- Evaluate the given integral Q.

Q: d² +4 + dt² dy - 6y = −12 ; y (0) = 1 dt y (0) = 4, y" (0) = -2

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Q: The center of curvature C (h,k) is at A (2, 1) (B) (3, 0) © (4, -1) (5,-2) (D)

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Q: (e) In an inductive proof that for every positive integer n, n(n+1)(2n+1) = -1 what must be proven…

A: This is the problem of Mathematical Induction.

Q: * When a cold drink is taken from a refrigerator, its temperature is 4 degrees Celsius. After 20…

A: Please see the attachment

Q: Problem Four: In a dental clinic with one dentist, the average number of patients from time to time…

A: Solution

Q: State the principal of inclusion and exclusion. When is this used? Provide an example. 1. State the…

A: Solution

Q: Solve the following system of equations by Newton-Raphson method y-sin(x+y)=0 x-cos(y-x)=0

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Q: (13): p²+q²-2px-2qy+2xy=0

A: Q(13) Given the partial differential equation   p2+q2-2px-2qx+2xy=0 To solve it using Charpit's…

Q: c) Consider the third-order truncation error (0 (Ax )³) with the step size Ax and also (-Ax ) then,…

A: Both approximation is second order O((∆x)^2)

Q: sin(²) En=1 is 18 √n a. 1 b. 12/12 c. Converge d. Diverge d O C O a O b O

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Q: 3. The sum of the lengths of the two diagonals of a parallelogram is 18 m. One diagonal is 2 meters…

A: Solution : Let the diagonals of parallelogram are d1,d2. and d1<d2 given, d1+d2=18d1-d2=-2…

Q: Solve the system of differential equations. X1' = 6x1 + 2x2 = - 2x1 - 10x2 x1 (0) = 2, x₂(0) = 22 x₁…

A: Solution

Q: 1. Evaluate the given integral Q. (y - 2x) dA, R where R is the region bounded by ax = 0, y = x, x =…

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Q: 4. f(x)= 3x5 + 5x³

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Q: A topological space is Hausdorff iff limits of all nets in it are unique

A: This is a problem of Topology.

Q: Find the root of the equation x-x-10=0 using chebyshev method.

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Q: Find the directional derivative of f (x, y, z) = 2z²x + y³ at the point (2, 2, 1) in the direction…

A: The solution is given as

Q: Solve the following linear equations 2x, +8x₂+2x₂ = 14 6x, +6x₂-x₂ = 13 2x₁ + x₂ + 2x, =S using…

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Q: 9. E is the binary relation defined on Z as follows: For all m, n E Z, m Enm-n is even. Is this an…

A: This question is from topic relation of real analysis

Q: Construct the truth table for the following 1. p V q 2. р А -q 3. (p A q) V ¬(p V q)

A: Since you have posted a multi subparts question according to guildlines I will solve first three…

Q: 2. Write the equations of functions satisfying the given properties, in expanded form. a. Cubic…

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Q: Qu Evorate & 6 f Z+1 Z4-273 C:/Z-i/=3 ₂d², C₁/2-11 = 2 (2241)³

A: Solution:-

Q: for 0≤t≤2, 3 fort≥2 f(t) = {1-3

A: To find the laplace transform of given f(t) we will use the definition of laplace transform and then…

Q: Find a real solution of the equations x²-5x+4=0 3xy²-10y+7=0 nitial approximation as (0.5, 0.5).

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Q: Find the matrix A, so that the following equality is satisfied. 4+ [28]-[83] A -4 1

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Q: 9. E is the binary relation defined on Z as follows: For all m, n E Z, m Enm-n is even. Is this an…

A: Equivalence relation

Q: d²x dt.² +2 d'y (1² - y = = cos 21. 2 da 9=0

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Q: in a graph What is vertex coloring and upper bounds ? And give examples

A: To find what is vertex coloring and upper bound .

Q: A roast turkey is taken from an oven when its temperature has reached 190 degrees Fahrenheit and is…

A: This is the problem of the Application of the Calculus.

Q: 1. A railway truck of mass 300 kg is travelling at a speed of 7 m/s, It collides with a second…

A: Solution :-

Q: P21. The y-axis and the line x = c are the banks of a river whose current has uniform speed a in the…

A:

Q: 9. E is the binary relation defined on Z as follows: For all m, n E Z, mEnm-n is even. Is this an…

A: Here, E is an equivalence relation on Z. To show this,  we will show that E is reflexive relation,…

Q: b) Consider the following metric: ds² = e²A(r) dt² - e²B(r) dr² — r² (d0² + sin² 0do²), with A(r)…

A: Solution :Consider the following 4D-curved spacetime metric.ds2 =…

Q: A bacteria culture is known to grow at a rate proportional to the amount present. After two hours,…

A: Let dx/dt = the rate of growth of the bacteria  Let t = time (in hours) after start of culture  Let…

Q: 3. a) Describe the translations applied to the graph of y=x² to obtain a graph of the quadratic…

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Q: hello, I appreciate your answer but the answer looks funny it is difficult to understand. Would you…

A: Solution

Q: 4) y=3x-2 x+y=6 X+

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Q: 5. Find the general solutions of 56x + 72y = 40. 2020

A: This is a linear diophantine equation. We first find a solution via hand and then give the general…

Q: (c) Two of these functions preserve orientation. Which are they? Select exactly two options. If you…

A: Follow the steps.

Q: 1. function f from {a, b, c, d] to itself, where f(a) = d, f(b) = b, f(c) = a, f(d) = c 2. f: ZxZ→…

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Q: Find the centre of mass of the 2D shape bounded by the lines y = +1.1x between x = 0 to 3.1. Assume…

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Q: Find integration + dx Cos (x-1)

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Q: Let f (u, v) = (tan(u - 1) - eº, 7u² − 6v²) and g (x, y) = (e8(x−y), 8 (x − y)). Calculate f. g. - -…

A: Given,      f(u, v)=tan(u-1)-ev, 7u2-6v2, and g(x, y)=e8(x-y), 8(x-y)

Q: 1 use that transformations e Jaco Je √y=0 p√x=0 %cty octy=u dy dx = e = 1 2 and your to prove

A: given transformations x+y=u and y=uv To Prove:-∫x=01∫y=01-xeyx+ydydx = 12(e-1)

Q: Determine if the following arguments are Valid or Invalid. Using Rules of Inference. 26. All…

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Q: Determine angles a, banda...

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Q: in a graph What is color-critical or k-critical? And give an examples

A: What is color critical or k-critical .

Q: Use Newton’s Divided Difference Formula to interpolate f (1), if the polynomial has given points…

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Q: * A pan of warm water (47°C) was put into a refrigerator. Nine minutes later, the water's…

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Q: The y-axis and the line x = c are the banks of a river whose current has uniform speed a in the…

A: