What region in R° do each of the following equations represent? Explain your reason- ing. (a) x2 + y? = 49 (b) x² + y² = 49, z = 1 (c) r? + 2? < 49

Q: Q.2)(A) Find a formula for the area of the triangle in the xy-plane with vertices at A(0, 0), B(a1,…

A:

Q: 2. f(2y+3)y+2 dy

A: Since we only answer 1 question. Please submit a new question specifying the one you’d like answered

Q: Using Ralston's Method, calculate ys for the following: y xy² = 0, y (0) = 1, - h = 0.1

A:

Q: C3x -y sin xy) de - x sin sy dy o HSin

A:

Q: y(6) – 4y(5) +3y/9) =-27 %3D

A:

Q: 6) The insulation resistance of the cable with length F in ohm and a radial thickness (r2 -r1) is…

A:

Q: The length of the curve y= is equal to x =3: from to 을(x2 + 2) O a. 12 Ob. 1 O c.9 Od. 3

A: We can use the application of integration in order to solve the given problem.

Q: Calculate the value of x in the figure: AB = BC = DA and BD = DC (Not drawn to scale). %3D %3D 21 2x…

A:

Q: 1. Find the total length of the curve r = 4(1 - sin 0) from 0 = 90° to 8 = 270° and also the total…

A: The given problem is to find the total length and the perimeter of the given curve. Given curve…

Q: Q4) The standard formula for the tangent of the sum of two angles is tan x + tan y tan(x +y) 1- tan…

A:

Q: An engineer takes a large number of independent measurements of the length of a component and…

A:

Q: Use the Newton-Raphson method to obtain successive approximations of v2 as the ratio of two…

A: Newton's Raphson method

Q: Use the method of undetermined coefficients to find the solution to y''+y=4x+10sin(x) that is…

A: Method of undetermined co-efficient: For given a non- homogeneous ODE of the form…

Q: Find Df and Duf to:- XZ on the point (,,1) inthe direction of V = 2i -3j+6 K. %3D soLiin ansi- lo

A: Directional derivative of the function.

Q: 2 b.f V1 + x³ dx

A: The given integral is√(1+x3) limit from 1 to 2.

Q: The Composite Trapezoidal Rule applied to the itegral I = gives the error E = 12 Suppose 2+2r -e…

A: The double derivative test is used to optimize (maximize or minimize) a function. Follow the steps…

Q: 4,y² – 25 3. dy 4. V21+4z-z? dz

A:

Q: A point on a rolling circle of radius traces out a cycloid, which can be parameterized by c(t) = (Rt…

A: We have to show  that the length of this arch is always four times the diameter of the rolling…

Q: The position of a particle is given by x(t) = (t – 1)³(2t – 3). At what value(s) of t is the…

A: Given, The position of particle  xt =t-132t-3  We have to find the values of t for which particle at…

Q: +y²)dx + (x² – y²)dy where C is the triangle with vertices (0,0), (2,1) and (0,1).

A:

Q: Evaluate the approximate value of f (2æ² + 2) dæ at n = 3. Solve also for TV and percentage of…

A:

Q: Find the length of the spiral r = eθ/√2 from θ = 0 to θ = π.

A: Given Differentiating r with respect to thita ,we get

Q: Q3) find the soluation of differention equation 1) 2y' = y cot(x)

A: To find the solution of the differential equation 2y'=y cot(x) Formulae used : ∫dxx=ln |x|∫cot(x)=ln…

Q: (1) Using the second order Runge-Kutta method (Modified Euler's method), plot the solution of the…

A: Given equation is y'=10y-y2 , 0≤t≤5 With initial condition y0=0.5 Given step size is h=0.01…

Q: 3. The distance between two distinct points (x1, y1) and (x2, y2) is given by the formula

A: Given: Points x1, y1 and x2, y2

Q: B Fig 1 1 y = (3x)3 A I. Find the co-ordinates of A and B X II. Find the area enclosed by the curves…

A: Please see the below picture for detailed solution.

Q: dx Evaluate LJv by using Trapezoidal rule (up to three 1 + x? decimal places). [Ch-4(B), Expl-2]

A: We have to evaluate ∫01 dx1+x2 by using Trapezoidal rule.

Q: 2) Find the length of the spiral: r = 0² from 0 = 0 to 0 = V5?

A:

Q: To find the points on the cone z? = x² + y² that are closest to the point (5,2,0) , we need to solve…

A: Given  z2=x2+y2 let the P (5,2,0) and P (x,y,z) so, d = x-52+y-22+z-02 d=x-52+y-22+z2d=…

Q: Determine the largest interval in which the unique solution of (t-3)y +tant y = t, y(7)3D0 is…

A: The given differential equation is: (t-3)y'+ (tan t) y=t ;      y(π)=0

Q: 3. Find the area in the first quadrant by the curves x? + y? = 9 and 4x² + 9y? = 36 on the first %3D…

A:

Q: (1) Using the second order Runge-Kutta method (Modified Euler's method), plot the solution of the…

A: y'=10(y-y2)    0≤t≤5,     h=0.01,     y(0)=0.5 y1p=y0+hf0 f0=F(t0,y0) t=0, y0=0.5 f(x,y)=10(y-y2)…

Q: 4. In the given circle 0, OC 1 AB. If AD = (4x + 9) cm and (Sx+2) cm. What is AB? BD = Solution and…

A: Topic:- circle peroprties

Q: C Reduction OF Crder and Variation OF Parame te 1. : tan 2x

A:

Q: /| 9(x + y) dA where R is the region that lies to the left of the y-axis between the circles x2 + y?…

A:

Q: a) Consider the IVP y" + y = sin nt + et – 6t³ , y(0) = 1, y'(0) = 2, y"(0) = 3 Find the image of…

A:

Q: SS, xy dA {(r,0)|0 <r<1, | and the region in the first quadrant }

A:

Q: Find the folution of di fteven tial equation Ufing the variation of parame terg method y - Ily' =…

A: We are given the following differential equation.      y'''-11y'=sec t,  -π2&lt;t&lt;π2 As per the…

Q: What are the coordinate points of triangle J'K'L' using the scale factor of 2 and (0,0) as the…

A: Given,  Scale factor=2 Centre of dilation= (0,0). From the graph we can get the coordinates of…

Q: Find the area of the region inside the circle r= 32 cos 0 and to the right of the vertical line r= 8…

A:

Q: y (+zy'+y= ctDsint %3D

A: Given an ordinary non- homogenous differential equation : y(4)+2y'+y=(t+1)sint We need to find the…

Q: The area of the region inside the circle r = 6 cos 0 and outside the cardioid r = 2(1 + cos), a > 0…

A: Given: the circle r =6 cos θ and the cardioid r=2(1+cosθ )

Q: What is the general solution of ydx (* + Vy? - t²) dy %3D = cy arcsin In y = C %3D O arctan In y = C…

A: Convert this equation into the homogeneous differential equation.

Q: Use the method of Variation of Parameters to solve the following DE: у" — у %3D2х2 —х— 3.

A:

Q: Solve the variational problem 8 Ix (y ? +2y (x+y)] dx = 0, given y (1) = y (2) = 0. %3D

A:

Q: 8. Use variation of parameters. а. (D? — 1)у %3D ех + 1 Show Complete Solution Answers: a. y = c,e*…

A:

Q: By expanding (x – h)² + (y – k)² = r², we obtain x² – 2hx + h? + y² – 2ky + k² – r² = 0. When we…

A: