Exam 18: Mathematics in Engineering

The term rate of change always refers to how a physical quantity varies with time.

Calculate the average rate of change for the following functions: between and

Find the slope of the line that passes thru the points (2,1) and (8,5).

Many engineering problems are modeled using differential equations with a set of corresponding boundary and/or initial conditions.

In general, engineering problems are mathematical models of physical situations.

The path of flight (trajectory) of a football thrown by a quarterback is described by the following function: where y = vertical position of football relative to the ground (m) x = horizontal position of football relative to launch position (m) How high above the ground is the football as it leaves the quarterback's hand?

Calculate the average rate of change for the following function: between and

Given the following matrix: calculate the determinant of .

The pitch of a roof refers to its "steepness" and is expressed in terms of the number of inches the roof rises for each 12 inches of run.For example, an 8-12 pitch means that the roof rises 8 inches vertically for each 12 inches of horizontal run.What is the slope of a roof with an 8-12 pitch?

The quantity or numerical value within a linear model that shows by how much the dependent variable changes each time a change in the independent variable is introduced is known as

The position of an object subjected to constant acceleration can be described by the following function: where position (m) initial position (m) initial velocity (m/s) acceleration (m/s^2) time (sec) Which type of mathematical model is used here to describe the object's position?

Calculate the average rate of change for the following function: between and

Find an equation of the line through (5,2) that is perpendicular to the line .

For nonlinear models (equations) the slope is constant.

Given the following matrix: calculate the determinant of .

Perform the following operations on the given matrices:

The velocity of an object under constant acceleration can be modeled using the following function: v(t) = v0 + at where v = velocity V0 = initial velocity A = acceleration T = time Which type of mathematical model is used to describe velocity in this application?

Greek alphabetic characters quite commonly are used to express angles, dimensions, and physical variables in drawings and in mathematical equations and expressions.It is therefore very important to be familiar with these characters in order to communicate with other engineers.

Solve the following set of equations using the Gaussian method:

Calculus is commonly divided into two broad areas: