/*! 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 sculptor finds that the profit... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 65

A sculptor finds that the profit \(P\) (in dollars) earned if \(x\) pieces are produced is given by the equation \(P=100 x-x^{2} .\) Find the profit if the sculptor produces 30 pieces, 50 pieces, and 90 pieces.

Short Answer

Expert verified
Profit at 30 pieces: \(2100, at 50 pieces: \)2500, at 90 pieces: $900.

Step by step solution

01

- Understand the Equation

The profit equation is given as: \[ P = 100x - x^2 \] where \(P\) is the profit in dollars and \(x\) is the number of pieces produced.
02

- Plug in 30 for x

To find the profit when the sculptor produces 30 pieces, substitute \(x = 30\) into the equation: \[ P = 100(30) - (30)^2 \] Simplify to get: \[ P = 3000 - 900 \] Therefore, \( P = 2100 \).
03

- Plug in 50 for x

To find the profit when the sculptor produces 50 pieces, substitute \(x = 50\) into the equation: \[ P = 100(50) - (50)^2 \] Simplify to get: \[ P = 5000 - 2500 \] Therefore, \( P = 2500 \).
04

- Plug in 90 for x

To find the profit when the sculptor produces 90 pieces, substitute \(x = 90\) into the equation: \[ P = 100(90) - (90)^2 \] Simplify to get: \[ P = 9000 - 8100 \] Therefore, \( P = 900 \).

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.

Quadratic Equations
Quadratic equations are polynomial equations of degree 2. They take the form:

Polynomial Functions
Polynomial functions are a type of mathematical expressions involving a sum of powers in one or more variables. In this context, the term 'polynomial' specifically refers to expressions of the form:
Substitution Method
The substitution method is a technique in algebra used to solve equations. It involves replacing a variable with a given value to simplify and solve the equation. Here鈥檚 a brief guide on how it works:



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

Do your computation using scientific notation. $$\frac{0.003}{6000}$$

Multiply out each of the following. As you work out the problems, identify those exercises that are either a perfect square or the difference of two squares. $$(2 y-5)(4 y+3)$$

Do your computations using scientific notation. If light travels \(5.87 \times 10^{12}\) miles in 1 year, how long will it take light to reach us from a star that is \(3 \times 10^{22}\) miles away?

Solve for x. $$5-2 x \geq 17$$

Convert each number into scientific notation. $$56 \times 10^{-2}$$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

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.