miles from its starting point.

Step by step solution

01

Identify the given information

The ship sails 2 miles north (in the vertical direction) and 5 miles west (in the horizontal direction). This information represents the lengths of the legs in a right triangle.
02

Draw the right triangle

In order to visualize the concept, draw a right triangle in which one leg is vertical (representing the 2-mile distance the ship sails north) and the other leg is horizontal (representing the 5-mile distance the ship sails west). The hypotenuse represents the straight-line distance between the ship's starting point and its current location.
03

Apply the Pythagorean theorem

Using the Pythagorean theorem, calculate the square of the length of the hypotenuse by adding the squares of the lengths of the legs of the right triangle together. Let the distance between the starting point and the ship's current location be represented as D. Then, \[D^2 = 2^2 + 5^2\]
04

Evaluate the expression

Next, calculate the sum of the squares of the lengths of the legs of the right triangle: \[D^2 = 2^2 + 5^2 = 4 + 25 = 29\]
05

Find the length of the hypotenuse

Finally, find the length of the hypotenuse (the straight-line distance between the ship's starting point and its current location) by taking the square root of the value obtained in Step 4: \[D = \sqrt{29}\]
06

Express the answer in terms of distance

The ship is approximately \(\sqrt{29}\) miles from its starting point. This is the final answer.

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

Write the indicated expression as \(a\) polynomial. $$ (q(x))^{2} $$

Find a polynomial \(p\) of degree 3 such that \(-2,-1,\) and 4 are zeros of \(p\) and \(p(1)=2\).

Explain why the polynomial \(p\) defined by $$ p(x)=x^{6}+100 x^{2}+5 $$ has no real zeros.

Suppose \(r\) is the function with domain \((0, \infty)\) defined by $$ r(x)=\frac{1}{x^{4}+2 x^{3}+3 x^{2}} $$ for each positive number \(x\). (a) Find two distinct points on the graph of \(r\). (b) Explain why \(r\) is a decreasing function on \((0, \infty)\). (c) Find two distinct points on the graph of \(r^{-1}\).

Give an example of polynomials \(p\) and \(q\) such that \(\operatorname{deg}(p q)=8\) and \(\operatorname{deg}(p+q)=2\).
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

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.