if x=9 inches and y=18,and the area of the brown frame is 92 inches2'what is the area of the inner red box
955995
Something is missing. Your brain maybe?
322681
For the first, if one side is x, then another side would be 9-x (so that they would add up to 18).  The area is then\n\nA = x(9-x)\n= 9x - x^2\n\nTo find the maximum area, take the first derivative and set it to 0:\n\nA' = 9 - 2x\n0 = 9 - 2x\n2x = 9\nx = 9/2\n\nSince the parabola opens down, the maximum area happens when x = 9/2.\n\nSo if x = 9/2, the other side is 9 - 9/2, or 9/2 - it turns out to be a perfect square!  And the area is then (9/2)^2, or 81/4.\n\nFor the second, you already have an area and you need to find the perimeter.  So, lw = 36, and we're trying to find the smallest 2l + 2w.  Well, l = 36/w, so the perimeter can be expressed as\n\nP = 2l + 2w\n= 2(36/w) + 2w\n= 72/w + 2w\n\nWe can take a derivative and set it to 0 to find the minimum value here:\n\nP' = -72/w^2 + 2\n0 = -72/w^2 + 2\n72/w^2 = 2\nw^2 = 36\nw = 6\n\nSo if w = 6, then l = 6 as well, and the perimeter would then be 24.
766270
im assumuing you mean a rectangle? If it was a square itd be 400, if its a rectangle its 80l-l^2
2156
5x+9y=18\nsubtract 5x from both sides because you want Y by itself\n\n9y=18-5x\ndivide both sides by 9 because you want Y by itself\n\ny=2-5/9x<---------------There you have it, simplified
1013701
9x4 + 82x6 - 24x12 + 87\n\n36 + 41x12 - 24x12 + 87\n\n36 + 17x12 + 87\n\n36 + 120 + 84 + 87\n\n156 + 84 + 87\n\n240 + 87\n\n327
1168044
93.5 sq in\nMultiply by 2.54^2 to get\n603.2246 sq cm
932598
The exterior angle is equal to the sum of the two interior angles.  So 18+98=116, your answer should be 116.  I'm assuming that the exterior angle is supplementary to angle 3, not angle 1 or 2.
23547
78.75\n\ntimes .035 x 750 x 3
1073502
Once again you will see that this is a rectangle.\nA = length times width\nA = 7*2\nA = 14
492961
Yes 152 cm is correct.\n\nTo solve the problem factor 2002 = 2x7x11x13\n\nThe closer the box is to a perfect cube the lower the ratio of the surface area to the volume.\n\nThis occurs when the sides are  11, 13 and 2x7=14\n\nIn the cube, each edge appears 4 times and so the sum of the edges will be 4 times (11+13+14) = 4x38 = 152 cm
804335
Call the side of the square you cut out x, then the box you make will have a square base of side (24 - 2x) and the height will be x. \n\nThe area of this box is then (24 - 2x)^2*x = 2x*(12 - x)^2. Call this a function of x, and we need to find the maximum.\n\n2x^3 -48x^2 + 288x = f(x)\n\n6x^2 - 96x + 288 = f'(x) = 0\n\nx^2 - 16x + 48 = 0\n\n(x - 12)(x - 4) = 0\n\nSo this has the 2 answers x = 12 and x = 4.\n\nx = 12 gives a minimum (volume = 0), so x = 4 is a maximum,  1024\n---------------\nI just looked at the above answers. JimBurnel made a careless error, the volume should be x(24 - 2x)^2, not x(24 - 2x). The rest of his logic is right, but the equation is wrong.\n\nAnd Paritosh Vasava assumes by "largest" you want surface area, I assume you mean volume. Of course the largest surface area comes when the squares you cut out are of size 0, your box is then 24*24*0, area = 576, volume = 0.
863802
area=(1/2)d1*d2\n=(1/2)*28*13\n=14*13\n=182 sft
351129
Take the number of red blocks and divide by the total number of blocks.\nnumber of red = 18\nTotal number of blocks = 27+18+12+43 = 100\n18/100\n= 9/50
924059
(11.5+9) x 18= 369 sq feet if you are covering both the kitchen and living room\n\nIf you are just covering the kitchen , you look at 162 sq feet..
140477
If it's only the front, and assuming it's rectangular, it's 30 x 30 =900. If it is not rectangular, information is not sufficient to tell.
760569
small area=2in^2\nbig sides are 3x as long so area is 3^2 x as long\n2*3^2=18 in^2
950600
Let z be the amount to multiply each dimension by:\nLet A be the original area\nLet A' be the new area\n\nA = W * L\nA' = zW * zL\nA' = z²(W * L)\nA' = z²A\n\nWe want the new area (A') to be 4/9 the old area (A).\n\nThat means z² = 4/9\nAnd therefore:\nz = sqrt(4/9)\nz = 2/3\n\nIf the original dimensions are 18 cm * 24 cm.  The new dimensions will each be 2/3 of that (12 cm * 16 cm).\n\nThe old area will be 432 cm², the new are will be 192 cm² which is 4/9 the original.\n\nThus the new dimensions should be 2/3 the old or 12 cm * 16 cm.