Lebesgue measure

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Euler's Theorem

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One question with 4 sub sections (i think involves maxima & minima)

A manufacturer produces cardboard boxes that are open at the top and sealed at the base. The base is rectangular and its length is double its width. Let x denote the width in metres. the surface area of each such box is fixed to be 3 square metres. The manufacturer wishes to determine the height h and the base width x, in metres ...continues

Implicit Function Theorem

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sketch the parabola first finding the Vertex, Foci and Directrix for equation below

Sketch parabola first finding the vertex, foci and directrix for this equation y+3=1/8(x-5)squared meaning the (x-5) part of equation is squared

Using first two equations determine 3 possible points that the 2 conic sections that you get from equations meet. Then adding a third equation figure out the one point that all three conic sections meet

First equation is 9(x-squared)+25(y-squared)-72x=81 Second equation is 9(x-squared)-15(y-squared)=9 Graph these two conical sections and let us know how you get the graphs with such things as vertex and foci or whatever. Show three common points of these two conical sections. Then add the third equation:12x+6y=-12 and determ ...continues

sketch hyperbola after finding Center, Vertex and Foci of this equation?

Sketch hyperbola after finding Center, Vertex and Foci of this equation: (y+5)squared/16 - xsquared/9 =1 Please show steps needed

write 2 equations in standard form first equation is a hyperbola second is a parabola

Write this equation in standard form(PLEASE SHOW STEPS): xsquared-4(ysquared)-2x+16y-19=0 Write this equation in standard form (PLEASE SHOW steps): 6x-xsquared=8y+1

If the equation of the earth with its center at the origin is xsquared + ysquared =65 where x and y are distances in thousands of kilometers will either of two meteroites with equations below strike the earth.

The earth with center at the origin has equation of xsquared + ysquared =65 where x and y are distances in thousands of kilometers. sketch and show how you did it. Will either of these two meteorites whose equations I will give you strike the earth. The first meteorite is a parabola whose equation is 18x-ysquared = -144 Ple ...continues

Sketch the vector fields and flow lines

Sketch the vector fields and flow lines (See #34 Attached for full question)