Show that 2π de (5-3 sin 0)² 5T 32

Q: Suppose p = 22 +1 is prime, with m > 1. Show that () = -1

A: p=22m+1 is prime, with m≥1.

Q: Q1: A: Expand the function f(t) by using cosines series. 0 < t < 4 8-t 4 < t < 8 f(t) = {8²-₁

A: Given   ft = t0 &lt; t &lt; 48 - t4 &lt; t &lt; 8      The cosine series of ft is…

Q: Solve the initial value problem x'(t)=Ax(t) for t20, with x(0)=(5,4). Classify the nature of the…

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Q: 3. Suppose G is the group of symmetries of the square. Determine whether the following subgroups are…

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Q: Use induction to show that for any n ≥ 0, then (n/e)" ≤n! where e is base of the natural log and it…

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Q: Find the orthogonal projection of ✓ = projw(u) = 61 90 904 45 281 30 52 45 8-60 onto the subspace W…

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Q: 3. Consider the function f(x) = (a) Find the Taylor series of f(x) at a = 5 using the definition of…

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Q: Question 5 Let f(t) be a continuous function for t20 and F(s) = f(t)est dt. Select all that apply…

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Q: Let V be set of all polynomials p(x) = ao + a₁x + a²x² + • anx" for which -5 is a root. Mark the…

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Q: f(u) 22 Write an equation for the function graphed above. f(u) = -0.3333(u+2) (u-1) Round to 4…

A: Clearly above graph is a downward parabola passing through (-2,0) , (1,0) and (0,1) We know standard…

Q: Question 34 please

A: Use the binomial series to expand the function as a power series and state the radius of…

Q: Suppose ₁ and ₂ both have the property of being an additive inverse of v. That is, for this arb…

A: If u and v are additive identities then u+v=v+u=0

Q: c. Prove using weak induction that for all positive integers n 1² + 3² +5² +...+(2n − 1)² : - = 4n³…

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Q: ive an example of vectors u, v E V that demonstrate why u + v is not necessarily an element of V.…

A: The given vector space is V={(x,y)∈ℝ2 | x.y≥0} We have to find two vectors u and v such that u+v is…

Q: Given a data set with μ=40  and σ=5.3, find the z-score for each data point listed below. Round each…

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Q: Q1. A software company is considering the format of its login passwords. Which of the following…

A: Counting principle of addition and multiplication will be used.

Q: Consider the following. Year 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920…

A: (a) Given that t is years since 1790. So, for the year 1790, t=0. For the year 1860, t=1860-1790t=70…

Q: 1 Consider y(x) to be: y(x) and that point P (2, 1/5) lies on that curve. 1+2x (0) Find the slope of…

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Q: Let f(x, y) = 7x cos (y). Find the conservative vector field F, which is the gradient of f. (Give…

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Q: 3. Solve the integral equation y(t) + 3 y(t) sin(t - t)dt = t by Laplace Transform.

A: The given problem is to find the solution for the given integral equation by using the Laplace…

Q: Solve the system of equations and inequalities below simultaneously using graphical methods only.…

A: Given: y=2x–3,y=(x–6)2–4 and y&lt;x3+3. Objective: To solve the system of equations and inequalities…

Q: Find, by the method of Lagrange multipliers, the critical points of the function, subject to the…

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Q: The domain

A: Note that: The functions cos(x) and sin(x) oscillates between -1 and 1 for real values of x.

Q: Thirty-two people were chosen at random from employees of a large company. Their commute times (in…

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Q: y (4) + 32y"+256y = 0 y(0) = 2, y'(0) = 0, y"(0) = -16, y""(0) = 128

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Q: Find the surface area of that part of the plane 8x + 6y + z = 5 that lies inside the elliptic…

A: Given that the equation of a plane                                         8x+6y+z=5. To find the…

Q: Prove that the groups A and DXZ are not isomorphic. 5

A: The given in the question is the two groups A5 and D6×Z5, and the objective is to prove that these…

Q: prove that ਰ Apply the calculus of residues to dx (1 + x²)² - π 4 .

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Q: Let y = 4 6 -2 - 1 u₁= -4 4₂= 2 LO 6 Find the distance from y to the plane in R³ spanned by u, and…

A: The given problem is to find the distance from the given vector y to the plane R3 spanned by given…

Q: Calculate the Riemann sum for f (x, y) = x - y and the shaded domain 1) in Figure 22 with two…

A: A function: fx ,y=x-y To Find: Reimann Sum for the given function and domain.with two choices of…

Q: Describe the zero vector (the additive identity) of the vector space. P3 + X +

A: This question is about vector space

Q: 4. Let X be a non-empty set and p E X be a specific point. Let T = {UC Xpe U} U {0}. Answer each of…

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

Q: It was not 126. I cannot figure it out

A: We have to Find the fifth root of -32i that graphs in the fourth quadrant.

Q: Suyin has 56 pennies and 196 nickels. She wants to place them all in stacks so that each stack has…

A: Given that, Suyin has 56 pennies and 196 nickels. She wants to place them all in stacks so that each…

Q: 4. Let the torus T be the image of the map T(u, v) = (x(u, v), y(u, v), z(u, v)) = ((R+r cos v) cos…

A: Let the torus T be the image of the map. Therefore,…

Q: d²y dy +2 + 2y = e-t dt² dt y(0) = 0, y'(0) = 0

A: d2ydt2+2dydt+2y=e-t y0=0y'0=0

Q: Given ellation is using Laplace! 4²-3x + 2x=4e²² коказ ду сод==ђ

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Q: Find the volume of the tetrahedron having the given vertices. (4, -5, 1), (5, -3, 4), (2, 1, 1), (0,…

A: Given that the vertices 4,-5,1 , 5,-3,4 , 2,1,1,0,0,1  . Let  A4,-5,1  ,  B5,-3,4 , C2,1,1  and…

Q: Assume that T is a linear transformation. Find the standard matrix of T. T: R³ →R², T (e₁) = (1,3),…

A: Te1=1,3Te2=-5,4Te3=3,-2

Q: correct graph below a U C (ATD 0.0 A

A: A few functional properties of a real-valued function are given.

Q: Suppose p = 22 +1 is prime, with m > 1. Show that the order of 3 mod p is p-1, so 3 is a primitive…

A: Results used in this problem will be 1) Euler's Theorem 2) Law of Quadratic Reciprocity 3) Eulers…

Q: 5. Determine whether the statement is true or false. Justify your answer. (a)There exists n × n…

A: Check whether given statements are true or false.

Q: Find the Fourier Series for the following function. f(t) = |t| + 1 − 1 ≤ t ≤ 1

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Q: Q3) Evaluate triple integral ffydz dx dy.

A: Triple integration found by successive integration

Q: Graph the hyperbola given below using the transverse axis, the center, the vertices, and the…

A: Given equation of the hyperbola is y-1216-x-2225=1 or, y-1242-x-2252=1 , Which is of the form…

Q: 33. f(x) = -2x + 3 3x-2 if x < 1 if x ≥ 1

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Q: Use an Euler diagram to determine whether the argument is valid or invalid. All frogs are poisonous.…

A: The argument is: All frogs are poisonous. A tree frog is a frog.___________________________ A tree…

Q: In this problem, your task is to list all the constants, free variables and bound variables in each…

A: We know that, in formal symbols: a,b,c,…,l,m,n,… are represents constants. x,y,z represents…

Q: Two chemicals A and B are combined to form a chemical C. The rate, or velocity, of the reaction is…

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Q: This exercise uses the population growth model. The population of a country has a relative growth…

A: We have to find the relative growth  The procedure is given below