/*! 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 59 Write a sentence using the varia... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 59

Write a sentence using the variation terminology of this section to describe the formula. Area of a triangle: \(A=\frac{1}{2} b h\)

Short Answer

Expert verified
In the formula \(A=\frac{1}{2} b h\), the area 'A' of a triangle varies directly as the product of the base 'b' and the height 'h'. It can be said that 'A' is directly proportional to both 'b' and 'h' with the constant of variation being \(\frac{1}{2}\).

Step by step solution

01

Understanding the formula

Firstly, one must understand the formula for the area of a triangle: \(A=\frac{1}{2} b h\). It's known that 'A' is the area of the triangle, 'b' is the base of the triangle and 'h' is the height.
02

Understanding direct variation

When two quantities are multiplied to get a constant, we say they are directly proportional. This means that as one increases, the other does as well. In this formula, 'A' is directly proportional to the base 'b' and the height 'h'.
03

Describing the formula using variation terminology

Now, it can be said that in the formula \(A=\frac{1}{2} b h\), the area 'A' of a triangle varies directly, or is directly proportional to, both the base 'b' and the height 'h', with the constant of variation being \(\frac{1}{2}\).

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!

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 a mathematical model for the verbal statement. \(h\) varies inversely as the square root of \(s\).

(a) find the inverse function of \(f\), (b) graph both \(f\) and \(f^{-1}\) on the same set of coordinate axes, (c) describe the relationship between the graphs of \(f\) and \(f^{-1}\), and (d) state the domain and range of \(f\) and \(f^{-1}\). $$ f(x)=\frac{x+1}{x-2} $$

Determine if the situation could be represented by a one-to-one function. If so, write a statement that describes the inverse function. The depth of the tide \(d\) at a beach in terms of the time \(t\) over a 24 -hour period

The direct variation model \(y=k x^{n}\) can be described as " \(y\) varies directly as the \(n\) th power of \(x\)," or "y is _____ _____to the \(n\) th power of \(x.\) "

Use the given value of \(k\) to complete the table for the direct variation model $$y=k x^{2}$$ Plot the points on a rectangular coordinate system. $$\begin{array}{|l|l|l|l|l|l|} \hline x & 2 & 4 & 6 & 8 & 10 \\ \hline y=k x^{2} & & & & & \\ \hline \end{array}$$ $$ k=2 $$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

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.