A hemisphere of radius R is cut with a plane parallel to the base of the hemisphere, at a height of 2/3 of the radius. Find the volume of the larger of the two zones into which it is divided. (Express the result as a function of R)

Q: 4. The formula for the volume of a cylinder is V=pi r^2 h What is the volume of a cylinder that has ...

A: We have to find the volume of the cylinder from the given data.

Q: 6. y" + y' – y = 0; when y(-4) = 7,y'(-4) = 1

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Q: Linearly independent. please Prove it. e set A is orthogonal if Por every zeA, we have

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Q: 1) IP a normed space X is Pinite dimen sional then every Livear operator on X is bounded. please pro...

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Q: Find the roots/s using Secant Method a) x* – x – 10 = 0 Ans. x = -1.697 and 1.855

A: The equation in form f(x)=0 is called a transcendental equation. If the function is continuous on  [...

Q: Q4] A complex function in term of polar coordinates, (r,0) is described as f(z)=u(r,0) +j v(r,0). Th...

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Q: n the Compact subset M of X under Tis compact. image of se prove it.

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Q: S 3(x – 1)² |S /1 + (t – 1)*dt dx 6) This is a calculus 2 problem.

A: To calculate the below integral. ∫013x−12∫0x1+t−14dtdx

Q: t F H. E Determine whether the graph above has Hamiltonian circuit. Show and prove your answer.

A: The Hamiltonian circuit is the path in a graph in which you can start from a vertex, visit other ver...

Q: ): Let y(t) = x(t)*h(t), where x(t) = e-2tu(t) h(t) = e-4tu(t) Compute the Fourier transform of y(t)...

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Q: Reduce the quadratic ferm 34*+5y+32²- Caronical form matrix of t rans 2 2 + 2z x to the and 8pecity ...

A: Our main interest lies in finding a suitable orthogonal transformation X=PX' which will reduce the e...

Q: Let G be the solid in the first octant that is bounded by the cone z = V3x2 + 3y? and the planes z 3...

A: Use the following formulae, to convert the Cartesian coordinates into spherical coordinates. x=ρsinϕ...

Q: Problem 4. a) Diagonalize the following matrix if possible 1 A = 1 b) Compute A2000

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Q: ez Let ƒ (2) = . Let C be the circle |2| = 7 in the 1 counter-clockwise direction. What is 2ri | f (...

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Q: Let G be the solid inside the sphere x2 + y2 + z2 = 9 but outside the cylinder x² + y2 = 1, bounded ...

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Q: 3 Determine whether the graph above has an Euler circuit or Euler trail. Show and prove why is it Eu...

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Q: 1) IP a normed space X is Pinite dimen siona) then every Lixear operator on X is bounded. please pro...

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Q: 1) IP a normed space X is Pinite dimen sional then every Livear operator on X is bounded. please pro...

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Q: 1. Let

A: Given,       A=1-10-12-i0i1

Q: у %3D 3x? + 6х — 4 + 2ex — 3ln x

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Q: Use the continuous compound interest formula to find the indicated value. A=$18,543; P=$10,500; t=72...

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Q: Problem: The end behavior of the graph of P(x) = -x²(3 – x)(2 - x)² is As x → +00, P(x) → -00 As x-0...

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Q: Con tinuoUS mapping the image of Compact subset M of X under Tis Compact.

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Q: Sj 3(x – 1)² |So V1 + (t – 1)*dt dx 6)

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Q: h one is correct? Answer: 1 а + 10 — о(а), х — 0 te-2n 10п В. : о(1/п), п — 1 — о(е "), п 0 sin æ = ...

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Q: A manufacturing company produces four parts that require the use of a lathe and a drill press. The t...

A: We will use basic knowledge of linear optimization to answer this question.

Q: Write out the Cayley table for the group {1, -1, i, -i} under multiplication where i = sqrt(-1). (In...

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Q: the image of compact subset Mof X under Tis Compac prove it.

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Q: a Con n the image of Compact subset M of X under Tis a

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Q: Use the continuous compound interest formula to find the indicated value. A= $87,000; P = $63,270; r...

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Q: Given ADEF andAJKL and the information in the table. What statement completes the table and proves t...

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Q: A firm faces a demand function of the form P = 90 – 2Q? (a) Plot the graph for their total revenue (...

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Q: Consider the following first-order ODE: dy = (1 +2x) /ỹ, х 3D [0, 1], у (х %3D 0) —D 1 dx

A: According to Runge-Kutta forth order iteration method; dydx=f(x,y)yn+1=yn+kk=k1+2k2+2k3+k46k1=h f(xn...

Q: answer will be fined worth a correct answer. a real matrix A satisfies AT - A then it is diagonaliza...

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Q: 3) The space C is the set of all Convergent sequences in e. please Prove that C is complete.

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Q: Complete the following table. g(x) f(x) (f• g)(x) Vx-1 a. х-1 8x + 48 b. x+6 8x C. Vx-1

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Q: 1. (i) The functions u(x, y) and v(x, y) satisfy the following system of partial differential equati...

A: I think here one characteristic is misprint. See my answer to verify.

Q: I. Given f do the following: A. Find all possible points of inflection of the graph of f in I. Ident...

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Q: 2. A wheel has a diameter of 90 cm and completes 4 revolutions in 1 minute at top speed. a) Determin...

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Q: Use Stokes' Theorem to set up (do not evaluate) the definite integral equal to the total circulation...

A: We will use basic knowledge of vector calculus and Stokes' theorem to answer this question.

Q: More Volumes: Find the volume of the solid obtained by rotating the region bounded by the given curv...

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Q: Answers must be clear to read and sho teps. You can type your solutions nswers.

A: In this question, the concept of the average rate of change is applied. The average rate of change T...

Q: Let f(x1, x2)= -4x +4x1x2– x;. Which one of the following statements is true? Select one: O a. f(x1,...

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Q: m ーT<X<-π/2 flx)={k f -π/2<x<π/2 if f(x+2n)= f(x) m π/2<x<π

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Q: Consider the force fields F,(x, y) = (y² + 2xe", x(3y+ xe + 1)) and F2(x, y) = (M, N). Let C be the ...

A: For a vector field F=Pi +Qj ∮CF.dr=∫C(Pdx+Qdy) If curve C enclosed the region A ,  By greens theorem...

Q: Prove that e“ p.w. on R. n! n=0 M8

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Q: aluate the Cauchy principal value of the given improper integral. dx (x² + 1)²(x² + 9)

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Q: V4 – x2 – y², above the 1, and outside the cone z = V3x² + 3y². Sketch the solid G (label the coordi...

A: Solution:

Q: Amanda has a total of two hundred four coins. She has three times as many dimes as nickels and one-h...

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Q: X and y be metric spaces and T.X-zy a Continuous mapping Then the image of Compact subset M of X und...

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