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Find and interpret the rate of change and initial value. A phone company charges for service according to the formula: C (n= ) 26 + 0.04n , where n is the number of minutes talked, and C (n) is the monthly charge, in dollars. Find and interpret the rate of change and initial value.

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Solution. In cylindrical coordinates the region E is described by 0 ≤ r ≤ 1, 0 ≤ θ ≤ 2π, and 0 ≤ z ≤ 2r. Thus, ZZZ E x2 dV = Z 2π 0 Z 1 0 Z 2r 0 (r cosθ)2 rdzdrdθ = Z 2π 0 cos2 θdθ Z 1 0 2r4 dr = 2π 5. 4. Use spherical coordinates in the following problems. (a) Evaluate RRR E xe(x2 +y2 z2)2 dV , where E is the solid that ...

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Nov 15, 2008 · Homework Statement Use polar coordinates to find the volume bounded by the paraboloids z=3x2+3y2 and z=4-x2-y2 Homework Equations The Attempt at a Solution Somehow, through random guessing, I managed to get the right answer, it's just that I don't understand how I got it. Also, because the...

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Using cylindrical coordinates: z = 16(x^2 + y^2) = 16r^2. z = 32 - 16(x^2 + y^2) = 32 - 16r^2. Curve of intersection: 16r^2 = 32 - 16r^2 ==> r = 1, a circle.

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It seems such as you're meant to be doing a triple necessary (which simplifies to a double necessary) You combine from z= 2+x^2+(y-2)^2 to z=a million in the z direction. This in simple terms supplies the function 2+x^2+(y-2)^2 - a million = a million+x^2+(y-2)^2 then you evaluate the double necessary of a million+x^2+(y-2)^2 as widely used ...

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Show that there is no intersection point of the line y = x + 5 with the ellipse x2 + 5 x2 y2 x 2 y2 Find the points of intersection of the curves + = 1 and + = 1. Show that 4 9 9 4 the points of intersection are the vertices of a square. 6 x 2 y2 Find the coordinates of the points of intersection of + = 1 and the line with 16 25 equation 5x = 4y. 7 Z 2 1 Z 3y+7 y 1 y2 dx dy = Z 2 1 xy2 3y+7 y 1 dy = Z 2 1 ( 3y +7)y2 (y 1)y2 dy = Z 2 1 4y3 +8y2 dy = y4 + 8 3 y3 2 1 = 24 + 8 3 23 1+ 8 3 = 11 3 15.3.24Find the volume of the given solid under the surface z = 1 + x2y2 and above the region enclosed by x = y2 and x = 4. (x;y) is in the region , 2 y 2; y2 x 4 volume = Z 2 22 Z 4 y 1+x2y2 dx dy ...

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