Find all the first order partial derivatives for the following function.f(x, y) = ln 

A.  =  = 
B.  = -ln ;  = ln 
C.  = -ln  ;  = ln 
D.  = -  = 


Answer: D

Mathematics

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Simplify. Write your answers in the form of a+bi, where a and b are real numbers.(7 + 2i)2

A. 53 + 28i B. 45 - 28i C. 53 - 28i D. 45 + 28i

Mathematics

A hypothesis test is to be performed. State the null and alternative hypotheses.The governor of a state claims that since his tax cuts have taken effect, the unemployment rate has dropped. The unemployment rate in the state had been 6.3% prior to the tax cuts.

A. Null hypothesis: unemployment rate < 6.3%   Alternative hypothesis: unemployment rate = 6.3% B. Null hypothesis: unemployment rate > 6.3%   Alternative hypothesis: unemployment rate < 6.3% C. Null hypothesis: unemployment rate = 6.3%   Alternative hypothesis: unemployment rate ? 6.3% D. Null hypothesis: unemployment rate = 6.3%   Alternative hypothesis: unemployment rate < 6.3%

Mathematics

Provide an appropriate response.An oil tanker is losing oil at a rate of R'(t) =  where t is the time in minutes and R(t) is the radius of the oil slick in feet. Use n = 6 and Simpson's rule to approximate the size of the radius after 5 seconds.

Fill in the blank(s) with the appropriate word(s).

Mathematics

Find an equation in slope-intercept form of the line that passes through the given point and has slope m.(-5, -1); m = 0

A. y = - 5x + 0
B. y = -1
C. y = - x + 0
D. x = -5

Mathematics