Solve %| 1+9x² ) dy + x³y² = 0 .

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Q: Question 2. (7 Points: 3+2+2) (a) Prove that if a and y are rational numbers then x+y is rational.…

A: (a) To prove: If x and y are rational then x+y is also rational. (b) To prove: If x is irrational…

Q: Final Answer for a1,a2,and az a, =S° - -1dx +- " 1dx = ? 2n-T 2n (1)()(x) 1 | 1 cos- (1)(1)(x) a1 -1…

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Q: Use the Euler, improved Euler and Runge-kutta methods to solve the following ODES: y co) = し h=o.2…

A: Given the ODE y'+5x4y2=0 and  y0=1⇒x0=0, y0=1   Step size h=0.2 Solve using Euler's Method at a…

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Q: d'y dy Consider the second-order equation +p + qy = 0, where p and q are positive. dt 5. %3D dt2 (a)…

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Q: 3. The square is dilated under the dilation (x, y) → (0.25x, 0.25y). 4 2- -2 2 -2 a. Graph the…

A: Dilation: It is a type of transformation in which the size of an image in a coordinate plane changes…

Q: Does there exist an 8 x 8 matrix A = (as) satisfying the ? hen aj = 0 (a1s denotes the entry in the…

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Q: 6. "Find the mserse Laplaie fnanform 10 11 25+3 12

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Q: Q5: Suppose B is real. Show that le2ßt - 1|< 27|B| , 2 πβί

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Q: Which of the following is a subspace of R? O A. All vectors of the form (a, 0, 0). B. All vectors of…

A: To choose correct option we will use the following theorem Theorem: A non-empty subset W of a vector…

Q: The system in Section 3.2 - Exercise 3 (previous page): dy dr 5x + 4y dt 9x dt

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: II. Consider the function g defined by 1 g(x, y) = sin (7 /æy) + log3 (r – 3y) Do as indicated. 1.…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: Show, using truth tables, that (a) ¬(p V q) A r = -p^ (¬q ^ r), (b) -4 v (q V p) is a tautology.

A: (a) To show ¬p∨q∧r≡¬p∧¬q∧r using Truth tables. (b) To show ¬q∨q∨p is a tautology using Truth tables.

Q: Consider the function g defined by g (x, y) = sin (n V xy) + logs (x- 3y). Do as indicated. 1.…

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Q: a+14 if a 8 Analyze the function f (x) Your classmates may be analyzing different functions, so in…

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Q: QULSTION O s-3 F(s) = is The inverse Laplace Transform of O f() = sin 3t– 3 cos 3t O f() = /3 sin…

A: Since  you have posted a multi  questions according to guildlines I will solve first question(Q8)…

Q: tind the remainder when 53751 is divided by 11

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: (a) Evaluate the integral (cosx+ (b) Find the total area between the region and x-axis…

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Q: dw dw and + Arc tan z. Get the partial derivatives given that w = dx' dy dz

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Q: 22 Suffosethent fco)-cosg()-e unedicalafforonimatson fncb f60-8),9G0) fox the Values ofhas…

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Q: Consider the following integral. e" du (5 – e“)² Find a substitution to rewrite the integrand as -z…

A: We have to find a substitution to rewrite the integrand as -1x2dx Then, we can proceed further.

Q: In order to evaluate the diagnostic accuracy of a new rapid test for COVID-19, results of the…

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Q: 1. Evaluate the following integrals. · | (csc 0)(1+ sin² 0 + sin 0 cot? 0) d0 а.

A: Properties of integration ∫sinθ dθ=-cosθ+C∫cosecθ dθ=-ln|cosecθ+cotθ|+C∫cosec2θ dθ=-cotθ+C

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Q: Find the equation for the plane through the points Po(5, - 4, - 4), Qo(2,0. – 2), and Ro(4,1, – 2).…

A: Introduction: A plane is a three dimensional geometrical structure. When there is a projection of a…

Q: (a) Evaluate the integral using integration by parts rule if x' cos' 2x dx (b) Express the…

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Q: Which of the following is true? 0. 1 0 O A. is a basis for M22. O B. is a basis for M22. 1 0. 0. 0.…

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Q: Construct a graph from this map where the vertices are the cities and are connected by an edge if…

A: Given the map of some cities. To construct a graph where the cities are represented by vertices and…

Q: L(sin² at)

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Q: 3. If the radius of the circle were 2, would that change the value of the sin, cos, tangent for each…

A: Let us write the reasons of the circle based problem in the next step.

Q: 1 3-2s Find the inverse Laplace of Y (s) = + s²+49 3-4s teit + sin 7t – 2 cos 7t -jeit + sin 7t – 2…

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Q: Consider the following optimisation problem max f(r, y) = t/r y, subject to tx? + y 0, y > 0. a)…

A: Given: max fx,y=txysubject to x2+ty≤5x≥0,y≥0 To find: a) t=1 b) Envelope theorem c) Marginal effect…

Q: " + 8y' + 25y = 13e-2t y(0) = -1, y' (0) = 18 %3D

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Q: Consider f(x) = cos (x) In(x + 2). a. Find the local linear approximation of f(x) at xo = 0. (In 2…

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Q: II. Consider the function g defined by g(x, y) 3 = cos (Tx /y) + х — у Do as indicated. 1. Determine…

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Q: Kt<7

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Q: Find the Taylor series, centered at c = 3, for the function 1 f(x) : 1- 22 f(x) = E The interval of…

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Q: Let f(x) be defined on [0, 1] such that f(x) = min |x- n=D0, 1, 2,.... Find the area under fx)

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Q: 9. Find the radius of convergence, R, of the series. Find the interval of convergence of the series.…

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Q: іa + (2 — i)234- 3і (1+ i)x – x2 = -3 – i |

A: The solution is given as

Q: Problem Five: Dorian makes luxury cars and jeeps for high-income men and women. It wishes to…

A: We need to form a lineat programming and solve it by using graphical method to get minimum cost

Q: ) Let S be the subspace of Rº given by S = Span Find a basis for S4.

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Q: Hint: Use method of undetermined coefficient Solve using the differential operator D=d/dx y" - 2y' +…

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Q: Rotate the region bounded by y= x- 2x + 4 and y X+14 about the X- axis

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Q: 1) Consider the function defned by fCX,y) - y-ex (a) Find the domain and ran ge of f. (b) Draw a…

A: The given function is f(x,y)=y-ex. (a) To find: Domain and Range of f. (b) To sketch: contour map of…