Let a, n be positive integers. Knowing that 15a - 13n = 1, we deduce that the multiplicative inverse of a (mod n) %3D O does not exist is (n-13) (mod n) is 15(mod n) O None of the mentioned

Q: Evaluate the following integrals. (a) / (csc0)(1+ sin² 0 + sin 0 cot² 0) d0 (b) /: (e) / dr VI-2r2 +…

A: Part(a) We need to evaluate ∫csc θ1+sin2θ+sinθ cot2θdθ Consider: ∫csc θ1+sin2θ+sinθ cot2θdθ=∫csc…

Q: 4) Jamila runs a grocery store that sells bulk coffee bean blends by the pound. She wishes to mix 40…

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Q: Let z be defined implicitly as a function of x and y by the e e-zy əz find O UTM + cos (xy) = (4 –…

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Q: Solve the given ODE using Laplace Transform 1. y" – 4y' + 3y = 6t – 8 ; y(0) = 0,y'(0) = 0 %3D -

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Q: dy -4 Given a differential equation with the initial condition, y :2. dx y cos (2x) (a) State the…

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Q: The time period of the motion u" +192u =0 is a) T = 0.45345 b) T = 0.5345 c) T = 0.54345 d) T =…

A: We can solve this by given information

Q: y" (t) – 6y'(t) – 2y(t) = 4 cos 2t – 4t³; y(0) = -2, y'(0) = 3 %3D

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Q: 3. The table below shows the highest daily temperatures (in degrees Fahrenheit) averaged over the…

A: We will use the basic knowledge of trigonometry and the system of linear equations to answer this…

Q: 14-y2 구~ X 3 dy XP

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Q: QUESTION 2 F. as. where F(x,y.2)-( Y , and s is the surface of the unit sphere, oriented outward. 4n…

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Q: y" – 3y' – 10y = 8(t – 4), y(0) = 0,y'(0) = 0. %3D %3D

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Q: provide a fitch proof P Q¬R→ (Q → S) R → T T&P:Q &S

A: We have to prove the given arguments.

Q: Consider F and C below. F(x, y, z) = yzexzi + exzj + xyexzk, C: r(t) = (t2 + 1)i + (t2 − 1)j + (t2…

A: Given data F(x, y,z)=yzexzi+exzj+xyexzkC: r(t)=(t2+1)i+(t2-1)j+(t2-2t)k,  0≤t≤2

Q: Given f(r, y, z) = In(x² + y? + 2²), show that af, f, s dy? %3D dx² x² + y? + 22

A: The given function is fx,y,z=lnx2+y2+z2........(1) To show: ∂2f∂x2+∂2f∂y2+∂2f∂z2=2x2+y2+z2

Q: (b) Find the basis for the col(A) and null(A) 4 5 2 1 30 1 3 2 2 1 A ||

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Q: Q.3. Use the method of Laplace Transform to solve the initial value problem y"+y+y 3 sin(2t), y(0)…

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Q: 1 1 1 0100 0120 00 0 Let A = Write A as C DC , where D is a diagonal matrix. Hint: You can always…

A: Given : matrix A=1110010001200000 We have to write A as CDC-1, where D is a diagonal matrix.

Q: Express all answers in Rectangular Form. 1. (1 + j3)z² + (5 + j6)z + 7 – j6 = 0 2. 3z? – (5 – j4) z…

A: Since you post more than three subparts questions as per our guideline we can solve only first three…

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Q: 5. Sketch the graph of a function f with domain [1, 5] satisfying all the following conditions:…

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Q: Prove that ifH and K are subgroups of a group G with operation *, Question 8. then HNK is a subgroup…

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Q: Problem 1B. Solve the system of linear equations using Gauss-Jordan Elimination. -2 2 -4 7 [X1" 8.…

A: In Gauss-Jordan elimination method we first write the given system in augmented Matrix form and then…

Q: Canter e dn= り。 f(x)= 5-3X

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Q: Solve the given ODE using Laplace Transform 3. y"(t) – 6y'(t) - 2y(t) = 4 cos 2t – 4t³; y(0) =…

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Q: A population of middle school students contains 160 sixth graders, 180 seventh graders, and 140…

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Q: ||r(t) × r"(t)|| to find «(t). 3 Use the formula k(t) r(t) = t'i + t°j 126t5 K(t) (4+ 81d14) 3 2

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Q: The price of a jumper was reduced in a sale by . The new price was later reduced by . What fraction…

A: As per the company rule, we are supposed to solve the first three sub-parts of a multi-parts…

Q: Find all solutions between -2π and 2π of the equation:  Cos (θ) =  √3 / 2

A: We use the following: If Cos (θ)  = cos(α) [ 0 ≤ α ≤π ]      ...(i) then   θ = 2nπ ± α   ,where n is…

Q: Perform the following conversions 185.7510 to binary, octal and hexadecimal

A: The given decimal number is                                    185.7510

Q: Given the matrix 6 0 0 A= 0 2 2 0 2 2 find an orthogonal diagonalization of A: A = QDQ"

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Q: Derivatives of Algebraic Functions Directions: Prove the following statements. 13x + 20x* 2Vx3 +2…

A: Using the product rule of derivative, it can be written that: f·g'=f '·g+f·g'.

Q: 25 s3(s? + 4s + 5)

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Q: (*) 3. Let 2 = {A, |n = 1, 2, 3, ...}, where A, Find UN and N2, then !! %3D prove your conjecture.

A: We solve this problem using the basic properties of union and intersection. Also some basic steps of…

Q: Suppose 450 test scores are normally distributed with mean 73.7 and standard deviation 2.5. a. How…

A: (a) The 68-95-99.7 Rule for a Normal Distribution states that: About 68.3% of the data points fall…

Q: ). -18 -7 A = 3 ( 8 11 = -1 og 12 = 2. %3D

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Q: Prove the converse of the Pythagorean theorem based on this Proof of the Pythagorean Theorem. A…

A: We will use the basic knowledge of triangles and Pythagoras theorem to answer this question for you…

Q: x = y + Z y² = 0.000396707 - 0.24576 x2 z* = 0.00029753 – 0.12288 x²

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Q: (c) The motion of a mass-spring-damper system is given by the differential equation d?y +8 + 20 y =…

A: We have to solve the given problem.

Q: lx)にX sit. ors<I prove that inl Guernesto uniterady. Guveryes to

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Q: A. Problem Solving (Bracketing Method): Solve the following problem using Bisection Method and False…

A: We will use the basic knowledge of numerical analysis to answer these questions. This is a multipart…

Q: Design the network represents the following activities, and then find the critical path. Activity…

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Q: c) Mr Jason deposited $5000 into an account paying 6% annual interest compounded monthly, how long…

A: Solution :-

Q: Describe the graph of the equation. r = 10 sin 17ri+ 10 cos 17t j O Itis a circle of radius 10 in…

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Q: Use Newton's Method to approximate the root of x In x = 2 accurate to five decimal places. Begin by…

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Q: 12 n 12 n+ 3.64 2 n converges to The sequence an = Note: You may need to use the command.evalf() to…

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Q: Describe the graph of the equation. r = 10 cos ti + 3 sin t j – k O Itis an ellipse in the z = -1…

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Q: 50. S sin*2x cos“2xdx

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Q: Q3. Find the area of the region R that lies outside the cardioid r = and inside the circle r a(1+…

A: q-3 find the area of the region R that lies outside the cardioid r=a1+cosθ and inside the circle…

Q: Mary can clecn Working together.y baitle Johng Cn office is S horiis. snd Mary cen 3.5 hours- How…

A: Solution

Q: 4. For each matrix shown below, state the dimensions and name the specific type of matrix shown…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…