Compute $\langle 5 \rangle$ in integers November 29    2

Compute $\langle 5 \rangle$ in integers. I thought the answer would have been $$\{5^n| \text{ for $n$ in integers }\}$$ However my teacher has marked it $$\{5*n|\text{ for $n$ in integers }\}$$ What have I done wrong?The integers do not form a group

Solid Ellipsoid Volume Evaluation November 29

Evaluate ∭H((x^2/a^2)+(y^2/b^2)+(z^2/c^2))dV, where H is the solid ellipsoid: ((x^2/a^2)+(y^2/b^2)+(z^2/c^2)) <= 1, where a,b&c are positive numbers.We've been using the Jacobian determinant to evaluate transformations, however I am not sure how to

Volume of a general ellipsoid November 29    2

Can somebody please show me at least one derivation of the volume of a general ellipsoid? I've been trying to derive by considering it a surface of revolution. The answer I keep getting is $4\pi(abc^3)/3$ but I know it's supposed $4\pi(abc)/3$. Could

Count Planar Graphs November 29

I have an assignment due tomorrow, i am stuck with these two questions. Can someone give me a hint ? I don't know where to start..5. Planar Graphs. Let G = (V, E) be a planar graph.(a) A graph is k-regular if every vertex degree is exactly k. How man

Volume of Ellipsoid with a hole November 29

How would I go about computing the volume of an ellipsoid with spherical caps removed and a cylindrical hole through it? I'm thinking about finding dV of a cross section (the ellipsoid has a circular horizontal cross section). Would this be the best

what is the handwritten notation for a random vector November 29    1

Not sure if this is a maths question but didn't know where to turn. I'm learning probability theory on my own using a textbook. It uses capital letters with subscripted number to denote random variables (eg, X1,...,Xn) and bold subscripted capital le

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