Complete all of the problems and questions below. See submission information below.
Crossed ladder problem
Practice using LaTeX by posting a solution to the following problem.
A narrow street is lined with tall buildings. The base of a 20 foot long ladder is resting at the base of the building on the right side of the street and leans on the building on the left side. The base of the 30 foot long ladder is resting at the base of the building on the left side of the street and leans on the building on the right side. The point where the two ladders cross is exactly 8 feet from the ground.
Approximately, how wide is the street (to the nearest tenth)? Justify your answer.
Similar triangles are your friends. Of course, you need to justify that similar triangles exist.
The Pythagorean theorem might also be helpful.
A possible goal may be to create an equation with only a single variable.
If using Maple 14, fsolve() only seems to work if there are no variables in the numerator. Wolfram Alpha seems to work more consistently.
Riemann sums
Create a calculator program to estimate the area under a curve.
Provide the code for a calculator program that could be used to calculate the Riemann sum:
Inputs
Function of x
Lower bound of x
Upper bound of x
Output
Estimated net area based on 3 equally spaced rectangles using "midpoints"
Annotate your code by explaining each line of code that contains mathematics.
Run your program for the instructor on the due date.
See Programming help for important commands on different calculators.