Derive a formula for xsp if the equation is mx′′ + cx′ + kx ? F0 sin(ωt). Assume c > 0.

Q: Find the exact value of sin(20) given sec e 11 and 0<e <". 2-4-V112-4 А. 3-3-V13-92 С. 112 132…

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Q: 3. Simplify x(t) = 3 cos(27200t + + sin(27200t + to the form x(t) = a cos(27200t + 0) where a and 0…

A: To convert an expression of the form Acosx ±Bsinxmultiply and divide by A2+B2=A2+B2AcosxA2+B2…

Q: Find the value of A. (A-B+C) + (2A + B) sin (2y) - (2B - A) cos (2y) = (4 + j3) − (6-j2) sin² (y)

A: Hint: The given equation is A-B+C)+(2A+Bsin(2y)-(2B-A)cos(2y)=(4+j3)-(6-j2)sin2y. Solve the given…

Q: Prove the formula eix cos(x) + i sin(x) %3D Use this to evaluate e2i

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Q: If f(x) = cos(3r), then f(77)(x) %3D (A) 37 cos(3æ) (B) 377 sin(3x) (C) –37 cos(3æ) (D) -377 sin(3x)

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Q: Solve sin a – cos? x = 1 on the interval 0 < x < 27. 0, T T 57 - 4 4 о 0, п, 2т T 37 - 2 2

A: We know that  sin2x + cos2x = 1 According to question : sin2x - cos2x = 1 1 - cos2x - cos2x = 1 1 -…

Q: Verify if y = c, sin 3x + c2 cos 3x + 9x2 - 2 is a solution to y' +9y = 81a?. Show your solutions…

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Q: OBTAIN THE GENERAL SOLUTION 1. X cos? ydx = + tan ydy

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Q: Let sin A = -3/5with 270° &lt;= A &lt;= 360° and cos B = - 8/17 with 90° &lt;= B &lt;= 180° and find…

A: Given: sinA=-35  ,270°≤A≤360°CosB=-817 ,90°≤B≤180°

Q: Solve the given ODE using the method of undetermined coefficients. y" – 4y = (x² − 3)(sin2x)

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Q: a Find the exact Vailse of: ton to t tan to II fanI |- tan Fo ten TE b) Solve 4 sin "X +3 sink-1=0…

A: question a)  we know the formula of tan(A+B) = tan(A)+tan(B)1- tan(A).tan(B) we compare the given…

Q: Because r = √x2 + y2 cannot be ________, the sine and cosine functions are ________ for any…

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Q: Substitute the expressions for u and for du to write tan(5x + 8)dx in terms of u. tan(5x + 8)dx = |…

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Q: Given sin(a) - and T < a < 3/2 and cos(3) 24 and 0 < B <T/2. Use sum and difference formulas

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Q: By Eliminating the arbitrary constant of the following equation: y = C1e2*cos3x + C2e2*sin3x Prove…

A: Explained below

Q: lse the method of undetermned coofficients to solve the differenticl eqination: y°+9y=@osCat)…

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Q: Evaluate sin2(x) cos*(x) xdx 32 C. 32 A. 32 в. D. 32 O A В

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Q: sin 3t? limt-o 1-cos 2t

A: To evaluate: limt→0sin 3t21-cos 2t 00 form

Q: Without using a calculator, find all the solutions of cos(t) 2 where – T < t< T.

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Q: 4. (cos 2y – 3x²d²)dx + (cos 2y – 2x sin 2y – 2x³y)dy = 0 %3D

A: As it is a multiple type question , so I am solving just the 4th question   (4) The differential…

Q: Find the solutions of the following equations that are in the interval [0, 2n). sin2a 14. cosasin2a

A: Authoring guidelines:…

Q: Make the substitution u = 7 cos e in the expression 1/V 49 - u2, and simplify the result. (Assume…

A: Make the substitution u=7cosθ in the expression 149-u2.

Q: Given a function f(x,y,z) = (x+5) In (4y - 5) sin (10z). Find the domain of the function.

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Q: B. For the given values of the variables, verify that the equation is not an identity. 1. x² - y² =…

A: Given equation,x2-y2=(x-y)2 for x=1 and…

Q: 4. 2 cos(2x – y) dx – cos(2x – y)dy = 0 - %3D

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Q: Given that the characteristic equation has the following complementary solution, what are its roots?…

A: To find The roots of the given complementary solution.

Q: sin x sin ydx+ cos x cos ydy = 0

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Q: Зл 2n), then 2 D 7.7. Prove that If a E ν1-cos2(α-π) 1 +a)+ =0 sin( 5π+ α) tg 37 – 2a 1- sin 2

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Q: 1 s¯¹(x) 2 cos √1-x² -dx

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Q: 1. What is the value of tan30°? V3 а. 2 3 b. 2 d. 1 2. What is the value of sin45°? 1 a. 2 C. 2 d. 1…

A: 1. tan 30°2. sin 45°3. sec 60°+csc 30° Note:     Question contain multiple part, we are answer only…

Q: Solve the equation for x in terms of y if x is restricted to the given interval.

A: Given: y=2+3 sinx x∈-π2,π2

Q: Given cos*(4x) - sin*(4x) = cos(g(x)), determine the value of g(x). А. 4х В. 8х С. 16х D. 32x

A: We have to determine the value of the polynomial gx which satisfies the equation…

Q: VĀ(VB – 1) Use an addition or subtraction formula to find the exact value of sin 165° 4 A = B =

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Q: Find the exact value of the expression. sin 165° O A. - v2(V3 – 1) O B. - v2(V3 + 1) VZ (V3 - 1) Oc.…

A: We need to evaluate the exact value of the following expression sin165°

Q: Find all real solutions to the following equation: sin(nx) + sin(2nx) + sin(3nx) = 0.

A: Given: The equation sinnx+sin2nx+sin3nx=0 To find: All real solution or given equation.

Q: olve the following equation for (a) where 0<a<2pi cos(2a)=1-sin(a)

A: Given equation cos(2a)=1-sin(a) ;    0&lt;a&lt;2π

Q: If P = A sin 0 + B cos 0 and Q = A cos 0- B sin 0, find the value of A2 + B² in terms of P and Q. А.…

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Q: Given cos*(4x) - sin*(4x) = cos(g(x), determine the value of g(x). А. 4х С. 16х В. 8х D. 32x

A: To find the value of g(x) use the following formulas. sin 2x + cos 2x = 1 x2 - y2 = (x - y)(x + y)…

Q: Find all solutions of the equation sin – 1 = 0. - Your answer is A + BkT, where A = with 0 < A T,…

A: We have to solve

Q: Find all solutions to cos(6t) – cos(2t) = sin(4t) on 0 <t < r t = Give your answers as a list…

A: The given expression is, cos(6t)-cos(2t)=sin(4t) The interval defined for the expression is 0≤t≤π…

Q: p = 0 is Select an answer | of f(x) = sin(x) – 6

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Q: Given that the characteristic equation has the following complementary solution, what are its roots?…

A: We will find out the required roots of given complementary solution.

Q: Find the value of A. (A-B+C) + (2A + B) sin (2y) - (2B - A) COS (2y) = (4+j3) (6-j2) sin² (y)

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Q: Find all solutions to sin3x =1, 0<x<2n Select one: п 5п а. 2 5 TT b. 6' 6 c. None of these d. 6 5π…

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Q: e. Using your answers from part d, express ( x, + X2). (2x- 4x2), and (x, + x2)( 2x1 4x2) in a…

A: Consider the equation

Q: tind the geneval solurion to the D.E 4) (3) you Know that 4o)s sinx is one of the solurions

A: We will find out the required general solution for given differential equation.

Q: Use the reduction formula a cos(aE) + b sin(r) = Va² 6- sin(a + 0) to find all solutions to: Cos(20)…

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Q: Given x sin4t, y = -cos4t, then find at t =.

A: x=sin4t   ,y=-cos4t