A pyramid can be formed using equal-size balls. For example, 3 balls can be arranged in a triangle, and then a fourth ball placed in the middle on top of them. The function p(n) = -n(n + 1)(n + 2) gives the number of balls in a pyramid, wheren is the number of balls on each side of the bottom layer. (For the pyramid described above, n = 2. For the pyramid in the picture, n = 5.) If you had 1000 balls available and you wanted to make the largest possible pyramid using them, what would be the size of the bottom triangle, and how many balls would you use to make the pyramid? How many balls would be left over?

A pyramid can be formed using equal-size balls. For example, 3 balls can be arranged in a triangle, and then a fourth ball placed in the middle on top of them. The function p(n) = -n(n + 1)(n + 2) gives the number of balls in a pyramid, wheren is the number of balls on each side of the bottom layer. (For the pyramid described above, n = 2. For the pyramid in the picture, n = 5.) If you had 1000 balls available and you wanted to make the largest possible pyramid using them, what would be the size of the bottom triangle, and how many balls would you use to make the pyramid? How many balls would be left over?

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Concept explainers

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.

Question

A pyramid can be formed using equal-size balls. For example, 3 balls can be
arranged in a triangle, and then a fourth ball placed in the middle on top of
them. The function p(n) =-n(n + 1)(n + 2) gives the number of balls in a
pyramid, where n is the number of balls on each side of the bottom layer. (For
the pyramid described above, n = 2. For the pyramid in the picture, n = 5.)
If you had 1000 balls available and you wanted to make the largest possible pyramid using them,
what would be the size of the bottom triangle, and how many balls would you use to make the
pyramid? How many balls would be left over?

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