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Consider the function f(x,y,z) = (e^z)ln(x^2 + y^2)
a) Is there a vector r such that the directional derivative of f at (1,1,0) in the direction of r equals 1? If there is, find one such vector. If not, explain why not.
b) Is there a vector r such the directional derivative of f at (1,1,0) in the direction of r equals to -2? If there is, find one such vector. If not, explain why not.
What similarities and differences do you see between functions and linear equations? Are all linear equations functions? Is there an instance when a linear equation is not a function?
If a system of m linear equations in four unknowns has a unique solution, then m must be greater than or equal to four. If a system of m linear equations in four unknowns has no solutions, then m must be greater than or equal to four.
Explain why a point on the boundary line cannot be used as a test point when graphing a linear inequality in two variables. Provide an example.
The table below shows the number of gallons of heating oil delivered to a residential customer each December from 1986 to 1993.
Review Chi Square analysis & create an example of how you would use the tool to help make a business decision.
For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v^3. It is believed that migrating fish try to minimize the total energy required to swim a fixed distance.
Let A be a positive definite matrix. Show that X has a unique positive square root. That is, show that there exists a unique positive matrix X such that X^2 =A.
The law of cosines and Pythagoras theorem.
For this module you will design some simple digital circuits based on Boolean expressions. Draw circuits that implement the following Boolean expressions using some combination of AND, OR, NOT, NAND, and NOR gates.
Problem solving on population mean
For solving a system of equations, is there a difference between using an algebraic method and using the graphical method? Explain why or why not
The solution to Queuing Analysis. The Bay City Police Department has eight patrol cars that are on constant call 24 hours a day. A patrol car requires repairs every 20 days, on average, according to an exponential distribution
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