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Consider the vector field F(x, y, z) = 2xyi + (x2 + 2yz)j+ y2 k.
a. Calculate the curl of F.
b. Calculate the divergence of F.
c. How does one know when a vector field is conservative?
d. Find the scalar field f(x, y, z) such that F =∇f
e. Evaluate the integral ∫c F · dr where C is the curve defined as r(t) = ti + tj + t2k and 0 ≤ t ≤ 1.
Determine whether the mean value Theorem applies to the following functions on the given interval [a,b] and if, so find or approximate the point(s) that are guaranteed to exist by the mean value theorem.
Your boss has asked you to put together a report showing the relationship between these two variables. What could you present and why?
Find an equation of the tangent line to the curve y(x) = (9/(sin(x)cos(x))+(3sin(x)/(sec(x)cos(x)) at the point (1/5 Pi, y(1/5 Pi))
What are the rate and minimum distance for this code?
A furniture factory needs 32.5 ft2 of fabric to upholster on a chair. Its Dutch supplier sends the fabric in bolts of exactly 200 m2. What is the maximum number of chairs that can be upholstered by 3 bolts of fabric (1 m = 3.281 ft)?
Show that every subfield of complex numbers contains rational numbers. Show that the prime field of real numbers is rational numbers. Show that the prime field of complex numbers is rational numbers
Find the minimum and maximum values of Z=6x+5y, if possible, for the following sets of constraints.
Find the potential alpha inflation
Draw a scatter diagram. Using the scatter diagram (no calculations), would you estimate the linear correlation coefficient to be positive, close to 0, or negative? Explain your answer
refer to and use the following abbreviations for the problems belowbt box of teasamph shipping and handlingp desired
Construct a table that shows all the possible results.
complete assignment. solutions code based on matlab. solution output to be included as well. ltbrgt
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