1. Compute the volume of the torus given in the figure below using the change of variables x = (R+ucos v) cos w, y = (R+ucos v) sin w, z = usin v. with 0

Q: 2 Q) Let A € M₁ C4) such that A² = A ENA show that det (I+A) = 2

A: If minimal polynomial is totally factorizable that is product of linear factors. Then matrix is…

Q: IV. Consider the plane : +3y - 2z = 6 and the line with parametric equations l:x=4-3t, y=2+t, z = 2t…

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Q: y dy Find using the substitution +5= √√y+2. √x+2 A²/(√y+2-5)(-5√/y+2+y+21) +C 3 ® ²/(√y+2-5)…

A: ∫ydyy+2 Substitute, u+5=y+2 Then , du=12y+2dy ⇒2y+2 du =dy ⇒2u+5 du =dy and y=u+52-2=u2+10u+23

Q: Given the periodic function defined in one period by the function: (bt, f(t) = a, (0, 0 0.

A: The following formulae are used to find the Fourier coefficients of the function fx on the interval…

Q: 13. Estimate fcos (x²) dx using (a) the Trapezoidal Rule and (b) the Midpoint Rule, each with 0 n =…

A: (a) Estimate by Trapezoidel Rule for n=4in this case f(x) = cosx2 , a= 0 , b = 1 , n = 4  and ∆x =…

Q: The volume of the solid generated by revolving the region bounded by x²=4y and y2=4x about y=4 is to…

A: Option (A) is correct.

Q: acid, HO₂C H, the first ionizatio Ka₂=4.2. Why is the second carboxyl g

A: Acids will sour substances with the pH values less than 7. Acids can donate their protons. There are…

Q: . SOLVING NHLDECC USING VARIATION OF PARAMETERS (D² + 2D + 1)y = (ex-1)² ANSWER: y = ex(C₁+C₂x -…

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Q: Find the fourier transform of the following. functions by making use of Jordan's Lemma. a) 1 (x² +…

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Q: ?

A: 1. The measure of arc is twice the angle formed at the circumference, therefore RS⏜=250° Therefore…

Q: / Fit a curve of the form y = ax + bx² to the data

A: Given,    x 1 2 3 4 5 y 1.8 5.1 8.9 14.1 19.8 To find             y=ax+bx2…

Q: 10. Determine the value for k for which the two lines are parallel and the value for k for which the…

A: The given lines are       L1: x, y=3, 2+t4, -5   and      L2: x, y=1, 1+s7, k

Q: Find the length of the curve. Hand written plzz √2ti + etj + etk, 0 ≤t≤ 3

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Q: 1. Solve by Euler's method and by classical 4th-order RK method: dy₁ = 2y₁ - 4y2, dx dy₂ = y₁ - 3y₂…

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

Q: Find the value of x. X+ 5-

A: Incentre is a point that lies in a triangle. The bisector os all the angles of a triangle meets at…

Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y=4 is to…

A: Consider the given curves, x2=4y and y2=4x Draw the diagram of the region revolving,

Q: Evaluate the following definite Integrals by using Gamma or Beta Functions: f¹[V√2x In (√x)]³dx CS…

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Q: A family has two cars. The first car has a fuel efficiency of 25 miles per gallon of gas and the…

A: Given that there are two cars. First car has fuel efficiency of 25 miles per gallon of gas. Second…

Q: The volume of the solid generated by revolving the region bounded by x²=4y and y²=4x about y=4 is to…

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Q: 9.W.1 The Gram matrix of an inner product on R2 with respect to the standard basis is G = 1 2 -1…

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Q: A={1, x, x²} and A'= *-·A·D· Let Z: P₂ → R³ be the linear transformation given: a + 2b + c…

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Q: Find the Fourier series representation of f(x) = { x ₁ 0, π< x≤ 0 0 < x < T X, **Box your answers…

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Q: Let x and y be two real numbers such that x + y is rational. Prove by contrapositive that if x is…

A: Introduction: Rational and irrational numbers are two very important divisions of real number…

Q: Consider the following. B = {(0, -1, -2), (4, 1, 2), (12, 3, 7)}, B' = {(−3, −2, −6), (2, 1, 3), (2,…

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Q: Inz) = Inr ei ) = Inr) + In ( e°0 )=ln r+iᎾ z = reie

A: A complex number is expressed in various ways. Apart from rectangular representation, a complex…

Q: Let A = (0,1]-{\n € N}. (a) Find the set Aº of its interior points. (b) Find the set A' of its limit…

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Q: Find the angle a between the vectors α= | and

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Q: 2. Given the figure below, find a single vector that is equivalent to D B a) E-A tw IA tu F to G

A: given vector bundle

Q: 4.1. Find a power series representation for the function 8 using summation 2x-15 sign, 4.2.…

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Q: Which of the following can be solved by both trapezoidal rule and Simpson's 3/8 rule? How to solve…

A: Trapezoidal Rule: For applying this rule, the number of subintervals must be a multiple of 1.…

Q: Define R as the region that is bounded by the graph of the function f(x) = x3 +1, the x- 6 axis, x =…

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Q: Determine the Laplace Transform of sin³3t

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Q: Part 1 of 3 Find a solution to the system [x'y']=[−62−2−10] [xy][x′y′]=[-62-2-10] [xy] by solving…

A: Introduction: The eigenvalues and respective eigenvectors of a matrix plays an important role in…

Q: Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. What type of quadric is S? Find an…

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Q: x"" (t)- 3x"(t) − 4x' (t) + 12x(t) = 12e-t; x(0) = 4, x'(0) = 2, x'(0) = 18

A: The solution is given as

Q: Answer Questions 8 & 10 please and thank you

A: Note: We are entitled to solve only one question at a time. So we are doing Question 8 only. Please…

Q: Q.Let g: [1,4] → R be continuous function. Define G(x) = g(t)dt. Then dx dG a. G(x) is…

A: Here given g:1, 4→ℝ be a continuous function. Also, define Gx=∫ax2g(t)dt

Q: By using the method of least squares, find the best line through the points: (2,-3), (-2,0), (1,-1).…

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Q: Find a set of parametric equations for the curve of intersection of the paraboloid x² + 4y² − z = 0…

A: To find the parametric equations for the intersection of given surfaces.

Q: QUESTION 19 The volume of the solid generated by revolving the region bounded by x2 = 4y method. The…

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Q: 3) Find the derivative f(z) = 100 a) f(z) = 400z(z²-1) (2²+1) 100 99 b) f(z)= c) f(z) = d) f(z) = e)…

A: As per the policy of bartleby the provisions is to solve only one question at a time

Q: For each of the given paths, verify Green's Theorem by showing t dA. Also, explain which integral is…

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Q: There are three numbers in geometric progression whose sum is 26. If the first is increased by 2,…

A: The arithmetic and geometric progressions are two important rule that terms of a sequence follow to…

Q: POSSIBLE -10-8-6-4-2 -X 8 10 -2 -4 -6 -8 10 Triangle LMN is reflected across the x-axis, then…

A: Direct calculation.

Q: Exercise 4. Show that the function f is not differentiable at (0,0) f(x, y) = x³ + y³

A: We have given that ,  fx , y = x3 + y33 Here , ∂f∂x = 3x23x3 + y323 ∂f∂x = x2x3 + y323 At , x , y =…

Q: - - 2y = 0, y(0) = a. Let I = (-1,1). Which statement below is NOT true? Consider the equation a (A)…

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Q: II. Consider the circle C₁: r= 1 and the roses C₂ : r = cos 20 and C3 r = 2 cos 20, each of which is…

A: Given,C1: r = 1 ,      C2 : r = cos2θand  C3 : r =2cos2θ

Q: A = {]-[²]} and A'= "={[_¹₁]-[i]}. If B=[32] is the matrix representation of linear operator Z: R² →…

A: We have to find the transition matrix and matrix representation of linear operator w.r.t. basis.

Q: A lady 1.65 meters tall walks towards a lamp post 2.65 meters high at a speed of 1.5 m/s. How fast…

A: Given: Height of lady=1.65 m Height of lamp post=2.65 m Speed of lady=1.5 m/s To find: Shadow of…

Q: Find the power series representation for f(x) = 2x (1-x²)² and then find its radius of convergence.

A: