Please solve this question and sketch the region. Thank you!

Q: f(t)=e³¹; b) f(t) = cos(at); c)

A: We know  ℒeat=1s-aℒcosat=ss2+a2ℒtn=n!sn+1

Q: Using mathematical induction, show that for positive integers greater than 1, 2+6+10+…+(4n-2)=2n^2

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Q: O-16 0-9 -15 Select the values that make the inequality b-8 true. (Numbers written in order from…

A: Given: The given number line is shown below. To find: We have to select the values that make the…

Q: The values of C₁and C₂ so that y(x) = C₁ sin x + C₂ cos x satisfies the following conditions; y(0) =…

A: Here we have to find the value of c1 and c2 using given conditions.

Q: 32 ft2 16, 36, 48 48 ft2 4.8.12 96 ft2 32, 48, 96 24, 32, 48 32 ft2 Which values represent the…

A: Notice that the surface of 32 square centimeters is formed by 8 times 4, which gives 28 square…

Q: Obtain the particular solution satisfying the initial conditions indicated. 2. (t²-x)dt-tdx = 0;…

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Q: ind the volume of the tetrahedron shown using the order dz dx dy. The tetrahedron is bounded by the…

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Q: Prove that the group of complex numbers under addition is isomorphicto R ⨁ R.

A: To prove: The group of complex numbers under addition is isomorphic to ℝ ⊕ ℝ.

Q: Sketch the vector field in the xy-plane. 7(7) = -7/11711³ O O y y X X O O y y X X

A: F→r→=-r→r→3

Q: Find The volume of the solid bounded by The Paraboloid X=-4+ 2x² + 2y² and Z= 7-3x²-3y²

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Q: what is the solution of the given integro differential equation (with use of laplace transform and…

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Q: What is the equation of the tangent to the curve y = 3x³ 15 at x = 2? A. 81x-y +153=0 153=0 B.…

A: Ans-To find the equation of the tangent to the curve y = 3x3 - 15 at x = 2, we need to find the…

Q: Let 71, 72, 73, 74, 75, 76 be six planes in three-dimensional projective space such that each of the…

A: Given: π1, π2, π3, π4, π5, π6 are six planes in three-dimensional projective space such that π1, π2,…

Q: Prove: if Σ1 fn is convergent on D, then limn→∞ fn(x) = 0 for each x = D. n=1

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Q: Find the smallest number of terms of the series Σ (-1)² = 3/ k k = 1 we need to add in order to…

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Q: 1. Given the first derivative of a Conference function is h'(t) = -8t + t2 - 9, where t represents…

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Q: In an Excel file, show the approximation of the indicated value using the Improved Euler's and Runge…

A: Ans-In this question we have to the approximation of the indicated value using the ImprovedEuler's…

Q: Determine if S = {(1, 3, 0),(2, 4, 1),(-1, 1, 5)) is a basis of R³.

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Q: (b) ||ū× w|| (u • w) (c) (d) (r+s) ux v + w s(v+w• w) × (rv)

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Q: Let g(x)= x³ - 4x² + 2x - 4 and f(x) = x + 2 be polynomials in Q[r]. so that g(x) = f(x)q(x) +r(x).

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Q: What is the equation of the asymptote for the function f(x) = 0.5(4*-2). + 3? C. x=3 d. y = 4 4. a.…

A: The given problem is to find the equation of asymptote for the given function f(x). Given function…

Q: 1. a. 37 b. 38 For the given triangle, use one of the reciprocal ratios to determine to the nearest…

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Q: What is the general solution to the equation? 2 sin² x + 5 sin x-3=0 Drag solutions to the box to…

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Q: 7. Alice is riding a Ferris wheel, where t is time in seconds. Suppose the Ferris wheel is 22 m…

A: Given: Function ht=11 cos12t.To find: The lowest height achieved relative to the centre of the…

Q: ons athematical induction to prove the following. that for all positive integer n

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Q: 3) ]We looked at quadratic/quadratic rational functions that had a 'hole' or 'gap' discontinuity.…

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Q: 1. a. √8 b. 6 8 Which of the following is equivalent to the expression 86? C. d. 1 8⁰ (-8)°

A: We have to equivalent to the expression 8-6.

Q: Let T: R^3 --> R^3 be the linear transformation represented by the matrix in the image. (a) Let…

A: M=-4372-1-321-1

Q: Expand f(x) = 0 if 0 < x < 1 if 2 in a half-range: (a) Sine series. (b) Cosine series. KIN 2 < < x…

A: Given: fx=0if 0&lt;x&lt;π21if π2&lt;x&lt;π We have to find the half range sine and cosine series.

Q: ) The area A of a circle of diameter d is given for the following values: d (Diameter) 80 85 90 95 A…

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Q: 2.6-2. Given the difference equation (* + 2) - (* + 1) + 3(k) = e(k) where y(0) = y(1) = 0, e(0) =…

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Q: The following differential equation y" (x) + 2 x y(x) - sin (xy) = 0 is a partial differential…

A: Ans- False. The given differential equation is not a partial differential equation, but rather a…

Q: A bus driver planned a 2 day trip. He travelled 360 km at a certain speed on the first day. He…

A: Let the speed on the first day be  X  km/hour. He travelled 360 km on the first day. So, travelling…

Q: Problem #4: Let v₁ = (4, 1, 0, -1), v2 = (0, 1, 4, 1), and b = (1, 3,-1,-6). Let W be the subspace…

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Q: Which one of the following is equal to Scot (™) do? 2 ○ 2/4 sec² \sin (12) ○ 2) | + c 2 In sin (18)…

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Q: Find the Laplace transform Y(s) = L{y} of the solution of the given initial value problem. y" + gy…

A: Given:  y''+9y=1, 0≤t&lt;π0, π≤t&lt;∞, y0=9, y'0=5 We have to find Ys.

Q: factor x as a product of three linear polynomials in Z/30Z[x] by using Chinese remainder theorem

A: Ans- To factor x as a product of three linear polynomials in Z/30Z[x], we first need to factor 30…

Q: 5. Consider the following linear programming problem: Maximize: P=12x₁ +10x₂ subject to: 5x₁ +3x₂…

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Q: The solution of the non-exact differential equation (3xy - y²) dx + x(x − y) dy = 0 is: O O O None…

A: The given differential equation is           (3xy - y2)dx + x(x - y)dy = 0     =&gt; dy/dx = (y2 -…

Q: Find the inverse Laplace transform L-¹{F(s)} of the given function. 8s² 49s + 294 s(s² +49) Your…

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Q: The following differential equationx 2 (4x)² False - 2)² +2. = 0 is of order 3. dy dx True

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Q: kercises 9 and 10, find the change-of-coordi dard basis in R". · ®= {[ ²], [!]} 2

A: The change of coordinate matrix from basis B={b1,b2,....,bn} to the standard basis in ℝn is PB=b1,…

Q: For each subspace in Exercises 1-8, (a) find a basis, and (b) state the dimension. S 2t {} s + t :…

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Q: In Exercises 5-8, find the coordinate vector [x] of x relative to the given basis B = {b₁,..., bn}.…

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Q: If   C(t)=53.2te−0.21t measures the​ concentration, in ngml​, of a drug in a​ person's system t…

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Q: Change of Basis 4 H -3 an eigenvector of A = 2. Is 3 HE 2 79 -4 -5 1? If so, find the eigenvalue. 44

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Q: Q1. Determine the solution of the given problems: (CLO_4): (Cognitive Level C5, i.e., Evaluating)…

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Q: For each n 2, let an S= 4 n=2 an+1 an anan+1 2n³n 9n²6n-4 -sin (). Evaluate the following series:…

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Q: {( º ) | a,b,c € z}. (a) Show a 0 b c that L is a subring of M₂(Z). (b) Show that the map f: L→ Z…

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Q: consider an invertible matrix A and indicate which of the following statements is true: A. The…

A: A is an invertible matrix.