14. Function f and g are defined by formulas as shown below. f (x) = x3 and g(x) = x - 1, for all real number x. i) Find gof and fog. ii) Determine whether gof equals fog.
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Discrete Structure.
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- 38. The geometric mean g of n numbers x; is defined as the nth root of the product of x;: g=Vx1x2X3•…Xn (This is useful, for example, in finding the average rate of return for an investment which is something you'd do in engineering economics). If an investment returns 15% the first year, 50% the second, and 30% the third year, the average rate of return would be (1.15*1.50*1.30)") Compute this.Ql: The Collatz conjecture function is defined for a positive integer m as follows. (COO1) g(m) = 3m+1 if m is odd = m/2 if m is even =1 if m=1 The repeated application of the Collatz conjecture function, as follows: g(n), g(g(n)), g(g(g(n))), ... e.g. If m=17, the sequence is 1. g(17) = 52 2. g(52) = 26 3. g(26) = 13 4. g(13) = 40 5. g(40) = 20 6. g(20) = 10 7. g(10) = 5 8. g(5) = 16 9. g(16) = 8 10. g(8) = 4 11. g(4) = 2 12. g(2) = 1 Thus if m=17, apply the function 12 times in order to reach m=1. Use Recursive Function.7. The roots of the quadratic equation ax² + bx + c = 0, a 0 are given by the following formula: -b = √b² - 4ac 2a In this formula, the term b² - 4ac is called the discriminant. If b²-4ac0, then the equation has a single (repeated) root. If 200
- 1. A set of integers are relatively prime to each other if there is no integer greater than 1 that divides all the elements. Furthermore, in Number Theory, it is known that the Euler function,ϕ (n), expresses the number of positive integers less than n that are relatively prime with n. Choose the alternative that has the correct value of ϕ(n) for every n below. A) ϕ(5) = 4 B) ϕ(6) = 2 C) ϕ(10) = 3 D) ϕ(14) = 6 E) ϕ(17) = 166. X is (a,b,c,d), Y is {1,2,3,4). {(a,1), (b,2), (c,2), (d,4)) is a function from X to Y.Find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have the following properties: (a) are divisible by 5 but not by 7. (b) are divisible by 5. (c) have distinct digits. (d) are divisible by 5 or by 7 (inclusive or).
- INTRODUCTION: Heat conduction from a cylindrical solid wall of a pipe can be determined by the follow T1-T2 q = 2nLk R2 In R. where: q is the computed heat conduction in Watts. k is the thermal conductivity of the pipe material in Watts/°C/m. L is the length of the pipe in cm. Ri is the inner radius of the pipe in cm. R2 is the outer radius of the pipe in cm. Ti is the internal temperature in °C. T2 is the external temperature in °C. ASSIGNMENT: Write a C program that will allow the user to enter the inner and outer radii of the pipe, the the internal and external temperatures. Once the user enters the input values, the program7. Let A and B be integers from one to five. For the following expression: a + b = 3, prove if the expression is reflexive, symmetric, asymmetric, and/or transitiveMake a function which will calculate the pressure of a gas using Van der Waals Equation: The Van der Waals function will have arguments: temperature (T) in Kelvin,molar volume (Vm) in L/mole,critical temperature (Tc) in Kelvin andcritical pressure (Pc) in atm.(Tc and Pc are characteristics of the substance.) Within the function also define the gas constant R= 0.08206 L·atm/mole·K. The Van der Waals equation to calculate the pressure, P is: Where Within the function, create variables a, b and Vc, and calculate the value for each prior to calculating P. Using the MATLAB editor, make a script m-file for the following: Calculate the pressure withTemperatures over the range 255 to 315 K at intervals of 2 K, and Vm = 25.35 L/mole, Consider two substances:For ammonia: Tc = 141.15 K and Pc = 111.5 atm.For carbon dioxide: Tc = 241.9 K and Pc = 73.0 atm. Make a table with temperature in column 1, pressure for carbon dioxide in column 2 and pressure for ammonia in column 3, and write the…
- Q1: Y=f{A,B,C.D,E.F)=Em (0,1,2,4,5,6,7,9,13,15,17,19,21,23,26,27,30,31,33,37,39,40,42,44,45,4 6,47,49,53,55,57,59,60,61,62,63) Design the function with minimal logic gates and simplify the functions Using Karnaugh Map Method.Find the minimum product of sums for the following function. Each drop down menu has a number of choices. You must select an answer from each drop down menu. The choices include possible terms in the function. Another choice is "none", and should be used when none of the terms from that drop down menu are needed for the minimum solution. Finally, the choice "two or more" should be selected if more than one of the possible terms appearing in that drop down menu are required for the solution. There are too many possible 3 and 4 literal terms for automatic checking, so just select how many of them are required. f(a,b,c,d) = m(0, 1, 2, 4, 5, 6, 12, 13) + Σd(8, 14) Terms involving a and b: [Select] Terms involving a and c: [Select] Terms involving a and d: [Select] Terms involving b and c: [Select] Terms involving b and d: [Select] Terms involving c and d: [Select] Terms involving 3 literals: [Select] Terms involving 4 literals: [Select] > >Please do not give solution in image formate thanku. 5.Lael is always on the lookout for students who might be interested in running for office in student groups. In cell M2, enter a formula using a nested IF function as follows to determine first if a student has already been elected to office in a student group, and if not, whether that student meets the qualifications to run in the future: a. If the value in the Elected column is equal to the text "Yes", the formula should display Elected as the text. b. Otherwise, the formula should determine if the value in the Finance Certified column is equal to the text "Yes" and return the text Yes if true And No if false.