Give 2 examples for each using postulates. (Group theory)

1)Semi_Group, 2)Monoid, 3)Group with your own explanation and own answers are appreciated. Do not copy and paste.

consider the relation where each elements of the domain are the vowels of the alphabet. If the elements of the range are all the elements of the subset of {P,Q,R} and each domain element is associated with an image, can this relation be a function? Can it be one to one, justify your answer.

a) Find the Fourier Cosine Transform of ?(?) = sin ? ; 0 < ? < ?.

b) Solve, by using Laplace Transform: ?" + ? = 3 ??? 2?; ?(0) = 0, ?′(0) = 0.

In order to grow a certain crop, it is recommended that each square foot of the ground be treated with 10 units of phosphorus, 9 units of potassium and 19 units of nitrogen. Suppose that there are three brands of fertilizer on the market - X, Y and Z. One pound of X contains 2, 3, 5 units of phosphorus, potassium and nitrogen respectively. One pound of Y contains 1, 3, 4 units of phosphorus, potassium and nitrogen respectively. One pound of Z contains 1, 0, 1 units of phosphorus, potassium and nitrogen respectively. Using matrixes:

(i) Determine whether or not it is possible to meet exactly the recommendations by applying some combination of the three brands of fertilizer?

(ii) Take into account that a negative number of pounds of any brand cannot be applied, and suppose that each brand is sold only in integral amounts. Under these conditions, determine all possible combinations of the three brands that can be applied to satisfy the recommendations exactly.

(iii) Suppose X costs $1 per pound, Y costs $6 per pound and Z costs $3 per pound. Determine the least expensive solution that will satisfy the recommendations exactly as well as the constraints in (ii).

I need Q1,2 and 3 ASAP please, thanks

1. Identify three applications of integration.

2. Give two specific examples of how we use integration to solve real-world problems.

3. Write a paragraph about how integration is applied in non-STEM disciplines.

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Prove that the polynomial x^3 + x^2 – x + 1 has no integer roots

1. Here is a model:

Domain: {Wikipedia, 2, Isaac Newton}

Referents: ​n​: Isaac Newton

Extensions: P: Ø Q: {2} R: {Wikipedia, Isaac Newton}

Is the following proposition true or false on this model? Explain your answer.

∀​x​(​Qx ​∨​Rx​) → ​Pn

2. Is the following argument valid or invalid? If it is valid, explain why there cannot be a countermodel. If it is invalid, provide a countermodel.

ᄀ∀​xHx

∃​xMx

∴ᄀ​∃​x​(​Mx ​∧​Hx​)

Bunce’s farm has a 10 L water tank fed by a stream running from Boggis’ Chicken Ranch. Water from the stream flows into and out of Bunce’s tank at a rate of 10 L/minute which keeps it well-mixed. One day Bunce finds out that Boggis has been dumping chicken manure into the river which adds Salmonella to the stream at an unknown concentration of a mcfu/L (Note: mcfu is a unit of measurement for bacteria standing for “millions of colony forming units”). At the time of his discovery, Bunce measures the concentration of Salmonella in his tank to be 1 mcfu/L and one minute later measures it again to be 2 mcfu/L. Use these measurements to determine the concentration of Salmonella in the river and the limiting concentration of resulting Salmonella in Bunce’s tank.

Joan borrowed ​$17 comma 000.00 to buy a car. She repaid ​$4100.00 four months later and ​$7900.00 six months later. After twelve​ months, she borrowed an additional ​$6200.00​, and repaid ​$5100.00 after 20 months. She paid the entire​ balance, including the​ interest, after 24 months. Interest was 9​% compounded monthly for the first year and 9.6​% compounded monthly for the remaining time. What was the size of the final​ payment?

4. Compute the minimum square error for
f(x) =x/π (−π < x < π).

Suppose a 1 kg mass is attached to the end of a string that is stretched 0.2 m by a force of 500 N (newtons). An exterior force F0 cos 50t acts on the mass. Find the position function x(t) if the initial conditions are given by x(0) = 0, x′(0) = 50.

how to approach sets and relation type easy moderate problem and show some tips tecniques and shortcuts formula ..i would give positive response if you help me a little.... thankyou

how to approach function ( range and domain etc) type easy moderate problem and show some tips tecniques and shortcuts formula ..i would give positive response if you help me a little.... thankyou

please show some shortcut tricks and technique formula for CALCULUS to solve out easy difficulties questions
i would give a postive rating..if you help me a little