/*! 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 24 Use the four-step procedure for ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 24

Use the four-step procedure for solving variation problems given on page 424 to solve. The distance that a spring will stretch varies directly as the force applied to the spring. A force of 12 pounds is needed to stretch a spring 9 inches. What force is required to stretch the spring 15 inches?

Short Answer

Expert verified
To stretch the spring 15 inches, an approximate force of 20 pounds is required.

Step by step solution

01

Identify the Variation

Understand that the problem is discussing a direct variation. This is identified by the phrase 'varies directly'. So we can set up the direct variation equation as \(F = kD\). Where F is the force, D is the distance and k is the constant proportionality.
02

Find the Constant of Proportionality

We are given that a force of 12 pounds stretches the spring 9 inches. We can use these values to find k. Substituting F with 12 and D with 9 in the equation \(F = kD\), we get \(12 = k * 9\). Solving for k, we find that \(k = \frac{12}{9} = 1.333\).
03

Find the Unknown Force

Now, we need to find the force required to stretch the spring 15 inches. Substituting D with 15 and k with 1.333 in our variation equation \(F = kD\), we get \(F = 1.333 * 15\). Calculating this gives us \(F 鈮� 20\) pounds.

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

The functions $$f(x)=0.0875 x^{2}-0.4 x+66.6$$ and $$g(x)=0.0875 x^{2}+1.9 x+11.6$$ model a car's stopping distance, \(f(x)\) or \(g(x),\) in feet, traveling at \(x\) miles per hour. Function \(f\) models stopping distance on dry pavement and function g models stopping distance on wet pavement. The graphs of these functions are shown for \(\\{x | x \geq 30\\} .\) Notice that the figure does not specify which graph is the model for dry roads and which is the model for wet roads. Use this information to solve. (GRAPH CANNOT COPY). a. Use the given functions to find the stopping distance on dry pavement and the stopping distance on wet pavement for a car traveling at 35 miles per hour. Round to the nearest foot. b. Based on your answers to part (a), which rectangular coordinate graph shows stopping distances on dry pavement and which shows stopping distances on wet pavement? c. How well do your answers to part (a) model the actual stopping distances shown in Figure 3.43 on page \(411 ?\) d. Determine speeds on dry pavement requiring stopping distances that exceed the length of one and one-half football fields, or 540 feet. Round to the nearest mile per hour. How is this shown on the appropriate graph of the models?

Kinetic energy varies jointly as the mass and the square of the velocity. A mass of 8 grams and velocity of 3 centimeters per second has a kinetic energy of 36 ergs. Find the kinetic energy for a mass of 4 grams and velocity of 6 centimeters per second.

Use the four-step procedure for solving variation problems given on page 424 to solve Exercises 1-10. \(y\) varies directly as \(x . y=65\) when \(x=5 .\) Find \(y\) when \(x=12 .\)

Will help you prepare for the material covered in the next section. a. If \(y=k x^{2},\) find the value of \(k\) using \(x=2\) and \(y=64\) b. Substitute the value for \(k\) into \(y=k x^{2}\) and write the resulting equation. c. Use the equation from part (b) to find \(y\) when \(x=5\)

7\. The figure shows that a bicyclist tips the cycle when making a turn. The angle \(B,\) formed by the vertical direction and the bicycle, is called the banking angle. The banking angle varies inversely as the cycle's turning radius. When the turning radius is 4 feet, the banking angle is \(28^{\circ} .\) What is the banking angle when the turning radius is 3.5 feet? (Figure cannot copy)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure 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.