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$$int_Sz,dS$$$$S=big{ big(x,y,zbig):x^2+y^2+z^2=a^2,zge 0, a>0big}$$I've already calculate this surface integral " by hand " :$$z=sqrt{a^2-x^2-y^2}text{, thus,}$$$$int_SzdS=intint_{x^2+y^2le a^2}sqrt{a^2-x^2-y^2}cdotbigg(sqrt{1+z_x^2+z_y^2}bigg)dxdy$$$$=int_SzdS=intint_{x^2+y^2le a^2}sqrt{a^2-x^2-y^2}cdotbigg(sqrt{frac{a^2}{a^2-x^2-y^2}}bigg)dxdy=int_SzdS=intint_{x^2+y^2le a^2}adxdy=a^3pi.$$I want...
Asked on 01/06/2021 by John Mars
2 answerThe question is the following:We break a stick at a uniformly chosen random location. Find the probability that the shorter piece is less than $dfrac15$-th of the original.My...
Asked on 01/06/2021 by Ssendkrad Saizer
1 answerI need to calculate the following product: $x^{-1} cdot sqrt[3]{x} = ?$ First, I apply the rule $sqrt[n]{x^m} = x^{frac{m}{n}}$ to convert $sqrt[3]{x}$ to $x^{frac{1}{3}}$: ...
Asked on 01/06/2021
0 answerI have an idea of how one might go about doing it, but it's never explicitly mentioned in the books or anywhere on the net for that manner (at least...
Asked on 01/05/2021 by Leonid
1 answerIn my physics class, we are currently studying gradient, Laplacian, divergence, and curl, and we have a problem that states to compute all four of these (I.e., (1) gradient, (2)...
Asked on 01/05/2021 by Yelena
0 answerSuppose we conduct Buffon's needle experiment, randomly dropping a needle of length $Lin(0,1]$ between horizontal lines which are a distance of $1$ apart. It is well known that...
Asked on 01/05/2021 by Václav Mordvinov
1 answerQUESTION: There are $nge 3$ girls in a class sitting around a circular table, each having some apples with her. Every time the teacher notices a girl having more...
Asked on 01/05/2021 by Stranger Forever
1 answerLet $E_1,E_2,F$ three finite dimensional vector spaces. And let $f$ a mapping defined on $E_1times E_2 rightarrow F$ : My question is that if $f$ is...
Asked on 01/05/2021 by Robert-ben
0 answerI was trying to follow this proof of the uncountabilty of R and at first it seemed clear, but when I tried to explain it to myself...
Asked on 01/05/2021 by modo_mahu
1 answerI have to explain how the number of integer solutions to $x_1 + 2x_2 + 3x_3 + dots + nx_n = n$ with $x_i ge 0$ for ...
Asked on 01/05/2021 by Min
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