Find the mass of a wire in the shape of helix r(t) = cos πt i+sin πt j+8tk 0≤t≤1, where the density of the wire is P(x, y, z) = x² + y² + z².

Q: 8: [1 The matrix A = 4 L3 O True O False -2 31 1 -1 - 2 is a positive definite matrix. 21

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Q: 3 Factorise completely the expression 2x³-11x²-20x-7.

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Q: 14: Given three vectors u = [1 0 0], v= [1 0 -3]" and w= [1 -3 -5]". Which of the following matrix…

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Q: - Use the midpoint sum formula to calculate the area under the curve f(x) = x³ from x=0 to x-12…

A: Here h = b-an = 12-04 = 3

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Q: termine if F~ (x, y, z) ), where F~ (x, y, z) = e^x*sin (y)ˆi+e^y*sin (z)ˆj+e^z*sin (x)ˆk. is a…

A: Given,         F→x, y, z=exsin(y)i^+eysin(z)j^+ezsin(x)k^

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Q: 5: The Hessian matrix for f(X) = x}xy + x3x3 at the point (1 2 3], is given by: [6 0 31 [3 0 61 [18…

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Q: Q4. Differentiate term by term the power series E-o(x-7)". dy Q5. Solve: = y² (1+x²), y(0) = 1. dx

A: According to our guidelines we can answer only one question and rest can be reposted.

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Q: y = -x^2 + 4x, y = x^2 - 6x + 5, x=0, x= 1 O 2.012 sq. units O 2.022 sq. units O 2.032 sq. units…

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Q: I Use the bisection method to find p3 for f(x) = r - 16 2 on [0, 1]. 0 0100 نت | حظر 3 ده | د |- 4 د…

A: To reach the exact root halving the interval in each step. P3 is the third approximate step.

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Q: The standard form for (F.O.D.E) y = 3y' - 4x + 5 is 4 5 y'-y = 3x 3 Option 1 4 5 y' - 6y=3x-3 Option…

A: Firstly we make the coefficient of y' is 1 and convert into the standard form  y′+p(x)y=q(x)

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Q: Q1. Find the distance between the points A (-1, 3, 7) and B (2, -1, 6). please solve in steps…

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Q: x¹ + x² + 1 I(x² + 1)² -dx.

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Q: go, he has not finishec ce between the bracke

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Q: 4 The remainder when the expression x³ + x² - 5x-3 is divided by x-2 is 5 times the remainder whe…

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Q: 4.) Sketch the curve r = 1 + 5 sin by first sketching the graph of r as a function of in cartesian…

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Q: 3. Find the limit: 6x4 lim (x,y)-(0,0) 5x8 + 6y²

A: We have to find the limit :   lim(x, y)→(0,0) 6x45x8+6y2

Q: If f(X) is a convex function, then ef(x) is also convex function. O True

A: We have to check whether if f(x) is a convex function then ef(x) also convex. As per policy…

Q: Q1:/ Read the article below and answer the questions after. PM25 is the leading global environmental…

A: By using sentence mentioned in given paragraph i.e., PM2.5 is the leading global environmental…