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On the sphere, we have x2 y2 z2 = R2 so, using properties of integrals,, the integral for surface area, and the surface area of the sphere of radius R we obtain Z Z S x2 dS Z Z S y2 dS Z Z S z2 dS = R2 Z Z S dS = 4ˇR4 Consequently, Z Z S x2 dS = Z Z S y2 dS = Z Z S z2 dS = 4 3 ˇR4 10 Find the surface area of the part of the cone x2 y2 = z2 between the planes z = 2 and z = 5.
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1 Boolean Algebra Definition A Boolean Algebra is a math construct (B,, , ‘, 0,1) where B is a nonempty set, and are binary operations in B, ‘ is a unary operation in B, 0 and 1 are special elements of B, such that a) and are communative for all x and y in B, xy=yx, and xy=yx. Solution Integrating with respect to x and treating y as fixed gives f = Z y fixed x2 y 9dx = x3 3 xy 9xA(y), where A is an arbitrary function depending on the fixed variable y ⁄ Example 113 Find the general solution of the PDE, ∂2f ∂x∂y = 2x, where f is a function of two independent variables x and y Solution The PDE can be expressed as. Title Microsoft Word Document1 Author fannonr Created Date 3// PM.
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SOLUTIONS TO SECTION 1 5 Solution We have u x=u ss x u tt x= u s 2u t u xx=u sss x u stt x 2u sts x 2u ttt x= u ss 4u st 4u tt u xy=u sss y u stt y 2u sts y 2u ttt y= u ss 2u st u y=u ss y u tt y= u s u yy=u sss y u stt y= u ss Substituting these expressions into the given equation we nd. /0 12 3 2 0 452 0 156 12 7 8 9 4 2 ;. ö XIp=rm==tm=n=e n=m=/ v=s=udev=s=ut= dev=, ks=c===Urm=d*n=m=< dev=k0p=rm==n=nd, k&{= v=nde j=g=d.
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This particular question may baffle many people as most will think the order of the application in algebra will make a difference There is no specific answer o this question But however math(xy)(x−y)/math First, we need to remove the brac. UNIVERSITY OF ALBERTA Department of Chemical & Materials Engineering Edmonton, Alberta, T6G 2G6 K Nandakumar Ph , Fax , email kumar@shivaecheualbertaca. Theorem IfX ∼ U(0,1),thenY =−αlnX isexponentiallydistributedwithmeanα Proof LettherandomvariableX havethestandarduniformdistributionwithprobability.
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