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Calculate the Laplace transform of
• (t) integral from (0 to t) (T)e^(T)dT
Find the general solution for the differential equation
-y"=6x + xe^x
(a) using method of undetermined coefficients
(b) using variation of parameters
Some of the following statements below are true, and some are false. Prove all those statements are true, and for those are false explanation why the statement is false.
a. If R is an integral domain and about=av with a is not equal to 0 then b=c.
b. If F is a field then it must be an integral domain.
c. If R is an integral domain then it must be a field.
d. 4Z is an ideal of (Q,+,•), the ring of rationals.
e. 4Z is a subring of (Q,+,•), the ring of rationals.
Prove the following statement:
Every finite integral domain is a field.
Show directly that 7Z is a maximal ideal of (Z,+,•).
Show that the only ideals of a field F are the trival ideal {0} and F itself
Show that the only ideal of a field F are the trival ideal {0} and F itself.
Show directly that 7Z is a maximal ideal of (Z,+,•)
Transcribed Image Text:The profits of a City Center in Thousand R.O per day has the following probability distribution: Profits in Thousand R.O 10 12 14 18 20 22 Probability 12 a R 18 a R 24 a R a R 28 a R 17 aR Find the unknown a. R=31 а. b. Find the expected value of the daily profits in R.O. Find E(Rx-5). С. d. Find V(Rx-3).
Solve the following system of equations and provide a graphical representation of the solution.
y - x = 1
x2 + y2 = 13
#340153 on Dec 2023