# Polynomial/Integration questions

• MehhShell
In summary, the conversation discusses a design project for a suspension bridge feature using marine ply and a jigsaw to create symmetrical patterns. The questions focus on determining the amount of plywood needed for each side of the bridge and finding an appropriate function rule for cutting the decorative pattern. It is suggested to start by drawing a diagram and using a fourth-degree polynomial to fit the catenary shape of the bridge. The goal is to use a minimum amount of plywood sheets with minimal waste.
MehhShell
The questions that I'm having trouble with are:

"You have been given the opportunity to design a feature to go on a suspension bridge that is to be built as part of a landscaping project for a local company. The feature is to be made out of marine ply (wood) and is to have patterns that will be created using a jigsaw to cut the timber. The program for the jigsaw can be set to the follow a polynomical function of degree 4, or two sections of polynomical function of degree 4, or two sections of a polynomial function of degree 3 or a section of a trigonometrical function. The patterns need to be symmetrical.

The plywood will be placed on both sides of the suspension bridge, covering the area between the hanging cables and the floor (the idea is to have the vertical supporting cables hidden) the bridge spans a gap over an artificial creek of 5.0m, the hanging cable is 1.0m at the ends and 0.5m high at the centre of the bridge. The plywood comes in 1200mm x 1200mm sheets (1.2m x 1.2m)

QUESTION 1.
Determine how much plywood will be needed for each side of the bridge. Justify you choice by explaining all procedures used to determine the number of sheets needed. Keep in mind that minimal waste is ideal and that you should identify and explain any assumptions made.

QUESTION 2.
Determine an appropriate function rule for cutting the decorative pattern along the sides. Include an accurate diagram which shows the shape of the finished produce. Explore the advantages and disadvantages of each of the possible types of function, together with the variables involved in each model.

I have no, no idea whatsoever on how to do questions 1 and 2, any help would be greatly appreciated.

MehhShell said:
The questions that I'm having trouble with are:

"You have been given the opportunity to design a feature to go on a suspension bridge that is to be built as part of a landscaping project for a local company. The feature is to be made out of marine ply (wood) and is to have patterns that will be created using a jigsaw to cut the timber. The program for the jigsaw can be set to the follow a polynomical function of degree 4, or two sections of polynomical function of degree 4, or two sections of a polynomial function of degree 3 or a section of a trigonometrical function. The patterns need to be symmetrical.

The plywood will be placed on both sides of the suspension bridge, covering the area between the hanging cables and the floor (the idea is to have the vertical supporting cables hidden) the bridge spans a gap over an artificial creek of 5.0m, the hanging cable is 1.0m at the ends and 0.5m high at the centre of the bridge. The plywood comes in 1200mm x 1200mm sheets (1.2m x 1.2m)

QUESTION 1.
Determine how much plywood will be needed for each side of the bridge. Justify you choice by explaining all procedures used to determine the number of sheets needed. Keep in mind that minimal waste is ideal and that you should identify and explain any assumptions made.

QUESTION 2.
Determine an appropriate function rule for cutting the decorative pattern along the sides. Include an accurate diagram which shows the shape of the finished produce. Explore the advantages and disadvantages of each of the possible types of function, together with the variables involved in each model.

I have no, no idea whatsoever on how to do questions 1 and 2, any help would be greatly appreciated.

Try and divide and conquor. Draw a picture for starters showing the bridge cabling and the "tiling" of the area with the plywood sheets. Just work on a single, simple part of the problem now then worry about the larger picture later: you got a bridge 5, long, 1m high at the ends and 1/2 m in the center. Isn't that a catinary? Look it up in wikipedia. Now, just for now, assume all you want to do is fill-in the cabling with the 1.2 x 1.2 plywood but you can't cut the plywood using the formula for a catinary, rather you have to use a fourth-degree polynomial to cut it. How then do you "fit" the points of the catinary to a fourth-degree polynomial, then cut the plywood according to that fit, and use a minimum of plywood sheets to do it. Keep in mind the small part you cut of one sheet may be usable somewhere else on the tiling.

Now, I'm not saying that is the answer to your question but just the act of working on something that may be close to what needs to be done opens avenues towards what actually has to be done. So see if you can do just this part even if it's not the correct thing to do and remember sometimes the wrong one are on the road to the right ones. :)

## 1. What is a polynomial function?

A polynomial function is a mathematical expression that consists of variables and coefficients, and contains only the operations of addition, subtraction, and multiplication. It is typically written in the form of ax^n + bx^(n-1) + ... + cx + d, where a, b, c, and d are constants and n is a non-negative integer.

## 2. How do you identify the degree of a polynomial?

The degree of a polynomial is the highest exponent of the variable in the expression. For example, the polynomial 3x^4 + 2x^3 + 5x^2 has a degree of 4.

## 3. What is the process for dividing polynomials?

To divide polynomials, you can use the long division method or synthetic division. Both methods involve dividing each term of the dividend (numerator) by the divisor (denominator) and then subtracting the results to find the remainder. The final answer will be the quotient (result of the division) plus the remainder over the divisor.

## 4. What is integration?

Integration is a mathematical process that involves finding the area under a curve. It is the reverse operation of differentiation and is used to find the original function from its derivative. Integration is typically used to solve problems in calculus and physics, where the area under a curve represents a physical quantity.

## 5. How do you solve integration questions?

To solve integration questions, you need to first identify the function that you are integrating and the limits of integration. Then, you can use integration techniques such as substitution, integration by parts, or partial fractions to find the integral. Finally, evaluate the integral at the given limits to find the final answer.

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