2. Consider the region bounded by x = 4y - y³ and the y-axis such that y ≥ 0. Find the volume of the solid formed by rotating the region about a) the vertical line x = -1 b) the horizontal line y = -2. Please include diagrams to help justify your integrals.

Q: 12. Show that the set of all constant polynomials in Z[r] is a subring but not an ideal of Z[x]

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Q: ܒܢ J nπL s²L²+ n²π²] 22

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Q: 7. Suppose that f=u+ie is analytic and not identically constant. a) Show that ue is the real part of…

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Q: 3. Consider the vector field F(x, y) = (2xy, x² - sin y). Evaluate F.ds π where is the curve c(t) =…

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Q: 15. Let R be a ring, I, J be ideals of R and f: RR/I x R/J be the function defined by f(a) = (a +…

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Q: II. Use Theorem 6.1.1 or Theorem 6.1.2 to solve the following problem: What are the equations of…

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Q: 3. In the last work assignment, you computed the volume of the solid obtained by rotating the region…

A: Please see the attachment

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A: Note: Tree: A connected graph without any cycles is called a tree.

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Q: How many integers between 1 and 822 inclusive are divisible by 5 or 3?

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Q: Consider y' - 2y = 3e2x with y(0) = 2. Using Runge-Kutta method with h=0.1, find the relative error…

A: The given differential equation is : y'-2y=3e2x with y(0)=2. h=0.1.  To find: Relative Error on…

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Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler method with h=0.1, y(1.3) = y(A)…

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Q: 8. Using the Mean Value Theorem and Rolle's Theorem, show that³+x-1=0 has exactly one real root.

A: We are entitled to solve only one question at a time. Please post another questions separately. To…

Q: 3- 4- 2X 2X e dy dy + 2 (y e-x) dx === Sinx dy + + cosxy = tan x dx

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Q: ketch the surface

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Q: If a, ß be the roots of ax² + 2bx + c = 0 and a +8, ß+8 be those of Ax² + 2Bx + C = 0, then 2 6² b -…

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Q: du J²u D = 0, x>0, t>0 Ət əx² u(x,0)=0, x>0; u(x, t) →0, xx, t20; u(0,t) = uo. t20 = We consider the…

A: Solution : For difference equation to be invariant, ∂u∂t-D∂2u∂x2=0 u~=aγux~=axt~=aβt…

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Q: dx axy with r, K, a, s, b>0. dt 1) Find all steady-states for this model, and analyze their…

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Q: * Find y w.xy. Given z = Option 1 Option 3 Zy = -y-² Zy= -2y-2 Zy = y ² Option 2 none of the above

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Q: (ii) Prove the identity (2 – 2 cos 0) (sin 0 + sin 20 + sin 30) −(cos 40 — 1) sin 0 + sin 40 (cos 0…

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A: Solution : a) 1 , 1 , 2 , 3 , 5 , 8 , 13 b) lets check above Fibonacci series their is even coming…

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Q: If A and B are bounded subsets of R, then prove that AUB and AB are bounded.

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Q: A 60° 30° Name! Section: 30 m ACTIVITY (SPECIAL RIGHT TRIANGLES) Identification: Answer the…

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Q: 12 Two towers AB and PQ stand on level ground. The angles of elevation of the top of the taller…

A: Given that  ∠KAP=5o ∠QBP=20o Height of the taller tower = 70 meters

Q: By using Laplace transform to solve y + y = cosht y (0) = 0, what would the particular solution be?…

A: the given equation is y'+y=cosh t  y(0)=0 taking Laplace of the given transform Ly'+y=Lcosh t…