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POLYNOMIALS IN REAL LIFE
Transcript of POLYNOMIALS IN REAL LIFE
Some people believe in imaginary friends. I believe in imaginary numbers.
PEOPLE USE POLYNOMIALS WITHOUT EVEN KNOWING WHAT IT'S CALLED.
Construction or Materials Planning
Polynomials are applied to problems involving construction or materials planning. A polynomial equation can be used in any 2-D construction situation to plan for the amount of materials needed. For example, polynomials can be used to figure how much of a garden's surface area can be covered with a certain amount of soil. The same method applies to many flat-surface projects, including driveway, sidewalk and patio construction.
The rate at which objects fall can be calculated using polynomials. Polynomials also are used in scientific problems, including gravitational acceleration problems. The polynomial equation needs to include the object's initial position, which is its distance from Earth's center, its initial velocity and its acceleration due to gravity, which is a constant figure. The accepted standard acceleration due to gravity is 32.17 feet per second squared. That is a basic formula, and many other aspects such as air resistance or air density are factored in by a scientist seeking a highly specific solution.
Monday, February 17, 2014
Vol XCIII, No. 311
How and when are polynomials used in real life?
POLYNOMIALS IN REAL LIFE!
One application of polynomials is that for any smooth curve (from function) we can approximate this curve by a graph of a polynomal function with sufficient degree.
Here is one of the implication. Suppose you have a real life data up to certain time, you can sketch the graph of the data and you want to predict the behavior of the data in the future. One way to solve this is to approximate the curve that you obtained from your data by a graph of a polynomial function hoping that this polynomial function can also approximate the data in the future.
Polynomials can be used in financial planning. For instance, a polynomial equation can be used to figure the amount of interest that will accrue for an initial deposit amount in an investment or savings account at a given interest rate. If a savings account with an initial deposit of $3,000 gains 3 percent interest, then this polynomial equation shows the interest gained for three years: Interest = (3,000)(3%)(3). In this situation, the savings account would accrue $270 dollars of interest during the three years.
By: Gaurav P.
Polynomials In Real life
In mathematics, a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction ,multiplication, and non negative integer exponents. An example of a polynomial of a single indeterminate (or variable), x, is x2 − 4x + 7, which is a quadratic polynomial.
Polynomials appear in a wide variety of areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated problems in the sciences; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, central concepts in algebra and algebraic geometry BY GAURAV
WHAT IS A POLYNOMIAL
Mathematics is a core academic subject. In the real world, algebra and calculus concepts are essential to career paths in the areas of construction, architecture, aerospace and financial planning. Helping students understand the importance of concepts such as polynomials in mathematics will motivate them when memorizing and perfecting the techniques. Polynomials are expressions using lines of numbers and variables raised to whole number powers. BY GAURAV
POLYNOMIALS USED FOR COOKING FOOD!
When you reduce or double a recipe, you are using a polynomial.
1 cup flour (we'll call this A)
1/4 cup sugar (this is B)
1/3 cup milk (This is C)
2 eggs (D)
1/2 teaspoon of vanilla (E)
Pancakes = 1A +(1/4)B +(1/3)C + 2D +(1/2)E
if I want to double the recipe, you have to multiply everything by 2...see?
A rectangular swimming pool is twice as long as it is wide. A small concrete walkway surrounds the pool. The walkway is a constant 2 feet wide and has an area of 196 square feet. Find the dimensions of the pool.
(2x + 4)(x + 4) - (2x)(x) = 196
2x² + 8x + 4x + 16 - 2x² = 196
12x + 16 = 196
12x = 180
x = 15
The pool is 15 feet wide and 30 feet long.
What are polynomials?
Polynomials are algebraic expressions that add constants
and variables. Coefficients multiply the variables, which are raised to various powers by non-negative integer exponents. Although many of us don't realize it, people in all sorts of professions use polynomials every day. The most obvious of these are mathematicians, but they can also be used in fields ranging from construction to meteorology. Although polynomials offer limited information, they can be used in more sophisticated analyses to retrieve more data.
Polynomials for Modeling or Physics
Polynomials can also be used to model different situations, like in the stock market to see how prices will vary over time. Business people also use polynomials to model markets, as in to see how raising the price of a good will affect its sales. Additionally, polynomials are used in physics to describe the trajectory of projectiles. Polynomial integrals (the sums of many polynomials) can be used to express energy, inertia and voltage difference, to name a few applications.
Polynomials in industry
For people who work in industries that deal with physical phenomena or modeling situations for the future, polynomials come in handy every day. These include everyone from engineers to businessmen. For the rest of us, they are less apparent but we still probably use them to predict how changing one factor in our lives may affect another--without even realizing it
Example: New Sports Bike
You have designed a new style of sports bicycle!
Now you want to make lots of them and sell them for profit.
Your costs are going to be:
$700,000 for manufacturing set-up costs, advertising, etc
$110 to make each bike
Based on similar bikes, you can expect sales to follow this "Demand Curve":
Unit Sales = 70,000 - 200P
Where "P" is the price.
For example, if you set the price:
at $0, you would just give away 70,000 bikes
at $350, you would not sell any bikes at all.
at $300 you might sell 70,000 - 200×300 = 10,000 bikes
Let us make some equations!
How many you sell depends on price, so use "P" for Price as the variable
Unit Sales = 70,000 - 200P
Sales in Dollars = Units × Price = (70,000 - 200P) × P = 70,000P - 200P2
Costs = 700,000 + 110 x (70,000 - 200P) = 700,000 + 7,700,000 - 22,000P = 8,400,000 - 22,000P
Profit = Sales-Costs = 70,000P - 200P2 - (8,400,000 - 22,000P) = -200P2 + 92,000P - 8,400,000
Profit = -200P2 + 92,000P - 8,400,000
Yes, a Quadratic Equation. Let us solve this one by Completing the Square.
Solve: -200P2 + 92,000P - 8,400,000 = 0
Step 1 Divide all terms by -200
P2 – 460P + 42000 = 0
Step 2 Move the number term to the right side of the equation:
P2 – 460P = -42000
Step 3 Complete the square on the left side of the equation and balance this by adding the same number to the right side of the equation:
(b/2)2 = (-460/2)2 = (-230)2 = 52900
P2 – 460P + 52900 = -42000 + 52900
(P – 230)2 = 10900
Step 4 Take the square root on both sides of the equation:
P – 230 = ±√10900 = ±104 (to nearest whole number)
Step 5 Subtract (-230) from both sides (in other words, add 230):
P = 230 ± 104 = 126 or 334
What does that tell us? It says that the profit will be ZERO when the Price is $126 or $334
But we want to know the maximum profit, don't we?
It will be exactly half way in-between! At $230
And here is the graph:
Profit = -200P2 + 92,000P - 8,400,000
The optimum sale price is $230, and you can expect:
Unit Sales = 70,000 - 200 x 230 = 24,000
Sales in Dollars = $230 x 24,000 = $5,520,000
Costs = 700,000 + $110 x 24,000 = $3,340,000
Profit = $5,520,000 - $3,340,000 = $2,180,000
A very profitable venture.
JOEL JACK (L)