a manufacturer makes moulded plastic bowls, outside shape is defined by y=x^2 and inside by 5y=4x^2+4?
914496
Solve the two equations simultaneously:\n\ny = x^2 ---------- i\n5y = 4x^2 + 4 ---- ii\n\nsubstitute i in ii\n\n5x^2 = 4x^2 + 4\n x = 2 or -2\nand y = 4\n\nSo the points of intersection are (2,4) and (-2,4)\n\nTherefore, height of bowl = 4\n\nOk, I'm a bit rusty on volumes and areas, but I'll take a shot anyway:\n\nVolume of bowl = Volume generated when 5y = 4x^2 + 4 rotates completely about the y-axis\n= Volume of half an ellipsoid?\n= 2/3 (Pi) (2^2) (16/5)\n= 128/15 (Pi)\n\nAmount of plastic = total surface area of solid\n\nYou could try integrating if you fancy it.
768468
Diameter and height will be equal in this case.  As V = 55\npi r^2. 2r/3 = 55 giving r^3 = 165/4\n\nr = 3.455\n\nh = 2r = 6.91
40559
Just what are you asking? \n\nIf this were the Baking section, then you owe someone two pies. \n\nIf you are talking Math (this section), then I presume you are talking about PI (the value used in Circumference = 2 (PI) * radius, Area = PI * r^2, Volume = (1/3) PI * r^3). Following these derivations, I have no clue where PI^5 lies in Geometry.\n\nOr, finally, if you are thinking 3*PI - 5*PI, you get -2 * PI, or -2 * 3.14159..., = -6.28318...
877943
volume of cyllinder = area of circle times height\n\n= Pi x radius x radius  x height\n\nremember its just the same as finding the volume of any prism.\nfind the area of the shape of the end then multiply by its length!!
612878
xy = 4 then y = x/4\n\nx^2 +  4y^2 = 20\nx^2 + 4 x^2/16 = 20\nx^2 + x^2/4 = 20\n4x^2 + x^2 = 80\n5x^2 = 80\nx^2 = 80/5\nx^2 = 16\n\ntherefor\nx = 4\nthen \ny=1
471216
Well, 4 squared is 16, and 5 squared is 25.  So its between those two.
657525
If you have the equation of the curve then integrate it on the lower and upper limits of the variable. In some cases you can find devide the identical parts and find out area of a single identical part and multiply by the number of parts made (sine wave).\n\nIf shape is a simple square circle etc you can find area by simple formula.
990247
A sphere.  It has an inside and an outside.
637876
v=4/3 pi r^3 (four thirds x pi x (r cubed))
237156
Pi * r^2\n\n(Pi R Squared)\n\nwhere R is the radius (which is also equivalent to half the diameter)
868947
y^2-4y-5=(y-5)(y+1) not irreducible\n6t^2+5t+2 is irreducible
938684
If you desire the external surface area of the pipe,\n\nA = pi*d*L\n\nMake sure d & L are in the same units and your answer will be in those units squared.\n\nIf you are looking for the internal cross sectional area:\n\nAc = (pi*d^2)/4
1009002
y = x² - 4x - 5\n\nSimplify -5 = 4 - 9 to complete the square\ny = x² - 4x + 4 - 9\n\nSimplify the square\ny = (x - 2)² - 9\n\n^_^
745313
Not enough information. If the rectangle is also a square, then the length of each side would be 32/4 = 8 cm. Letting x be the length of one of an arbitrary pair of sides and y represent the length of a side from the other pair, you do know of course that x and y must satisfy the equation 2x + 2y = 32 cm --> x + y = 16 cm. Since you have two unknowns but just one equation, there are uncountably infinite many possibilities for (x, y).
568015
You add the areas of the six sides.\n.5 x .5 = .25 cm squared    (that's the area of one side)\n.25 cm squared x 6 sides = 1.5 cm squared
1169467
y = x^2 + 5x - 3\n2y=3x - 2\n----------------\n2y = 2x^2 + 10x - 6\n2y = 3x - 2\n-----------------------\n    0 = 2x^2 + 7x - 4\n=>2x^2 + 7x - 4 =0\n=>2x^2 + 8x - x - 4 = 0\n=>2x(x + 4) -1(x+4) = 0\n=> (2x - 1)(x + 4) = 0\ntherefore 2x - 1 = 0 => x = 1/2 or \nx + 4 = 0 or x = -4\nx = - 4 or 1/2  \ngot it?
227193
∫[(2x^4) - (4/x^5)]dx=\n\n∫(2x^4)dx - ∫(4/x^5)dx=\n\n2∫x^4dx - 4∫[x^(-5)]dx=\n\n2*[x^5/5] - 4*[x^-4/-4]=\n\n(2/5)x^5 + x^-4 + C=\n\n(2/5)x^5 + 1/x^4 + C