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# (a) draw a diagram for this scenario and introduce the variables.

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Hello there. Please read the below instructiosn very carefully and then accept the order. I will give you three math qquestions.

1. The lengths of the sides of a right angled triangle form an arithmetic sequence.

(a) Draw a diagram and introduce the variables.

(b) Prove that the three sides of the triangle are in the ratio 3:4:5.

(c) Assuming that the common difference is 15, find the area and the perimeter of the triangle.

2. A mass suspended from a spring is pulled down 2 feet from its rest position. The mass is released at time t = 0 and allowed to oscillate. The mass returns to this position after 1 second.

(a) Draw a graph to model one period for the function that shows the change in position of the mass, then find the equation that describes its motion.

(b) Find at what two times within one cycle is the spring at 1.5 feet above its rest position?

3. P is a point on the curve y = x(6-x) and Q is a point on the curve y = x(x-4), such as PQ is always vertical. The two curves meet in points A and B, while xA< xP< xB and xA< xQ< xB .

(a) Draw a diagram for this scenario and introduce the variables.

(b) Find the length of PQ.

(c) Find the coordinates of P and Q that would maximise the length of PQ.

PLEASE READ THE 3 ABOVE QUESTIONS VERY VERY CAREFULLY AND LET ME KNOW if you can explain them in a presentation or no. It is very important you read the questions first.

MAIN INSTRUCTIONS.

You are assigned a set of mathematical (problem solving) questions on various topics studied for

which you must provide explained solutions and present them in a PowerPoint presentation.

You must demonstrate you understand the problems and the mathematical concepts used to solve them,

while clearly explaining the steps in the worked solutions. And it should not be a plain read over

figures. In the presentation you must:

• describe the worded problem and demonstrate you understand how it translates to a

mathematical sentence/diagram that you must solve,

• explain how you will reach your result and the topics/formulae applicable,

• interpret the result and ensure it is appropriate,

• reflect on the solution you provided and potential different other ways to reach the answer.

You must provide a conclusion, which should include:

• the challenges (if any) you encountered following your completion of the project and the way

you overcame those,

• considering the four steps you had to take to complete the project (listed above), which one/ones

was/were the most important/helpful for you and why,

• your own thoughts on the applicability and usefulness of maths to real life.

THANK YOU.

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