/*! 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 93 Solve each formula for the indic... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 93

Solve each formula for the indicated variable. $$ s=\frac{1}{2} g t^{2}+v t \text { for } g $$

Short Answer

Expert verified
The formula for \( g \) is \( g = \frac{2(s - v t)}{t^2} \).

Step by step solution

01

Isolate the g term

Begin by isolating the term that contains the variable \( g \). In the formula \( s = \frac{1}{2} g t^2 + v t \), the term containing \( g \) is \( \frac{1}{2} g t^2 \). Start by subtracting \( v t \) from both sides:\[ s - v t = \frac{1}{2} g t^2 \]
02

Solve for g

Now, solve for \( g \) by getting rid of the coefficient in front of \( g \). Divide both sides of the equation by \( \frac{1}{2} t^2 \) to solve for \( g \).\[ g = \frac{2(s - v t)}{t^2} \]

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolating Variables
One of the fundamental skills in algebra is isolating variables. This means making the variable you are interested in the subject of the formula. When you isolate a variable, you perform operations to get the variable alone on one side of the equation. This involves rearranging the equation and performing inverse operations.
For example, in the equation \( s = \frac{1}{2} g t^2 + v t \), we want to isolate \( g \). The first step is to remove all other terms from the side of the equation where \( g \) is located.
  • Start by subtracting \( v t \) from both sides to move it to the left-hand side.
  • This gives us \( s - v t = \frac{1}{2} g t^2 \).
By isolating \( g \), you are simplifying the problem and preparing it for further manipulation, which is essential for solving it completely.
Solving for a Variable
Solving for a variable means finding a formula where one specific variable stands alone on one side of the equation. After you've successfully isolated the variable, solving for it involves reversing any operations that were applied to it.
For instance, after isolating the term with \( g \) in our equation, we are left with \( \frac{1}{2} g t^2 \). We need to get rid of the \( \frac{1}{2} t^2 \) that multiplies \( g \).
  • Since \( g \) is multiplied by \( \frac{1}{2} t^2 \), you can find \( g \) by dividing both sides of the equation by this term.
  • This results in \( g = \frac{2(s - v t)}{t^2} \).
Effectively, you've solved for \( g \) by eliminating the coefficients and simplifying the equation. This step completes the process of making \( g \) the subject, making it much easier to compute when the rest of the variables are given.
Quadratic Equations
Quadratic equations are polynomial equations of the second degree, generally represented as \( ax^2 + bx + c = 0 \). In many cases, they involve variables raised to the power of two, forming a parabolic curve when graphed.
In the exercise we're addressing, while we don't deal explicitly with a quadratic equation in the standard form that involves solving for a zero, the presence of \( t^2 \) indicates that we might work with such forms in different problems.
  • The term \( \frac{1}{2} g t^2 \) carries the quadratic nature within the equation.
  • Handling terms like \( t^2 \) is crucial because operations such as isolating and solving are often based on understanding the behavior of squares.
Understanding how to manipulate quadratic terms expands your ability to tackle a wide range of equations, both in simple rearrangements and in solving complex scenarios using factorization or the quadratic formula.

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

Find \(g(2)\) and \(g(3)\). \(g(x)=x^{3}-x\)

Write an equation for a linear function whose graph has the given characteristics. Slope \(2, y\) -intercept \((0,11)\)

Find \(h(5)\) and \(h(-2)\). \(h(x)=\frac{3}{x-4}\)

Find \(g(2)\) and \(g(3)\). \(g(x)=5 x^{2}+2 x+2\)

Fire Protection. City growth and the number of fires for a certain city are related by a linear equation. Records show that 113 fires occurred in a year when the local population was \(150,000\) and that the rate of increase in the number of fires was 1 for every \(1,000\) new residents. a. Using the variables \(p\) for population and \(F\) for fires, write an equation (in slope-intercept form) that the fire department can use to predict future fire statistics. b. How many fires can be expected when the population reaches \(200,000 ?\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Geometry

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.