27) Find the radius of a circle so that its area and circumference have the same value.

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A: We will form a differential equation and then solve it to get number of mice infected after a…

Q: r = 4 sin 0 r = 1+ sin 0 A Consider the polar curves (see figure above) r = 1+ sin 0 and r = 4 sin…

A: If f is continuous and non negative on the interval α≤θ≤β with 0<β−α≤2π. Then area of the region…

Q: Find the surface area of the plane ( 15x- 5z+20y=35) if it is in the first octant

A: Solution:-

Q: Write the simplex tableau, that should be used to: Maximize P = 5x1  + 2x2 subject to  x1+ 7x2 = 0…

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Q: Our aim is to check whether 179 is a prime number or a composite number. Which among the following…

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

A: The maximum rate if change of g occurs along gradient of g.

Q: Solve the system of differential equations Sx1' = 331x1 + 420x2 | x2' = – 264xı – 335x2 21(0) = 27,…

A: We can write the given system of differential equation in the matrix form as below:…

Q: (c) Find the characteristic polynomial PA(t) of the matrix A given below, and then the eigen- values…

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Q: The Taylor series for f(x) = e" at a = 4 is en (x – 4)". %3D n=0 Find the first few coefficients. Co…

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Q: Find the largest possible domain A, where all elements of A are non-negative and f: A → R, f(x) =…

A: Injective Function: A function f : X →Y is defined to be one-one (or injective), if the images of…

Q: Evaluate the surface integral ſſ, F · dS for the given vector field F and the oriented surface S. In…

A: Here we can use the Divergence theorem which states that if V is a solid inclosed by s surface S…

Q: Solve the system of differential equations x' = 16x + 36y y' = – 6x – 14y

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Q: H.W p.564/ use Trapezoidal method and Simpsons' rule to evaluate. dx 1) S V1+x2 n = 4 2) S dx n = 4…

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Q: The graph of the above f(t) is represented by: USE THE FOLLOWING INFORMATION TO ANSWER QUESTIONS 12,…

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Q: Determine whether the following series converges or diverges. (-1)"-1 Vn nput C for convergence and…

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Q: The integral X dx x² – 4 3

A: Solution

Q: Solve the system of differential equations - 5x + Oy y' = – 9x – 2y ly' x(0) = - 1, y(0) = 0 x(t) =…

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Q: By rewriting the summation of the power series E(n- 1)C„x" + E 2nC, x"-1 +E C,x+1 = 0, we obtain:

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Q: 25.2 Solve the following problem over the interval from x 0 to 1 using a step size of 0.25 where…

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Q: Sketch the region of integration and reverse the order the integration: S dy f(x,y)dx -1 - 3-2 y

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Q: 5. Write each symbolic statement as an English sentence. Use p, q, r, s, and t as defined below. p:…

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Q: (A) C =D (Simplify your answer. U your answer.)

A: We have to find the total daily cost C of producing x golf clubs.

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A:

Q: Question 3 equation x²y" + 3xy – 3y = 3x2 – 2x³. (a) Verify that yi x and y2 x3 are solutions of xy"…

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Q: In the right triangle ABC, AB = 2, BC = 4 and ED is a line parallel to AB. Find the angle a = angle…

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Q: For the differential equation (x – 4)y" + (x– 2)y' + 2y = 0, the singular points are: O None of them…

A: Here we use the basic definitions of singular point

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A:

Q: A stone is dropped from the top of a tower. it reached the ground in 2 s. what is the height of the…

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Q: X = 0 X + 0 Let g(x) = {sin Find all values of h for which g satisfy the following conditions on I =…

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Q: Using Sandwich Theorem, the sequence 2 1. an = 4 sin? 3 %3D n + 1 converges to 0 converges to 2…

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Q: If we use the method of undetermined coefficients, the particular solution of the following…

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Q: Solve y"+y = 0.

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Q: (п + 1)(2х + 1)" Σ (2n + 1)2" n=1 8

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Q: Find a generating curve on the xz-plane for the surface of revolution with equation x²+ y²+ z²= e2x

A: Solution: Given equation is x^2+y^2+z^2=e^(2x)

Q: Solve the following differential equation y'" +2y'+y= x-1 Select one: -2x + x-3 O a. YG.S= C,e+c2e'…

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Q: For the following exercises, match each function with one of the graphs pictured below D. E 14. f…

A: For the exponential function of the form: y=abx, b is called the growth/decay factor. If b>1,…

Q: 505. Two tangent lines at the endpoints of a given arc containing 120° are drawn, and a circle is…

A: Solution :-

Q: 2. Given these data | 1 | 3 6 DA 19 | 7 f(x) 3 99 291 Estimate using Newton's interpolating…

A: Newton's divided difference interpolation formula is:…

Q: Let U be the subspace of R5 deÖned by U =  (x1; x2; x3; x4; x5) 2 R5 : 2x1 = x2 and x3 = x5 : (a)…

A: Since R^5 is a finite dimensional (=5)inner product space so every subspace has orthogonal…

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Q: G is a set of all rational numbers except 1 and is defined by a*b = a + b + ab for all a, be G. In…

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Q: Inverse Trigonometric and Inverse Hyperbolic Functions of Complex Numbers Answer in polar form C =…

A: We will use the basic knowledge of complex-valued logarithm, trigonometric, and inverse…

Q: d the smallest distance from the point (0, c, 0) to the surface y = x² + z².

A: Lagranges Multiplier method is used

Q: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX Test if the following complex limit exists,…

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Q: (c) Find the natural domain in R of the function f (x) = V4 – x + Vx – 3 Express your answer as an…

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

A:

Q: Find the surface area of the plane ( 15x- 5z+20y=35) if it is in the first octant

A:

Q: 4e3t -2e-2t 5e If A(t) = %3D -5e3t dA find 4e-21 -4e' 7e3t dt -be-2t 5e ? ? ? ? ? ? ? ? ? II

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Q: Determine the general solution to the differential equation dy 2 e2 dr Vy n implicit form a

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Q: the Area that lies inside r=3+2 sin 0 out side r=2 is 24.315 O -24.187 O 23.957 O 24.187 O -23.957

A: Solution:-