# Numerical Methods

The extension, y, of a material with an applied force, F, is given by y = e^Fx1x10-3 a) Calculate the work done if the force increases from 100N to 500N using: i) An analytical integration technique ii) A numerical integration technique [Note: the work done is given by the area under the curve] b) Compare the two answers c) Using a computer spreadsheet increase the number of values used for your numerical method d) Analyse any affect the size of numerical step has on the result.

Given F(s) = L(f), find f(r). a, b, L, n are constants. Show the details of your work. \text { 27. } \frac{s}{L^{2} s^{2}+n^{2} \pi^{2}}

13) A researcher randomly selected 100 of the nation's middle schools and interviewed all of the teachers at each school.

To solve the ordinary differential equation. 3 \frac{d y}{d x}+x y^{2}=\sin (x), y(0)=5

3) (2, 3) 3) A) on B) below C) above

14) A community college student interviews everyone in a statistics class to determine the percentage of students that own a car.

Determine whether the data are qualitative or quantitative. 4) the number of seats in a movie theater

In order to make a pumpkin pie I need 5 pumpkins.If p is the number of pies I want to make and P(p)is the number of pumpkins I need. A reasonable function for this is a. P(p) =10pb. P(p)=5p+1c. P(p) =6pd. P(p)=5p

Use the given frequency distribution to find the (a) class width. (b) class midpoints of the first class. (c) class boundaries of the first class. 15) Phone Calls (per day)

In Probs. 33-36 find the transform. In Probs. 37-45 find the inverse transform. Show the details of your work. \text { 35. } 0.5 e^{-4.5 t} \sin 2 \pi t