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Q: 4. Apply half-angle formula to find b. sin 15° 5m C. COS a. cos 15°

A: The half-angle formulas are: sinθ2=±1-cosθ2cosθ2=±1+cosθ2   We know that the sine function is positi...

Q: Suppose your newspaper is trying to decide between two competing desktop publishing software package...

A: given, daily productivity or company is defined as  Ux,y=8x0.6y0.2+x where x is number of copies of ...

Q: foreor Series Si cosnt dt )on= auswer: Y(-1) ausweri o ) en- Set sin znt dt answpy: o,5()

A: Our guidelines we are supposed to answer only one question. Kindly repost other question as the next...

Q: s1+x,-1 <x <0 f(x) = {1-x,0 <x < 1 f(x) = f(x + 2). etch the graph of f(x) for-3 <x < 3. ud the Four...

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Q: (a) D'Alembert's formula for the solution of the wave equation on R is given by (x+ct U(x,t) = (F(x+...

A: Since you have asked multiple questions, we will solve first question for you. If you want other que...

Q: (3)Use a cylindrical coordinate system to find the volume of a solid surrounded by spherical r2 + z?...

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Q: 5. Tsering owns a landscaping business. He went to the garden supply centre to buy edging for the pe...

A: Laws of sine is very significant in geometry. It helps to find the the angle when two sides and one ...

Q: (b) Show by direct computation that D'Alembert's formula is a solution to the problem U-cUrx 0, U(x,...

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Q: ay Classic Nim. This version of the game will have 4 rows. The rows will have the ng amount of count...

A: In this question, the concept of xor-operation is used to calculate nim-sum. Conditions of winning I...

Q: In x dx = n a, (a>0) 2a 23. Show that

A: Definite integration is the area of a region that is enclosed by the integrand. The function must be...

Q: 2) Let m +0 be an integer. Show that Rm := { (a, b) E Z × Z|m divides a – b} is an equivalence relat...

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Q: Consider the function T: P3 → P2 that is defined as follows: T(ax³+ bx2+ cx + d) = (a - 2b)x² + (c+ ...

A: Given Pn be the vector space of polynomials of degree at most n together with zero polynomial. Consi...

Q: (a) Nrite the most general linear first order partial differential equation in two variables (x,y).

A: A partial differential equation (or briefly a PDE) is a mathematical equation that involves two or m...

Q: Use differentiation to find the gradient of the curve y : = ax sin(bx) at x = 3.

A: The solution is given as  

Q: Example 4.14. Set up the Numerical Method for solving the following PDE and complete the table below...

A: Using forward difference formula for differentiation.

Q: 2"3"

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Q: Consider the following periodic function (1+x,-1 <x < 0 f(x) = {1-x,0 <x< 1 f(x) = f(x + 2). a) Sket...

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Q: 1. Given sin B =in QII, and (6, -8) is on the terminal side of a, find the exact value of sin(a + B)...

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any ...

Q: Q22] A harmonic function; u (x, y) = ¿Log (2² + y²) is given. Show that the function is harmonic. Co...

A: Introduction: We know that for function z=u+iv, the functions u and v are harmonic functions if they...

Q: 11) Consider the linear differential equation y" – ly = 2e6z + 3x + 8 If the particular solution has...

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Q: (D +2D+3)(e sin(7)) = e" (10 sin(t)+6cos(t)) True False

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Q: Let L: R* → R* be the linear transformation that is represented by the following 4x4 matrix: [3 0 0 ...

A: Remark:  For a square matrix A, a non-zero vector v is said to be an eigenvector of A if there exist...

Q: A 3 cm length silver bar with a constant cross section area 1 cm (density 10 g/cm³, thermal conducti...

A: The equation is u t...

Q: There exists a linear system has exactly two solutions. O True O False

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Q: A manufacturer is testing its new grain moisture meter and sampled out 5 grain types (1, 2, 3, 4, 5)...

A: Given: A manufacturer was putting its new grain moisture meter to the test, so they took samples of ...

Q: 6 Non-linear equations Let K be a field, and let a e K. Prove that a? {Ок, 1к).. = a if and only if ...

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Q: A city has the following temperatures during a given year. Feb. Mar. Apr. May June July Aug. Sep. Oc...

A: When temperature distribution over a year is given, we use sinusoidal function to model the temperat...

Q: e-2t cos 3t cOS

A: The given question is related to Laplace Transform. The solution is explained below.

Q: 10) For the non-homogeneous linear differential equation, y" – 10y' + 24y = e4 + 6x² + 15, we can gu...

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Q: Perimeter? Student Page 1 of 5 Area? Volume? Surface A construction company has been hired to build ...

A: For the solution follow the next step.

Q: Solve the following optimization problem using the simplex method: Maximum z = 10x, + 11x2 + 9x3 wit...

A: The following steps are used to find the solution of the linear programming problem by simplex metho...

Q: Let L: R³ → R³ be the linear transformation defined by b 2a (E) 2 a a L 6b + c for b E R³. %3D 36 а ...

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Q: 4. Show that the real number VV2 – 2 is algebraic. (Here 2 is a real number that satisfies (2)3 = 2....

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Q: Five rodents in a population of 500 are infected with a new strain of corona virus to test a theory ...

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Q: ) Fill in the blanks to complete the proof of the following statement: .... “For all integers n > 1,...

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Q: Consider the following periodic function f1 +x,-1 <x < 0 f(x) = { 1- x,0 < x < 1 f(x) = f(x +2). a) ...

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Q: A linear system is described by the following equations: x1 – 3x2 + 4x3 3 - = 6 = 6 2x1 – 5x2 + 6x3 ...

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Q: Given the augmented matrix below, find the solution set. 1 1 | 1 1 0 -1 | 1 2 | 1 Then (x1, x2, x3) ...

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Q: (3)Use a cylindrical coordinate system to find the volume of a solid surrounded by spherical r? + z?...

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Q: (d) Using the method of characteristics, or otherwise, find the general solution to y²U, – x*u, = 0,...

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Q: Given the following series: (п + 1)x2п-1 3n n=0

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Q: Given the heat equation, ốt 00 with the boundary %3D conditions, u(0,t) = 0 and u(1,1)= 5 for t>0 an...

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Q: From the top of a cliff, 108m high, the angle of depression to a boat on the water is 8°. Determine ...

A: The angle of depression denotes the angle from the horizontal line down to an object. An observer's ...

Q: In Exercises 47-62, for each polynomial function: a. Find a function of the form y = cx* which b. Fi...

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want...

Q: y" - 4y' + 4y = 0; y(0) = 3, y'(0) = 5

A: Since you have posted a multiple question according to guildlines I will solve first question for yo...

Q: (d) Using the method of characteristics, or otherwise, find the general solution to y-uy – xu, = 0, ...

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Q: Throughout this question, consider the following problen Question 4, for the Laplace equation on a r...

A: As there are more than 3 sub parts in the question and you do not mentioned which sub parts are to b...

Q: Q11] Integrate counterclockwise around C. Show the details. sin3z 1) ,C:Iz| = t z2 5z3 2) ,C: Iz| = ...

A: Our guidelines we are supposed to answer only one question. Kindly repost other question as the next...

Q: Give an example of a converse error.

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Q: 9) Set both inequalities greater than (>) or less than (5 and 1 – 4y 5 1- 4y 4y + 7 b. a+ 2 >0 C. r...

A: When two expression are not equal, they can't be expressed using '=' sign. In that case, either one ...