13-Evaluate JSS zdV E where E lies between the spheres x2 + y? + z² = 1and x2 + y? + z? = 4 in the first octant. %3D
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- aIf HP=4, PJ=5, and PM=2, find LP. _ bIf HP=x+1, PJ=x1, LP=8, and PM=3, find x. _if d is the region in the first octant between the spheres x^2+y^2+z^2=1 and x^2+y^2+z^2=25 then. the rest of question in the following imageSuppose the temperature at the point (x, y, z) on the sphere x2 + y2 + ?2 = 16 is T= 800xy2z3 . Locate the lowest and highest temperatures on the sphere.
- show that a=(2x^2+8xy^2z)i+(3x^3y-3xy)j-(4y^2z^2+2x^3z)k is not a solenoidal but b=(xyz^2.A) is solenoidalUse n = 10^4 pseudo-random points to estimate the interior area of the ellipses(a) 13x^2 + 34xy + 25y^2 ≤ 1 in −1 ≤ x, y ≤ 1Consider two spheres, defined by x^2 + y^2 + z^2 = 1 and (x − 2)^2 + (y − 6)^2 + (z − 3)^2 = 16, respectively. How close are the spheres from touching?
- 5) Consider four points A, B, C, and D whose geometrical locations correspond to the corners of a square with sides of length 1 mm. Calculate the potential differences (in mV) VAB, VBA, VAC, VCA, VAD, VDA, VBC, VCB, VBD, VDB, VCD, VDC between the points in a uniform electric field of 3 V/m parallel to the two sides (and perpendicular to the other two) of the square. (Show your work)Compute the surface area of the cap of the sphere x2+y2+z2=49 with 6 ≤ z ≤ 7.Sketch the surfaces CYLINDERS z = y2 - 1
- Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 + y2 + z2 = 1 is T = 400xyz2. Locate the highest and lowest temperatures on the sphere.Explain why the hypercube Qn, n greater or equal to 2, is hamiltonian.If a bug walks on the spherex^2 + y^2 + z^2 − 4x + 4y + 4z + 3 = 0how close and how far can it get from the point P(1, −1, −1)?