Determine all prime numbers a, b and c for which the expression a² + b² + c² – 1 is a perfect square.

Q: The following table presents the implementation of Dijkstra's algorithm on the evaluated graph G…

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Q: 2.(a) Solve the following system of linear first-order differential equation (2D – 5)x + Dy = e' %3D…

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Q: Construct your own problem involving related rates.

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Q: Find the area of the interior of the four-petaled rose r=sin(2θ)

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Q: II. Find the determinant of the following matrices by row reduction: [1 1 1 11 a 1 1 11 1 3 3 3 3 1…

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Q: QU 5 a). A drug in the blood stream decays by according to the equation y'=ky, where y is the…

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Q: Using the Method of Undetermined Coefficients, determine the form of a particular solution for the…

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Q: Identify any extrema of the function by recognizing its given form or its form after completing the…

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

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Q: 1. Let l: R2 → R³, l : x+ Ax, where k k %3D 2k –1 9 a.) Establish for which value of k, the linear…

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Q: Show that the equation + 2x + (1– y²) - dx2 dx²y dy² is elliptic for values of x and in the region x…

A: Here we use B^2 -4AC to find this.

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: 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: 5. f(t)=-3t*e05t +3.8t²e24*

A: Note: according to our guidelines we can answer only 5th question  5)

Q: Study the patterns of numbers in each row of the table below. Each row relates to one of the figures…

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Q: Find the series radius and interval of convergence, then identify the value of x for (-1)" (2n- 2)!…

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Q: Solve the tollowing problems. 2. 2x°cos 5y+ x tan5y dy=0

A: Introduction: Separation of variables (also known as the Fourier method) is one of several methods…

Q: Performs the following operations on the indicated system b) F1 9.516 + B98.516 =

A: F19.516+B98.516=1AB1.A16

Q: Calculate sin(5) and cos(-270°). Include a sketch of each angle.

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Q: The rectangle M, lies in the (x, y) plane in the (x, y, z) space, and is given by: M1 =…

A: Parametric equation of line passing through  (0, 1) and (2,0) x(t) = 0 + t( 2-0)= 2t y(t) = 1…

Q: Q5) Find the integration by using (by part method): Se3x sin X dX

A: We can solve this using part method

Q: QUESTION 1 Consider the following LP model and its optimal solution: Maximize: z= 2X1 +3X2 + 4X3…

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Q: Solve using the differential operator D=d/dx. Use Method of Variation of Parameter [D2 - 8D + 16] y…

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Q: c). i. Find the general solution to this homogeneous equation using the auxiliary equation method…

A: Given: y''-2y'+10y=0

Q: Solve the initial value problem. dy =x*(y-2), y(0) = 9 dx The solution is (Type an implicit…

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Q: dy Given a differential equation dx -4 Q1 with the initial condition, y = 2. 8 y' cos (2.x) (а)…

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Q: QU 3 a). A drug in the blood stream decays by according to the equation y'= Cy, where y is the…

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Q: Vz - 2 limz→4 Z - 4

A: To find: limz→4z-2z-4.

Q: Con vert the first three terms of the Mac laqurin Ser ies e xpapsions for Ln(l+) into legendre…

A: Introduction: Legendre polynomials are a system of complete and orthogonal polynomials with numerous…

Q: T/2 S [costi-sit cos ti – sin 2tj +sin? tk |dt.

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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: 4. Find the temperature in a perfectly insulted bar with c=1, u,(0,t) =u,(T,t)=0 and u(x,0) = 3x

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

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Q: Which of the following is a general solution to the followin x²y"+xy'+ (x²– 1)y=0 y=c,(x) +cY_,(x) O…

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Q: d'r =-32k, fferential equation: dt2 dr = 8i +8 j, r(0)=100k. dt %3D tial conditions: It=0

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Q: Convert using a shortcut: 11100011011two to base ten.

A: 11100011011two= (1×210+1×29+1×28+0×27+0×26+0×25+ 1×24+1×23+0×22+1×21+1×20)ten…

Q: TOPOLOGY OF CompLEX KumBERI S. Find apara metri z0ton 9 cur ve thoat portion the 13 of the circle…

A: To parametrize the curve z=1, that joins 1 to i. (i) In a counterclockwise direction. (ii) In a…

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Q: Show by means of an algebraic proof that (A − B) ∪ (B − A) = (A ∪ B) − (A ∩ B).

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Q: (xdx ydy + zdz)2z {(z²x²y²) (xdx + ydy + zdz) dz + %3D

A: Differential equation

Q: Solve (yz + хуz) dx + (zx + хуz) dy + (ху + хуz) dz =

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Q: Problem 1A. Solve the system of linear equations using Gaussian Elimination. -71[X1 11 ||X2 X3 X4.…

A: According to our guidelines we are supposed to answer only one asked question.kindly repost other…

Q: Evaluate the following integrals. (a) / (csc0)(1+ sin² 0 + sin 0 cot² 0) d0 (b) / dr V-2r2+1 2 -49…

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Q: Find the direction in which f(x,y) = x²e-2y increases and decreases most rapidly at Po(1,0) and find…

A: Consider the given function, fx,y=x2e-2y Here we need to find the direction in which the function…

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

A: Since you have posted multiparts question and we can answer three subparts. So,  answered the first…

Q: Let C'be the curve represented by the equations x=t, y=3t^2, z=6t^3, where te[0,1]. Evaluate the…

A: Given that the curve C has the equations as,  x=t, y=3t2, z=6t3  where t∈0,1 To evaluate the line…

Q: 1 L(5x)sin dx dx+ J, (5x – 15)sin| 1.5 1.5 1.5

A: We will use integration by parts here  ∫u.v dx=u∫v dx -∫dudx∫v dxdx

Q: In 1980 the population of aligators in a particular region was esi mated to be 1600. In 2008 the…

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Q: Graph and determine the domain and range.show your solution .make a table of values from -5 to 5...…

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Q: FOrthe find all epuiGbicem solitious ond closify tiem lf possifle)

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