The ancient Pythagoreans studied figurate numbers, which are numbers that can be shown by taking dots...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
The ancient Pythagoreans studied figurate numbers, which are numbers that can be shown by taking dots or spheres and arranging them into geometric shapes. For example, the square numbers are 1, 4, 9, 16, 25, etc., and each of these numbers of dots can be arranged into a square. The tetrahedral numbers similarly specify the number of spheres needed to create a tetrahedron, which is a triangular-based pyramid. The tetrahedral numbers are 1, 4, 10, 20, 35, 56, 84, etc. Which of the following statements is true? A B C D The tetrahedral numbers are best modeled by a quadratic function because the 2nd differences are a nonzero constant. The tetrahedral numbers are best modeled by a quadratic function because the 3rd differences are a nonzero constant. The tetrahedral numbers are best modeled by a cubic function because the 2nd differences are a nonzero constant. The tetrahedral numbers are best modeled by a cubic function because the 3rd differences are a nonzero constant. The ancient Pythagoreans studied figurate numbers, which are numbers that can be shown by taking dots or spheres and arranging them into geometric shapes. For example, the square numbers are 1, 4, 9, 16, 25, etc., and each of these numbers of dots can be arranged into a square. The tetrahedral numbers similarly specify the number of spheres needed to create a tetrahedron, which is a triangular-based pyramid. The tetrahedral numbers are 1, 4, 10, 20, 35, 56, 84, etc. Which of the following statements is true? A B C D The tetrahedral numbers are best modeled by a quadratic function because the 2nd differences are a nonzero constant. The tetrahedral numbers are best modeled by a quadratic function because the 3rd differences are a nonzero constant. The tetrahedral numbers are best modeled by a cubic function because the 2nd differences are a nonzero constant. The tetrahedral numbers are best modeled by a cubic function because the 3rd differences are a nonzero constant.
Expert Answer:
Answer rating: 100% (QA)
The detailed answer for the above question is provided below The correct statement is D The t... View the full answer
Related Book For
An Introduction to Management Science Quantitative Approach to Decision Making
ISBN: 978-1337406529
15th edition
Authors: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran
Posted Date:
Students also viewed these chemical engineering questions
-
Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...
-
QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...
-
A garden has an area of 320 ft 2 . Its length is 4 ft more than its width. What are the dimensions of the garden? X x +4 X
-
What two measures are used to determine whether a firm has sufficient capital to operate and whether the firm has the ability to pay its debts?
-
In about 100 words, outline the key elements that should be a part of any electronic commerce software package.
-
The Tuckers owned an RV that they insured through American Family. On August 26, 2012, their RV was struck by lightning and damaged. The Tuckers reported the damage to American Family. In March 2013,...
-
A manufacturer is considering alternatives for building new plants, to be located closer to three of its primary customers with whom it intends to develop long-term, sole-supplier relationships. The...
-
X The function h is defined as h(x)=4-x2 x ln x, x>1 jh(x) Show that h(x) dx = 4ln 2- -1 15 16
-
Direct and indirect labour: manufacturer Sharpedge Cutlery manufactures kitchen knives. One of the employees. whose job is to cut out wooden knife handles, worked 49 hours during a week in January....
-
Consider a tree-structured factor graph, in which a given subset of the variable nodes form a connected subgraph (i.e., any variable node of the subset is connected to at least one of the other...
-
One of the principles of economics is that trade can make everyone better off. Explain why this might be so, grounding your discussion in the economic principles. Conversely, do you think trade...
-
Zinc has beginning equity of $271,000, total revenues of $71,000, and total expenses of $47,000. The company has no other transactions impacting equity. What is It's ending equity?
-
TC = 500 + 10Q + 0.05 Q*Q What is the firm's fixed cost What is the firm's average variable cost?
-
You are interested in an investment project that pays 10% of interest rate compounded every four weeks. Assume a 52-week year. What percent return would you effectively earn?
-
Suppose that the inflation premium is 2 percent and the nominal interest rate is 9 percent. Instructions: Round your answers to the nearest whole number. a. What is the real interest rate? percent b....
-
A 3 MWe wind turbine can be placed at either Site A or B, which have respective probability density functions for the wind velocity at the site (assume that the power output of the turbine varies as...
-
One study found that the elderly who do not have children dissave at about the same rate as the elderly who do have children. What might this finding imply about the reason the elderly do not dissave...
-
The Corporate Average Fuel Economy (CAFE) regulations were put into law by Congress in 1975 to promote the sale of fuel-efficient automobiles and light trucks. The law requires automakers to boost...
-
Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $63, $95, and $135, respectively. The production...
-
The Porsche Club of America sponsors driver education events that provide high-performance driving instruction on actual race tracks. Because safety is a primary consideration at such events, many...
-
Baggai Enterprises has an ROA of 10 percent, retains 30 percent of earnings, and has an equity multiplier of 1.25. Mondale Enterprises also has an ROA of 10 percent, but it retains two-thirds of...
-
International Business Machines (NYSE: IBM), which currently pays a dividend of \($3.40\) per share, has been the subject of two other examples in this reading. In one example, an analyst estimated...
-
An analyst is preparing a forecast of dividends for Hoshino Distributors for the next five years. He uses a spreadsheet model with the following assumptions: Sales are $100 million in Year 1. They...
Study smarter with the SolutionInn App