1. Double Integrals in Polar Coordinates a) Find the area of one petal of the rose r = cos 30 b) Find the area enclosed by the curve r = 4 + 3 cos 0 c) Find the area between the two circles r = cos 0 and r = sin 0

Q: (a) y" + 4y = t² + 3et, (b) y" - 2y + y = tet +4, (c) y" - 2y + y = 3te²t, y(0) = 1, (d) y" + 4y = 3…

A: Method of undetermined coefficient is used

Q: 6. Prove that if M E Mnxn (F) can be written in the form A = - (68). where A and C are square…

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Q: Suppose that the sequence x0, x1, x2... is defined by xo=4, x₁ = 6, and xk+2 = 4xk for k20. Find a…

A: Given Data: Let us consider the given data, xk+2 =4xk which can be written as, xk+2 -4xk=0with x0=4…

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Q: 1. Fit the data P1 = (-5, 3), P2 = (-4, 2), P3 = (-2, 7), P4 = (0, 0), P5 = (1, 5), P6= (3, 3), P7 =…

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Q: 3. (LT-1) Use the Laplace transform to find the solution to the following initial value problem: y"…

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Q: (2) (A) Let R be a ring with the property that r² = r for all r € R. Show that (i) if a € R, then a…

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Q: 2. (LI-2) Consider the equation r2y" - xy + y = 0. It is given that y₁ = z is one solution to this…

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Q: 2. Given the linear system of equations; X₁+2, X2 -2x₁ +x₂ 3x₂ -X₂ +2x4+x=6 a) Is the system under…

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Q: A solid E lies within the cylinder x2 + y2 = 9, below the plane z = 21, and above the paraboloid z =…

A: The solid E lies within the cylinder x2+y2=9 and the plane z=21, and above the paraboloid z=9-x2-y2.…

Q: 1) The diagram below shows part of the graph with equation y = x² + px +q. The graph cuts the x-axis…

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Q: Find the short test distanse between the two curves y = Sinx ² where the interset and x² + y² Point…

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Q: Evaluate the surface integral. (x² + y² + 2²) ds, S is the part of the cylinder x² + y² = 16 between…

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Q: Let f(x) = xe". (a) Apply the composite trapezoid rule with m = 6 to approximate comparing with the…

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Q: Prove the following formula for all integers n 21: 1/2+2 3+1 4+... 2.3 + n.(n+1) || n n+1

A: We need to show that for all integers n≥1, 11·2+12·3+13·4+......+1nn+1=nn+1 We will use principle of…

Q: Question 9) Find / = $z C = 2z -√2 z² +0.25i dz, where C⇒ |z+i| = 1,

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Q: Let N be a natural number with N> 10. We have π(N)

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Q: Write down the 3 by 3 matrix that has aij = 2i - 3j. This matrix has a32 = 0, but elimination still…

A: Given,               aij=2i-3j, and a32=0.

Q: Use the formula for the sum of a geometric sequence to write the following sum in closed form. + 8k,…

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Q: A water tank has the shape of an inverted circular cone with top radius 3m and height 5m. If water…

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Q: Total Coronavirus Cases in the United States Int logarithmic Total Coronavirus Cases 1500 1250 1000…

A: The exponential functions can be represented using the equation: y=abx. Here, a, b are constants and…

Q: Find the short test distanse between the two curves y = Sinx ² where the interset the oregen and x²…

A: Let us consider that the two curves are given by:…

Q: ht) Use a graph below of f(x) = In(8x² + 1) to estimate the x-values of any critical points and…

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Q: Prove the following statement using mathematical induction. Do not derive it from Theorem 5.2.1 or…

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Q: -. If X is a random variable such that E[X] = µ and P(X ≤ 0) = 0, show that 2 P(X> 21/(H) = 3²/34 3…

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Q: (g) 1302 3440 2 -2 3 2 1 -3 1 1 4 -1 3 0 (h) 1 -2 3 -12) -5 12 -14 19 -9 22 -20 31 -4 9 -14 15

A: We know that determinant of diagonal matrix, upper triangular matrix, lower triangular matrix is the…

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Q: Explain how to simplify a rational expression and how to find the domain of a rational function.…

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Q: 2. Solve the IVP u"(t) = cos² (t), u(0) = 0 = u'(0).

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Q: Write an exponential function f(x) that goes through the points (2,3) and (4,5). Round the…

A: Consider the exponential function  fx=abx  ---------- (1) Assume that the above exponential curve…

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Q: Find the mass of a thin funnel in the shape of a cone  z =    x2 + y2, 1 ≤ z ≤ 2,  if its density…

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Q: On the measurable space (R, B(R)), let u: B (R) → R be defined as: u(A) = The number of all rational…

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Q: Find the values of x, y and z that correspond to the critical point of the function: f(x, y) 5x² +…

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Q: Suppose that the sequence x0, x1, x2... is defined by xo=0, x₁ = 7, and xk+2 = xk for k20. Find a…

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Q: Given sets A, B, and C, express 1AUBUCT а достива

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Q: Compute the standard deviation for set ​{8​,8​,9​,9​,9​,10​,10​}.

A: Data set = ​{8​,8​,9​,9​,9​,10​,10​} Here, n=7 Mean of the data is (8​+8+9​+9​+9​+10​+10​)/7 = 63/7…

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Q: 1. Create a function where you need to use both and quotient rule and chain rule in to take the…

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Q: 11. A matrix ME Mnxn (C) is called skew-symmetric if Mt = -M. Prove that if M is skew-symmetric and…

A: 11. A matrix M∈Mn×nℂ is skew symmetry and n is odd. We have to prove that M is not invertible. Also,…

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A: A) It is given that vector A  has a magnitude of 2.5 ms at a direction of 18° and vector B has a…

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