Math Answers

Show that the square of an even number is an even number using a direct proof.

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Consider the 3-dimensional vector field F defined by F(x,y,z)=(2xyz,x²z+2yz²,x²y+2y²z+e^z).

1.write down the Jacobian matrix jf(x,y,z).

2.determine divF (x,y,z).

3.determine curl F (x,y,z).

4.does F have a potential function? Give reasons for your answer, referring to the relevant definitions and theorems in the study guide.

5.find a potential function of F .

1.approximately to what year does this evidence date back?

2.Give detail of how counting was done in the example which you chose.

3.where in caps is this type of counting covered as a topic?

Consider the R²-R function f defined by f(x,y)=x²+2y²-x²y.

Show that f has two saddle points

Prove that a ring with one consists only of zero if and only if 1 = 0

Consider the R²-R function f defined by f(x,y)=e^xIn(1+y).

Find the third order Taylor polynomial of f about the point (0,0)

A certain group of welfare recipients receives relief goods with a mean amount of Php 500.00 per week. A random sample of 75 recipients is survived and found that the mean amount of relief goods they received in a week is Php 600 and a standard decision of Php. 50.00. Test the claim at 1% level of significance is not Php 500.00 per week and assume that the population is approximately normally distributed. What type of test does the problem represent?

Find the four roots of z⁴=-1

A certain group of welfare recipients receives relief goods with a mean amount of Php 500.00 per week. A random sample of 75 recipients is survived and found that the mean amount of relief goods they received in a week is Php 600 and a standard decision of Php. 50.00. Test the claim at 1% level of significance is not Php 500.00 per week and assume that the population is approximately normally distributed. Which of the following is correct null and alternative hypothesis, in symbol?