3 Prove the identity: sin30 = sin® –sin30 using De Moivre's theorem.

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Q: Evaluate the moment Mx and My of the region bounded by x + 2y = 6, x = 0 and y = 0.

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Q: Find the particular solution of y' - 2y = e3x if y(0) = -5 using Laplace Transform. %3D %3D

A: The given initial value problem is                                               y'-2y=e3x , y(0)=-5...

Q: You will find Taylor polynomials for 2 functions, then graph them on Desmos and insert screen shots ...

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Q: Please solve the differential equation in the image attached. (Differential Calculus) Thank you.

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Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y? = 4(x2 – ...

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Q: Approximate cos(x) for /x/< T/4 using Taylor Series (polynomial) with a true error of no greater tha...

A: Please check step 2 for the solution.!

Q: ОЗх^2+2

A: x3-0.03x2+2.4×10-6=0

Q: Find the volume generated by revolving bout the line y = -1 the area bounded by (x - 2)2 = 4(y + 2) ...

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Q: 3. Let A be a set and P(A) the power set of A. Complete the following proof that there is no onto fu...

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Q: Find a primitive root modulo 2 * 19^2022

A: Consider the number n=2×192022. We know that a primitive root of modulo n is an integer g such that ...

Q: 3. Using conjunction, disjunction and negation, find an expression of p and q that is equivalent to ...

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Q: 5. Find the Taylor series for f(x) = centered at a = 4. 1.3.5..... (2n – 1) |1+E(-1)"- (r- 4)" n! 23...

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Q: x² + ax – 2bx – 2ab – x³ – 2ax² – 2bx² dx x* + ax³ – 2bx³ – 2abx²

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Q: The equation (3xcos (3a) + sin(3x)-3) dr + (2y + 5) dy = 0 is e rcos (3z)- 3 + y - 5y = C O zsin (3z...

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Q: + x

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Q: ~(W=A) = ((~Wv~A) · (~AÉW))

A: This is a problem of logic.

Q: A local Chocolate Factory produces 3 varieties of Chocolate A, B & C. Ron bought a chocolate of each...

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Q: Estimate the area under the graph of f(x) = over the interval [1, 5] using eight approximating %3D x...

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Q: Find the complete == px + qy-/25+ p² +q? and singular solutions of

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Q: Find the area of the parallelogram that has u = i-j+ 2k and v = 3j + 2k as adjacent sides. NOTE: Ent...

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Q: 2 + 2 + 2 = 6 . 3 3 = 6 4 4 4 = 6 5 = 6 6 = 6 7 = 6 8 = 6 6 6 7 7 8 8.

A: Use  BODMAS while evaluating2+2+2= 63×3-3= 64+4+4 = 65÷ 5+5 = 6

Q: 6. Let f(x) = 1-x for 0<x<1. (a) Sketch fo(x), the odd half-range expansion of f(x), over the interv...

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Q: [3/ (x- 4)] = [(3x + 36) / ?] [4/ (2x + 5)] = [? / (2x? – x– 15)] [(x + 2) / (3x + 2)] = [(3x? + 4x ...

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Q: 3. Determine whether the following series converges, and if so, find its sum. 1 ( a) Σ27l-n 4 (b) (n...

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Q: Consider the series In(k) k2 k=1 a) Enter an integral whose convergence or divergence is equivalent ...

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Q: 3. Describe and sketch the graph of the given equation in R³. 1If it is a sphere, find its center an...

A: We have to sketch the graph of given equations.

Q: 2. A number U is selected at random between 0 and 1. Let the events A and B be "U differs from 1/2 b...

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Q: Consider the two points P(-5, –4, -4) and Q(-7,–-4, –5) and the vector V = 1 -2 You are given that -...

A: We have to find the vector projection.

Q: How many years are required for your money to triple if it is invested at 9% compounded? a. annually...

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Q: Find the temperature u(x, t) in a rod of length L = 2 if the initial temperature is f(x) (0 < a < 1)...

A: To find - The temperature u(x,t) in a rod whose length is L=2 and if the ends are insulated from 0 t...

Q: Let f(2) = : Part (a) Find the integral of the function f(2)on the circle of radius 8 centered aroun...

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Q: Evaluate the expression 2 1+i 2 1+i (2i – 1) 1+i 1+i

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Q: Construct a logical statement for S(p,q) such that it has the following truth table. (The statement ...

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Q: Let f(x) and g(x) be described as in the graphic below, with the red function being f(x) and the blu...

A: Derivative of the product function

Q: Instruction: Solve the following system of homogeneous linear differential equations. Present your s...

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Q: Find the x+ iy form of tan(i), arctan(2i), and tanh(i 3º5).

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Q: 5.) Suppose z = f (x, y) , where x=x(t,r) and y= y(t,r). Assuming all the functions involved have co...

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Q: Let -2 V2 = iz = w = If possible, express w as a linear combination of the vectors v1, v2 and v3. Ot...

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Q: A. In the figure below, CE and LA are diameters of ON. Use the figure to answer the following. If mL...

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Q: Explain why F, contains a primitive nth root of unity if and only if p = 1 mod n. Hint : Use the dis...

A: To prove  Fp contains a primitive nth root of unity if and only if p≡1mod n (or n divides p-1).

Q: Find the graph of this arclength

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Q: Find the area bounded by y = sin(x) and y = sin (x) from 0 <xs. %3D %3D

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Q: If a simple disconnected graph has 7 vertices and 2 connected components what is the maximum number ...

A: Given question is If a simple disconnected graph has 7 vertices and 2 connected components what is t...

Q: 1 to x = 5 using a Left Endpoint Approximate the area under the curve graphed below from x approxima...

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Q: x²dx Evaluate x2Vx2-4

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Q: t/2 Evaluate using Wallis' Formula: sin? x cos5 x dx

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Q: 2. The relationship between the displacement S, velocity v, and acceleration a, of a piston is given...

A: Given: s+2v+2a=43s-3v+4a=253s+2v-a=-4 Rewriting the equation2a+s+2v=44a+3s-3v=25-a+3s+2v=-4

Q: Instruction: Answer the following. Show all your solutions. 7. a. Find the volume V(S) of the solid ...

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Q: (c) The function, y(x) = 2.0 sinx + 3.00 Inx + x is to be evaluate for x = 1.26. The constants and t...

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