0
Add your answer:
Earn +20 pts
What are all the 5-digit multiples of 11?
-6
How would you work out the smallest surface area for a rectangular box with dimensions x plus y plus z equals 150cm?
This is a classic max min problem using Lagrange multipliers. We do this when we have a function of several variables that we want to maximize or minimize and a constraint. Now the equation for surface area of a box is the areas of all the sides added together Total Surface Area = 2(Areahxw) + 2(Areahxl) + 2(Areawxl) using x,y and z we have f(x,y,z) = 2(xy+xz+yz) we need the gradient of that which is <(partial derivative wrt x,), partial derivative wrt y,(partial derivative wrt z)> where wrt means with respect to and i am using <> for a vector. 2 = ∇f(x,y,z) remember that the gradient is a vector and is normal to the curve. now let g be the other function, the one we have constraints on. In this case x+y+z=150 so that sum is constant and we write g(x,y,z)=x+y+z-150=0 we know that ∇f(x,y,z)=2 now the gradient, ∇g(x,y,z) is <1,1,1> since the partial derivative of x+y+z-150 wrt to x is 1 etc. so we have 2=<1,1,1>λ in order for these to be equal, the components must be equal =λ/2<1,1,1> now we have several equations y+z=λ/2 x+z=λ/2 x+y=λ/2 x+y+z=150 so we have y+z=x+z so x=y we also have y+x=y+z so x=z this means x=z=y and using the last equation we have 3x=150 or x=50 so y=50 and z=50 the rectangular box must be 50x50x50 the surface area is 2(2500+2500+2500) check a few other values of x, y and z and see what surface area you get. Perhaps, 100x49x1? we've only got one solution we might be tempted to assume that these are the dimensions that will give the smallest surface area.. The method of Lagrange Multipliers will give a set of points that will either maximize or minimize a given function subject to the constraint, provided there actually are minimums or maximums. So the points 100,49,1 give us info if we found a max or a min 50x 50 x 50 box has a surface area of 15000 the 100x49x1 box has a surface area of 2(100x49+100x1+49x1)=10098 which is less than 15000 so we found a max not a min! since we have x+y+z=150 if one of them gets very small the others have to get very large to compensate, They cannot all get very big or they won't work with our constraint. So the fact that we have a max them seems to make sense. In others, take very small x and y say .01 each then z=149.98 we get a surface area of about 6 or so. (much less than 15000) So now we wonder, do we have a minim value? We looked at .01,.01,149,98 let's take that one more step. x=y=.001 z=150-.002=149.998 surface area is around 1/3 so it looks like we could keep making x and y smaller and smaller and the surface area would continue to shrink. So no matter what values you give me for x and y and z, I can find a box with smaller surface area. remember that a zero derivative may mean a max or min, or may be a saddle point, but a max or min always has a zero derivative. For constrained optimization problems, look and see if the constraint is bounded, for example a circle. The graph is x+y+x-150=0 is a plane in 3 space and is not bounded. This tells us about the existence of max and min.
All the multiples of 11?
Oh, isn't that just lovely? Multiples of 11 are like little brushstrokes on a canvas, each one unique and special. You can find them by simply adding 11 to the previous number, creating a beautiful pattern that goes on and on. Just take your time, enjoy the process, and soon you'll have a whole collection of multiples of 11 to admire.
What are the first 2000 multiples of 11?
The first 2000 multiples of 11 can be calculated by multiplying 11 by each natural number starting from 1. The first few multiples are 11, 22, 33, 44, and so on. To find the 2000th multiple, you would multiply 11 by 2000, which equals 22,000.
What are the first 4000 multiples of 6?
You're asking me to type and post 4,000 numbers ranging from 6 to 24,000 ... a foolish and totally unwarranted waste of my time and the storage resources maintained by the operators of this website, particularly when you consider how easy it would be for you to generate the list on your own, and the fact that it'll be about as useful to you once you have it as it is now. However . . . As some feckless schlimazl once said, "The customer is always right." So here you go: 6 , 12 , 18 , 24 , 30 , 36 , 42 , 48 , 54 , 60 , 66 , 72 , 78 , 84 , 90 , 96 , 102 , 108 , 114 , 120 , 126 , 132 , 138 , 144 , 150 , 156 , 162 , 168 , 174 , 180 , 186 , 192 , 198 , 204 , 210 , 216 , 222 , 228 , 234 , 240 , 246 , 252 , 258 , 264 , 270 , 276 , 282 , 288 , 294 , 300 , 306 , 312 , 318 , 324 , 330 , 336 , 342 , 348 , 354 , 360 , 366 , 372 , 378 , 384 , 390 , 396 , 402 , 408 , 414 , 420 , 426 , 432 , 438 , 444 , 450 , 456 , 462 , 468 , 474 , 480 , 486 , 492 , 498 , 504 , 510 , 516 , 522 , 528 , 534 , 540 , 546 , 552 , 558 , 564 , 570 , 576 , 582 , 588 , 594 , 600 , 606 , 612 , 618 , 624 , 630 , 636 , 642 , 648 , 654 , 660 , 666 , 672 , 678 , 684 , 690 , 696 , 702 , 708 , 714 , 720 , 726 , 732 , 738 , 744 , 750 , 756 , 762 , 768 , 774 , 780 , 786 , 792 , 798 , 804 , 810 , 816 , 822 , 828 , 834 , 840 , 846 , 852 , 858 , 864 , 870 , 876 , 882 , 888 , 894 , 900 , 906 , 912 , 918 , 924 , 930 , 936 , 942 , 948 , 954 , 960 , 966 , 972 , 978 , 984 , 990 , 996 , 1002 , 1008 , 1014 , 1020 , 1026 , 1032 , 1038 , 1044 , 1050 , 1056 , 1062 , 1068 , 1074 , 1080 , 1086 , 1092 , 1098 , 1104 , 1110 , 1116 , 1122 , 1128 , 1134 , 1140 , 1146 , 1152 , 1158 , 1164 , 1170 , 1176 , 1182 , 1188 , 1194 , 1200 , 1206 , 1212 , 1218 , 1224 , 1230 , 1236 , 1242 , 1248 , 1254 , 1260 , 1266 , 1272 , 1278 , 1284 , 1290 , 1296 , 1302 , 1308 , 1314 , 1320 , 1326 , 1332 , 1338 , 1344 , 1350 , 1356 , 1362 , 1368 , 1374 , 1380 , 1386 , 1392 , 1398 , 1404 , 1410 , 1416 , 1422 , 1428 , 1434 , 1440 , 1446 , 1452 , 1458 , 1464 , 1470 , 1476 , 1482 , 1488 , 1494 , 1500 , 1506 , 1512 , 1518 , 1524 , 1530 , 1536 , 1542 , 1548 , 1554 , 1560 , 1566 , 1572 , 1578 , 1584 , 1590 , 1596 , 1602 , 1608 , 1614 , 1620 , 1626 , 1632 , 1638 , 1644 , 1650 , 1656 , 1662 , 1668 , 1674 , 1680 , 1686 , 1692 , 1698 , 1704 , 1710 , 1716 , 1722 , 1728 , 1734 , 1740 , 1746 , 1752 , 1758 , 1764 , 1770 , 1776 , 1782 , 1788 , 1794 , 1800 , 1806 , 1812 , 1818 , 1824 , 1830 , 1836 , 1842 , 1848 , 1854 , 1860 , 1866 , 1872 , 1878 , 1884 , 1890 , 1896 , 1902 , 1908 , 1914 , 1920 , 1926 , 1932 , 1938 , 1944 , 1950 , 1956 , 1962 , 1968 , 1974 , 1980 , 1986 , 1992 , 1998 , 2004 , 2010 , 2016 , 2022 , 2028 , 2034 , 2040 , 2046 , 2052 , 2058 , 2064 , 2070 , 2076 , 2082 , 2088 , 2094 , 2100 , 2106 , 2112 , 2118 , 2124 , 2130 , 2136 , 2142 , 2148 , 2154 , 2160 , 2166 , 2172 , 2178 , 2184 , 2190 , 2196 , 2202 , 2208 , 2214 , 2220 , 2226 , 2232 , 2238 , 2244 , 2250 , 2256 , 2262 , 2268 , 2274 , 2280 , 2286 , 2292 , 2298 , 2304 , 2310 , 2316 , 2322 , 2328 , 2334 , 2340 , 2346 , 2352 , 2358 , 2364 , 2370 , 2376 , 2382 , 2388 , 2394 , 2400 , 2406 , 2412 , 2418 , 2424 , 2430 , 2436 , 2442 , 2448 , 2454 , 2460 , 2466 , 2472 , 2478 , 2484 , 2490 , 2496 , 2502 , 2508 , 2514 , 2520 , 2526 , 2532 , 2538 , 2544 , 2550 , 2556 , 2562 , 2568 , 2574 , 2580 , 2586 , 2592 , 2598 , 2604 , 2610 , 2616 , 2622 , 2628 , 2634 , 2640 , 2646 , 2652 , 2658 , 2664 , 2670 , 2676 , 2682 , 2688 , 2694 , 2700 , 2706 , 2712 , 2718 , 2724 , 2730 , 2736 , 2742 , 2748 , 2754 , 2760 , 2766 , 2772 , 2778 , 2784 , 2790 , 2796 , 2802 , 2808 , 2814 , 2820 , 2826 , 2832 , 2838 , 2844 , 2850 , 2856 , 2862 , 2868 , 2874 , 2880 , 2886 , 2892 , 2898 , 2904 , 2910 , 2916 , 2922 , 2928 , 2934 , 2940 , 2946 , 2952 , 2958 , 2964 , 2970 , 2976 , 2982 , 2988 , 2994 , 3000 , 3006 , 3012 , 3018 , 3024 , 3030 , 3036 , 3042 , 3048 , 3054 , 3060 , 3066 , 3072 , 3078 , 3084 , 3090 , 3096 , 3102 , 3108 , 3114 , 3120 , 3126 , 3132 , 3138 , 3144 , 3150 , 3156 , 3162 , 3168 , 3174 , 3180 , 3186 , 3192 , 3198 , 3204 , 3210 , 3216 , 3222 , 3228 , 3234 , 3240 , 3246 , 3252 , 3258 , 3264 , 3270 , 3276 , 3282 , 3288 , 3294 , 3300 , 3306 , 3312 , 3318 , 3324 , 3330 , 3336 , 3342 , 3348 , 3354 , 3360 , 3366 , 3372 , 3378 , 3384 , 3390 , 3396 , 3402 , 3408 , 3414 , 3420 , 3426 , 3432 , 3438 , 3444 , 3450 , 3456 , 3462 , 3468 , 3474 , 3480 , 3486 , 3492 , 3498 , 3504 , 3510 , 3516 , 3522 , 3528 , 3534 , 3540 , 3546 , 3552 , 3558 , 3564 , 3570 , 3576 , 3582 , 3588 , 3594 , 3600 , 3606 , 3612 , 3618 , 3624 , 3630 , 3636 , 3642 , 3648 , 3654 , 3660 , 3666 , 3672 , 3678 , 3684 , 3690 , 3696 , 3702 , 3708 , 3714 , 3720 , 3726 , 3732 , 3738 , 3744 , 3750 , 3756 , 3762 , 3768 , 3774 , 3780 , 3786 , 3792 , 3798 , 3804 , 3810 , 3816 , 3822 , 3828 , 3834 , 3840 , 3846 , 3852 , 3858 , 3864 , 3870 , 3876 , 3882 , 3888 , 3894 , 3900 , 3906 , 3912 , 3918 , 3924 , 3930 , 3936 , 3942 , 3948 , 3954 , 3960 , 3966 , 3972 , 3978 , 3984 , 3990 , 3996 , 4002 , 4008 , 4014 , 4020 , 4026 , 4032 , 4038 , 4044 , 4050 , 4056 , 4062 , 4068 , 4074 , 4080 , 4086 , 4092 , 4098 , 4104 , 4110 , 4116 , 4122 , 4128 , 4134 , 4140 , 4146 , 4152 , 4158 , 4164 , 4170 , 4176 , 4182 , 4188 , 4194 , 4200 , 4206 , 4212 , 4218 , 4224 , 4230 , 4236 , 4242 , 4248 , 4254 , 4260 , 4266 , 4272 , 4278 , 4284 , 4290 , 4296 , 4302 , 4308 , 4314 , 4320 , 4326 , 4332 , 4338 , 4344 , 4350 , 4356 , 4362 , 4368 , 4374 , 4380 , 4386 , 4392 , 4398 , 4404 , 4410 , 4416 , 4422 , 4428 , 4434 , 4440 , 4446 , 4452 , 4458 , 4464 , 4470 , 4476 , 4482 , 4488 , 4494 , 4500 , 4506 , 4512 , 4518 , 4524 , 4530 , 4536 , 4542 , 4548 , 4554 , 4560 , 4566 , 4572 , 4578 , 4584 , 4590 , 4596 , 4602 , 4608 , 4614 , 4620 , 4626 , 4632 , 4638 , 4644 , 4650 , 4656 , 4662 , 4668 , 4674 , 4680 , 4686 , 4692 , 4698 , 4704 , 4710 , 4716 , 4722 , 4728 , 4734 , 4740 , 4746 , 4752 , 4758 , 4764 , 4770 , 4776 , 4782 , 4788 , 4794 , 4800 , 4806 , 4812 , 4818 , 4824 , 4830 , 4836 , 4842 , 4848 , 4854 , 4860 , 4866 , 4872 , 4878 , 4884 , 4890 , 4896 , 4902 , 4908 , 4914 , 4920 , 4926 , 4932 , 4938 , 4944 , 4950 , 4956 , 4962 , 4968 , 4974 , 4980 , 4986 , 4992 , 4998 , 5004 , 5010 , 5016 , 5022 , 5028 , 5034 , 5040 , 5046 , 5052 , 5058 , 5064 , 5070 , 5076 , 5082 , 5088 , 5094 , 5100 , 5106 , 5112 , 5118 , 5124 , 5130 , 5136 , 5142 , 5148 , 5154 , 5160 , 5166 , 5172 , 5178 , 5184 , 5190 , 5196 , 5202 , 5208 , 5214 , 5220 , 5226 , 5232 , 5238 , 5244 , 5250 , 5256 , 5262 , 5268 , 5274 , 5280 , 5286 , 5292 , 5298 , 5304 , 5310 , 5316 , 5322 , 5328 , 5334 , 5340 , 5346 , 5352 , 5358 , 5364 , 5370 , 5376 , 5382 , 5388 , 5394 , 5400 , 5406 , 5412 , 5418 , 5424 , 5430 , 5436 , 5442 , 5448 , 5454 , 5460 , 5466 , 5472 , 5478 , 5484 , 5490 , 5496 , 5502 , 5508 , 5514 , 5520 , 5526 , 5532 , 5538 , 5544 , 5550 , 5556 , 5562 , 5568 , 5574 , 5580 , 5586 , 5592 , 5598 , 5604 , 5610 , 5616 , 5622 , 5628 , 5634 , 5640 , 5646 , 5652 , 5658 , 5664 , 5670 , 5676 , 5682 , 5688 , 5694 , 5700 , 5706 , 5712 , 5718 , 5724 , 5730 , 5736 , 5742 , 5748 , 5754 , 5760 , 5766 , 5772 , 5778 , 5784 , 5790 , 5796 , 5802 , 5808 , 5814 , 5820 , 5826 , 5832 , 5838 , 5844 , 5850 , 5856 , 5862 , 5868 , 5874 , 5880 , 5886 , 5892 , 5898 , 5904 , 5910 , 5916 , 5922 , 5928 , 5934 , 5940 , 5946 , 5952 , 5958 , 5964 , 5970 , 5976 , 5982 , 5988 , 5994 , 6000 , 6006 , 6012 , 6018 , 6024 , 6030 , 6036 , 6042 , 6048 , 6054 , 6060 , 6066 , 6072 , 6078 , 6084 , 6090 , 6096 , 6102 , 6108 , 6114 , 6120 , 6126 , 6132 , 6138 , 6144 , 6150 , 6156 , 6162 , 6168 , 6174 , 6180 , 6186 , 6192 , 6198 , 6204 , 6210 , 6216 , 6222 , 6228 , 6234 , 6240 , 6246 , 6252 , 6258 , 6264 , 6270 , 6276 , 6282 , 6288 , 6294 , 6300 , 6306 , 6312 , 6318 , 6324 , 6330 , 6336 , 6342 , 6348 , 6354 , 6360 , 6366 , 6372 , 6378 , 6384 , 6390 , 6396 , 6402 , 6408 , 6414 , 6420 , 6426 , 6432 , 6438 , 6444 , 6450 , 6456 , 6462 , 6468 , 6474 , 6480 , 6486 , 6492 , 6498 , 6504 , 6510 , 6516 , 6522 , 6528 , 6534 , 6540 , 6546 , 6552 , 6558 , 6564 , 6570 , 6576 , 6582 , 6588 , 6594 , 6600 , 6606 , 6612 , 6618 , 6624 , 6630 , 6636 , 6642 , 6648 , 6654 , 6660 , 6666 , 6672 , 6678 , 6684 , 6690 , 6696 , 6702 , 6708 , 6714 , 6720 , 6726 , 6732 , 6738 , 6744 , 6750 , 6756 , 6762 , 6768 , 6774 , 6780 , 6786 , 6792 , 6798 , 6804 , 6810 , 6816 , 6822 , 6828 , 6834 , 6840 , 6846 , 6852 , 6858 , 6864 , 6870 , 6876 , 6882 , 6888 , 6894 , 6900 , 6906 , 6912 , 6918 , 6924 , 6930 , 6936 , 6942 , 6948 , 6954 , 6960 , 6966 , 6972 , 6978 , 6984 , 6990 , 6996 , 7002 , 7008 , 7014 , 7020 , 7026 , 7032 , 7038 , 7044 , 7050 , 7056 , 7062 , 7068 , 7074 , 7080 , 7086 , 7092 , 7098 , 7104 , 7110 , 7116 , 7122 , 7128 , 7134 , 7140 , 7146 , 7152 , 7158 , 7164 , 7170 , 7176 , 7182 , 7188 , 7194 , 7200 , 7206 , 7212 , 7218 , 7224 , 7230 , 7236 , 7242 , 7248 , 7254 , 7260 , 7266 , 7272 , 7278 , 7284 , 7290 , 7296 , 7302 , 7308 , 7314 , 7320 , 7326 , 7332 , 7338 , 7344 , 7350 , 7356 , 7362 , 7368 , 7374 , 7380 , 7386 , 7392 , 7398 , 7404 , 7410 , 7416 , 7422 , 7428 , 7434 , 7440 , 7446 , 7452 , 7458 , 7464 , 7470 , 7476 , 7482 , 7488 , 7494 , 7500 , 7506 , 7512 , 7518 , 7524 , 7530 , 7536 , 7542 , 7548 , 7554 , 7560 , 7566 , 7572 , 7578 , 7584 , 7590 , 7596 , 7602 , 7608 , 7614 , 7620 , 7626 , 7632 , 7638 , 7644 , 7650 , 7656 , 7662 , 7668 , 7674 , 7680 , 7686 , 7692 , 7698 , 7704 , 7710 , 7716 , 7722 , 7728 , 7734 , 7740 , 7746 , 7752 , 7758 , 7764 , 7770 , 7776 , 7782 , 7788 , 7794 , 7800 , 7806 , 7812 , 7818 , 7824 , 7830 , 7836 , 7842 , 7848 , 7854 , 7860 , 7866 , 7872 , 7878 , 7884 , 7890 , 7896 , 7902 , 7908 , 7914 , 7920 , 7926 , 7932 , 7938 , 7944 , 7950 , 7956 , 7962 , 7968 , 7974 , 7980 , 7986 , 7992 , 7998 , 8004 , 8010 , 8016 , 8022 , 8028 , 8034 , 8040 , 8046 , 8052 , 8058 , 8064 , 8070 , 8076 , 8082 , 8088 , 8094 , 8100 , 8106 , 8112 , 8118 , 8124 , 8130 , 8136 , 8142 , 8148 , 8154 , 8160 , 8166 , 8172 , 8178 , 8184 , 8190 , 8196 , 8202 , 8208 , 8214 , 8220 , 8226 , 8232 , 8238 , 8244 , 8250 , 8256 , 8262 , 8268 , 8274 , 8280 , 8286 , 8292 , 8298 , 8304 , 8310 , 8316 , 8322 , 8328 , 8334 , 8340 , 8346 , 8352 , 8358 , 8364 , 8370 , 8376 , 8382 , 8388 , 8394 , 8400 , 8406 , 8412 , 8418 , 8424 , 8430 , 8436 , 8442 , 8448 , 8454 , 8460 , 8466 , 8472 , 8478 , 8484 , 8490 , 8496 , 8502 , 8508 , 8514 , 8520 , 8526 , 8532 , 8538 , 8544 , 8550 , 8556 , 8562 , 8568 , 8574 , 8580 , 8586 , 8592 , 8598 , 8604 , 8610 , 8616 , 8622 , 8628 , 8634 , 8640 , 8646 , 8652 , 8658 , 8664 , 8670 , 8676 , 8682 , 8688 , 8694 , 8700 , 8706 , 8712 , 8718 , 8724 , 8730 , 8736 , 8742 , 8748 , 8754 , 8760 , 8766 , 8772 , 8778 , 8784 , 8790 , 8796 , 8802 , 8808 , 8814 , 8820 , 8826 , 8832 , 8838 , 8844 , 8850 , 8856 , 8862 , 8868 , 8874 , 8880 , 8886 , 8892 , 8898 , 8904 , 8910 , 8916 , 8922 , 8928 , 8934 , 8940 , 8946 , 8952 , 8958 , 8964 , 8970 , 8976 , 8982 , 8988 , 8994 , 9000 , 9006 , 9012 , 9018 , 9024 , 9030 , 9036 , 9042 , 9048 , 9054 , 9060 , 9066 , 9072 , 9078 , 9084 , 9090 , 9096 , 9102 , 9108 , 9114 , 9120 , 9126 , 9132 , 9138 , 9144 , 9150 , 9156 , 9162 , 9168 , 9174 , 9180 , 9186 , 9192 , 9198 , 9204 , 9210 , 9216 , 9222 , 9228 , 9234 , 9240 , 9246 , 9252 , 9258 , 9264 , 9270 , 9276 , 9282 , 9288 , 9294 , 9300 , 9306 , 9312 , 9318 , 9324 , 9330 , 9336 , 9342 , 9348 , 9354 , 9360 , 9366 , 9372 , 9378 , 9384 , 9390 , 9396 , 9402 , 9408 , 9414 , 9420 , 9426 , 9432 , 9438 , 9444 , 9450 , 9456 , 9462 , 9468 , 9474 , 9480 , 9486 , 9492 , 9498 , 9504 , 9510 , 9516 , 9522 , 9528 , 9534 , 9540 , 9546 , 9552 , 9558 , 9564 , 9570 , 9576 , 9582 , 9588 , 9594 , 9600 , 9606 , 9612 , 9618 , 9624 , 9630 , 9636 , 9642 , 9648 , 9654 , 9660 , 9666 , 9672 , 9678 , 9684 , 9690 , 9696 , 9702 , 9708 , 9714 , 9720 , 9726 , 9732 , 9738 , 9744 , 9750 , 9756 , 9762 , 9768 , 9774 , 9780 , 9786 , 9792 , 9798 , 9804 , 9810 , 9816 , 9822 , 9828 , 9834 , 9840 , 9846 , 9852 , 9858 , 9864 , 9870 , 9876 , 9882 , 9888 , 9894 , 9900 , 9906 , 9912 , 9918 , 9924 , 9930 , 9936 , 9942 , 9948 , 9954 , 9960 , 9966 , 9972 , 9978 , 9984 , 9990 , 9996 , 10002 , 10008 , 10014 , 10020 , 10026 , 10032 , 10038 , 10044 , 10050 , 10056 , 10062 , 10068 , 10074 , 10080 , 10086 , 10092 , 10098 , 10104 , 10110 , 10116 , 10122 , 10128 , 10134 , 10140 , 10146 , 10152 , 10158 , 10164 , 10170 , 10176 , 10182 , 10188 , 10194 , 10200 , 10206 , 10212 , 10218 , 10224 , 10230 , 10236 , 10242 , 10248 , 10254 , 10260 , 10266 , 10272 , 10278 , 10284 , 10290 , 10296 , 10302 , 10308 , 10314 , 10320 , 10326 , 10332 , 10338 , 10344 , 10350 , 10356 , 10362 , 10368 , 10374 , 10380 , 10386 , 10392 , 10398 , 10404 , 10410 , 10416 , 10422 , 10428 , 10434 , 10440 , 10446 , 10452 , 10458 , 10464 , 10470 , 10476 , 10482 , 10488 , 10494 , 10500 , 10506 , 10512 , 10518 , 10524 , 10530 , 10536 , 10542 , 10548 , 10554 , 10560 , 10566 , 10572 , 10578 , 10584 , 10590 , 10596 , 10602 , 10608 , 10614 , 10620 , 10626 , 10632 , 10638 , 10644 , 10650 , 10656 , 10662 , 10668 , 10674 , 10680 , 10686 , 10692 , 10698 , 10704 , 10710 , 10716 , 10722 , 10728 , 10734 , 10740 , 10746 , 10752 , 10758 , 10764 , 10770 , 10776 , 10782 , 10788 , 10794 , 10800 , 10806 , 10812 , 10818 , 10824 , 10830 , 10836 , 10842 , 10848 , 10854 , 10860 , 10866 , 10872 , 10878 , 10884 , 10890 , 10896 , 10902 , 10908 , 10914 , 10920 , 10926 , 10932 , 10938 , 10944 , 10950 , 10956 , 10962 , 10968 , 10974 , 10980 , 10986 , 10992 , 10998 , 11004 , 11010 , 11016 , 11022 , 11028 , 11034 , 11040 , 11046 , 11052 , 11058 , 11064 , 11070 , 11076 , 11082 , 11088 , 11094 , 11100 , 11106 , 11112 , 11118 , 11124 , 11130 , 11136 , 11142 , 11148 , 11154 , 11160 , 11166 , 11172 , 11178 , 11184 , 11190 , 11196 , 11202 , 11208 , 11214 , 11220 , 11226 , 11232 , 11238 , 11244 , 11250 , 11256 , 11262 , 11268 , 11274 , 11280 , 11286 , 11292 , 11298 , 11304 , 11310 , 11316 , 11322 , 11328 , 11334 , 11340 , 11346 , 11352 , 11358 , 11364 , 11370 , 11376 , 11382 , 11388 , 11394 , 11400 , 11406 , 11412 , 11418 , 11424 , 11430 , 11436 , 11442 , 11448 , 11454 , 11460 , 11466 , 11472 , 11478 , 11484 , 11490 , 11496 , 11502 , 11508 , 11514 , 11520 , 11526 , 11532 , 11538 , 11544 , 11550 , 11556 , 11562 , 11568 , 11574 , 11580 , 11586 , 11592 , 11598 , 11604 , 11610 , 11616 , 11622 , 11628 , 11634 , 11640 , 11646 , 11652 , 11658 , 11664 , 11670 , 11676 , 11682 , 11688 , 11694 , 11700 , 11706 , 11712 , 11718 , 11724 , 11730 , 11736 , 11742 , 11748 , 11754 , 11760 , 11766 , 11772 , 11778 , 11784 , 11790 , 11796 , 11802 , 11808 , 11814 , 11820 , 11826 , 11832 , 11838 , 11844 , 11850 , 11856 , 11862 , 11868 , 11874 , 11880 , 11886 , 11892 , 11898 , 11904 , 11910 , 11916 , 11922 , 11928 , 11934 , 11940 , 11946 , 11952 , 11958 , 11964 , 11970 , 11976 , 11982 , 11988 , 11994 , 12000 , 12006 , 12012 , 12018 , 12024 , 12030 , 12036 , 12042 , 12048 , 12054 , 12060 , 12066 , 12072 , 12078 , 12084 , 12090 , 12096 , 12102 , 12108 , 12114 , 12120 , 12126 , 12132 , 12138 , 12144 , 12150 , 12156 , 12162 , 12168 , 12174 , 12180 , 12186 , 12192 , 12198 , 12204 , 12210 , 12216 , 12222 , 12228 , 12234 , 12240 , 12246 , 12252 , 12258 , 12264 , 12270 , 12276 , 12282 , 12288 , 12294 , 12300 , 12306 , 12312 , 12318 , 12324 , 12330 , 12336 , 12342 , 12348 , 12354 , 12360 , 12366 , 12372 , 12378 , 12384 , 12390 , 12396 , 12402 , 12408 , 12414 , 12420 , 12426 , 12432 , 12438 , 12444 , 12450 , 12456 , 12462 , 12468 , 12474 , 12480 , 12486 , 12492 , 12498 , 12504 , 12510 , 12516 , 12522 , 12528 , 12534 , 12540 , 12546 , 12552 , 12558 , 12564 , 12570 , 12576 , 12582 , 12588 , 12594 , 12600 , 12606 , 12612 , 12618 , 12624 , 12630 , 12636 , 12642 , 12648 , 12654 , 12660 , 12666 , 12672 , 12678 , 12684 , 12690 , 12696 , 12702 , 12708 , 12714 , 12720 , 12726 , 12732 , 12738 , 12744 , 12750 , 12756 , 12762 , 12768 , 12774 , 12780 , 12786 , 12792 , 12798 , 12804 , 12810 , 12816 , 12822 , 12828 , 12834 , 12840 , 12846 , 12852 , 12858 , 12864 , 12870 , 12876 , 12882 , 12888 , 12894 , 12900 , 12906 , 12912 , 12918 , 12924 , 12930 , 12936 , 12942 , 12948 , 12954 , 12960 , 12966 , 12972 , 12978 , 12984 , 12990 , 12996 , 13002 , 13008 , 13014 , 13020 , 13026 , 13032 , 13038 , 13044 , 13050 , 13056 , 13062 , 13068 , 13074 , 13080 , 13086 , 13092 , 13098 , 13104 , 13110 , 13116 , 13122 , 13128 , 13134 , 13140 , 13146 , 13152 , 13158 , 13164 , 13170 , 13176 , 13182 , 13188 , 13194 , 13200 , 13206 , 13212 , 13218 , 13224 , 13230 , 13236 , 13242 , 13248 , 13254 , 13260 , 13266 , 13272 , 13278 , 13284 , 13290 , 13296 , 13302 , 13308 , 13314 , 13320 , 13326 , 13332 , 13338 , 13344 , 13350 , 13356 , 13362 , 13368 , 13374 , 13380 , 13386 , 13392 , 13398 , 13404 , 13410 , 13416 , 13422 , 13428 , 13434 , 13440 , 13446 , 13452 , 13458 , 13464 , 13470 , 13476 , 13482 , 13488 , 13494 , 13500 , 13506 , 13512 , 13518 , 13524 , 13530 , 13536 , 13542 , 13548 , 13554 , 13560 , 13566 , 13572 , 13578 , 13584 , 13590 , 13596 , 13602 , 13608 , 13614 , 13620 , 13626 , 13632 , 13638 , 13644 , 13650 , 13656 , 13662 , 13668 , 13674 , 13680 , 13686 , 13692 , 13698 , 13704 , 13710 , 13716 , 13722 , 13728 , 13734 , 13740 , 13746 , 13752 , 13758 , 13764 , 13770 , 13776 , 13782 , 13788 , 13794 , 13800 , 13806 , 13812 , 13818 , 13824 , 13830 , 13836 , 13842 , 13848 , 13854 , 13860 , 13866 , 13872 , 13878 , 13884 , 13890 , 13896 , 13902 , 13908 , 13914 , 13920 , 13926 , 13932 , 13938 , 13944 , 13950 , 13956 , 13962 , 13968 , 13974 , 13980 , 13986 , 13992 , 13998 , 14004 , 14010 , 14016 , 14022 , 14028 , 14034 , 14040 , 14046 , 14052 , 14058 , 14064 , 14070 , 14076 , 14082 , 14088 , 14094 , 14100 , 14106 , 14112 , 14118 , 14124 , 14130 , 14136 , 14142 , 14148 , 14154 , 14160 , 14166 , 14172 , 14178 , 14184 , 14190 , 14196 , 14202 , 14208 , 14214 , 14220 , 14226 , 14232 , 14238 , 14244 , 14250 , 14256 , 14262 , 14268 , 14274 , 14280 , 14286 , 14292 , 14298 , 14304 , 14310 , 14316 , 14322 , 14328 , 14334 , 14340 , 14346 , 14352 , 14358 , 14364 , 14370 , 14376 , 14382 , 14388 , 14394 , 14400 , 14406 , 14412 , 14418 , 14424 , 14430 , 14436 , 14442 , 14448 , 14454 , 14460 , 14466 , 14472 , 14478 , 14484 , 14490 , 14496 , 14502 , 14508 , 14514 , 14520 , 14526 , 14532 , 14538 , 14544 , 14550 , 14556 , 14562 , 14568 , 14574 , 14580 , 14586 , 14592 , 14598 , 14604 , 14610 , 14616 , 14622 , 14628 , 14634 , 14640 , 14646 , 14652 , 14658 , 14664 , 14670 , 14676 , 14682 , 14688 , 14694 , 14700 , 14706 , 14712 , 14718 , 14724 , 14730 , 14736 , 14742 , 14748 , 14754 , 14760 , 14766 , 14772 , 14778 , 14784 , 14790 , 14796 , 14802 , 14808 , 14814 , 14820 , 14826 , 14832 , 14838 , 14844 , 14850 , 14856 , 14862 , 14868 , 14874 , 14880 , 14886 , 14892 , 14898 , 14904 , 14910 , 14916 , 14922 , 14928 , 14934 , 14940 , 14946 , 14952 , 14958 , 14964 , 14970 , 14976 , 14982 , 14988 , 14994 , 15000 , 15006 , 15012 , 15018 , 15024 , 15030 , 15036 , 15042 , 15048 , 15054 , 15060 , 15066 , 15072 , 15078 , 15084 , 15090 , 15096 , 15102 , 15108 , 15114 , 15120 , 15126 , 15132 , 15138 , 15144 , 15150 , 15156 , 15162 , 15168 , 15174 , 15180 , 15186 , 15192 , 15198 , 15204 , 15210 , 15216 , 15222 , 15228 , 15234 , 15240 , 15246 , 15252 , 15258 , 15264 , 15270 , 15276 , 15282 , 15288 , 15294 , 15300 , 15306 , 15312 , 15318 , 15324 , 15330 , 15336 , 15342 , 15348 , 15354 , 15360 , 15366 , 15372 , 15378 , 15384 , 15390 , 15396 , 15402 , 15408 , 15414 , 15420 , 15426 , 15432 , 15438 , 15444 , 15450 , 15456 , 15462 , 15468 , 15474 , 15480 , 15486 , 15492 , 15498 , 15504 , 15510 , 15516 , 15522 , 15528 , 15534 , 15540 , 15546 , 15552 , 15558 , 15564 , 15570 , 15576 , 15582 , 15588 , 15594 , 15600 , 15606 , 15612 , 15618 , 15624 , 15630 , 15636 , 15642 , 15648 , 15654 , 15660 , 15666 , 15672 , 15678 , 15684 , 15690 , 15696 , 15702 , 15708 , 15714 , 15720 , 15726 , 15732 , 15738 , 15744 , 15750 , 15756 , 15762 , 15768 , 15774 , 15780 , 15786 , 15792 , 15798 , 15804 , 15810 , 15816 , 15822 , 15828 , 15834 , 15840 , 15846 , 15852 , 15858 , 15864 , 15870 , 15876 , 15882 , 15888 , 15894 , 15900 , 15906 , 15912 , 15918 , 15924 , 15930 , 15936 , 15942 , 15948 , 15954 , 15960 , 15966 , 15972 , 15978 , 15984 , 15990 , 15996 , 16002 , 16008 , 16014 , 16020 , 16026 , 16032 , 16038 , 16044 , 16050 , 16056 , 16062 , 16068 , 16074 , 16080 , 16086 , 16092 , 16098 , 16104 , 16110 , 16116 , 16122 , 16128 , 16134 , 16140 , 16146 , 16152 , 16158 , 16164 , 16170 , 16176 , 16182 , 16188 , 16194 , 16200 , 16206 , 16212 , 16218 , 16224 , 16230 , 16236 , 16242 , 16248 , 16254 , 16260 , 16266 , 16272 , 16278 , 16284 , 16290 , 16296 , 16302 , 16308 , 16314 , 16320 , 16326 , 16332 , 16338 , 16344 , 16350 , 16356 , 16362 , 16368 , 16374 , 16380 , 16386 , 16392 , 16398 , 16404 , 16410 , 16416 , 16422 , 16428 , 16434 , 16440 , 16446 , 16452 , 16458 , 16464 , 16470 , 16476 , 16482 , 16488 , 16494 , 16500 , 16506 , 16512 , 16518 , 16524 , 16530 , 16536 , 16542 , 16548 , 16554 , 16560 , 16566 , 16572 , 16578 , 16584 , 16590 , 16596 , 16602 , 16608 , 16614 , 16620 , 16626 , 16632 , 16638 , 16644 , 16650 , 16656 , 16662 , 16668 , 16674 , 16680 , 16686 , 16692 , 16698 , 16704 , 16710 , 16716 , 16722 , 16728 , 16734 , 16740 , 16746 , 16752 , 16758 , 16764 , 16770 , 16776 , 16782 , 16788 , 16794 , 16800 , 16806 , 16812 , 16818 , 16824 , 16830 , 16836 , 16842 , 16848 , 16854 , 16860 , 16866 , 16872 , 16878 , 16884 , 16890 , 16896 , 16902 , 16908 , 16914 , 16920 , 16926 , 16932 , 16938 , 16944 , 16950 , 16956 , 16962 , 16968 , 16974 , 16980 , 16986 , 16992 , 16998 , 17004 , 17010 , 17016 , 17022 , 17028 , 17034 , 17040 , 17046 , 17052 , 17058 , 17064 , 17070 , 17076 , 17082 , 17088 , 17094 , 17100 , 17106 , 17112 , 17118 , 17124 , 17130 , 17136 , 17142 , 17148 , 17154 , 17160 , 17166 , 17172 , 17178 , 17184 , 17190 , 17196 , 17202 , 17208 , 17214 , 17220 , 17226 , 17232 , 17238 , 17244 , 17250 , 17256 , 17262 , 17268 , 17274 , 17280 , 17286 , 17292 , 17298 , 17304 , 17310 , 17316 , 17322 , 17328 , 17334 , 17340 , 17346 , 17352 , 17358 , 17364 , 17370 , 17376 , 17382 , 17388 , 17394 , 17400 , 17406 , 17412 , 17418 , 17424 , 17430 , 17436 , 17442 , 17448 , 17454 , 17460 , 17466 , 17472 , 17478 , 17484 , 17490 , 17496 , 17502 , 17508 , 17514 , 17520 , 17526 , 17532 , 17538 , 17544 , 17550 , 17556 , 17562 , 17568 , 17574 , 17580 , 17586 , 17592 , 17598 , 17604 , 17610 , 17616 , 17622 , 17628 , 17634 , 17640 , 17646 , 17652 , 17658 , 17664 , 17670 , 17676 , 17682 , 17688 , 17694 , 17700 , 17706 , 17712 , 17718 , 17724 , 17730 , 17736 , 17742 , 17748 , 17754 , 17760 , 17766 , 17772 , 17778 , 17784 , 17790 , 17796 , 17802 , 17808 , 17814 , 17820 , 17826 , 17832 , 17838 , 17844 , 17850 , 17856 , 17862 , 17868 , 17874 , 17880 , 17886 , 17892 , 17898 , 17904 , 17910 , 17916 , 17922 , 17928 , 17934 , 17940 , 17946 , 17952 , 17958 , 17964 , 17970 , 17976 , 17982 , 17988 , 17994 , 18000 , 18006 , 18012 , 18018 , 18024 , 18030 , 18036 , 18042 , 18048 , 18054 , 18060 , 18066 , 18072 , 18078 , 18084 , 18090 , 18096 , 18102 , 18108 , 18114 , 18120 , 18126 , 18132 , 18138 , 18144 , 18150 , 18156 , 18162 , 18168 , 18174 , 18180 , 18186 , 18192 , 18198 , 18204 , 18210 , 18216 , 18222 , 18228 , 18234 , 18240 , 18246 , 18252 , 18258 , 18264 , 18270 , 18276 , 18282 , 18288 , 18294 , 18300 , 18306 , 18312 , 18318 , 18324 , 18330 , 18336 , 18342 , 18348 , 18354 , 18360 , 18366 , 18372 , 18378 , 18384 , 18390 , 18396 , 18402 , 18408 , 18414 , 18420 , 18426 , 18432 , 18438 , 18444 , 18450 , 18456 , 18462 , 18468 , 18474 , 18480 , 18486 , 18492 , 18498 , 18504 , 18510 , 18516 , 18522 , 18528 , 18534 , 18540 , 18546 , 18552 , 18558 , 18564 , 18570 , 18576 , 18582 , 18588 , 18594 , 18600 , 18606 , 18612 , 18618 , 18624 , 18630 , 18636 , 18642 , 18648 , 18654 , 18660 , 18666 , 18672 , 18678 , 18684 , 18690 , 18696 , 18702 , 18708 , 18714 , 18720 , 18726 , 18732 , 18738 , 18744 , 18750 , 18756 , 18762 , 18768 , 18774 , 18780 , 18786 , 18792 , 18798 , 18804 , 18810 , 18816 , 18822 , 18828 , 18834 , 18840 , 18846 , 18852 , 18858 , 18864 , 18870 , 18876 , 18882 , 18888 , 18894 , 18900 , 18906 , 18912 , 18918 , 18924 , 18930 , 18936 , 18942 , 18948 , 18954 , 18960 , 18966 , 18972 , 18978 , 18984 , 18990 , 18996 , 19002 , 19008 , 19014 , 19020 , 19026 , 19032 , 19038 , 19044 , 19050 , 19056 , 19062 , 19068 , 19074 , 19080 , 19086 , 19092 , 19098 , 19104 , 19110 , 19116 , 19122 , 19128 , 19134 , 19140 , 19146 , 19152 , 19158 , 19164 , 19170 , 19176 , 19182 , 19188 , 19194 , 19200 , 19206 , 19212 , 19218 , 19224 , 19230 , 19236 , 19242 , 19248 , 19254 , 19260 , 19266 , 19272 , 19278 , 19284 , 19290 , 19296 , 19302 , 19308 , 19314 , 19320 , 19326 , 19332 , 19338 , 19344 , 19350 , 19356 , 19362 , 19368 , 19374 , 19380 , 19386 , 19392 , 19398 , 19404 , 19410 , 19416 , 19422 , 19428 , 19434 , 19440 , 19446 , 19452 , 19458 , 19464 , 19470 , 19476 , 19482 , 19488 , 19494 , 19500 , 19506 , 19512 , 19518 , 19524 , 19530 , 19536 , 19542 , 19548 , 19554 , 19560 , 19566 , 19572 , 19578 , 19584 , 19590 , 19596 , 19602 , 19608 , 19614 , 19620 , 19626 , 19632 , 19638 , 19644 , 19650 , 19656 , 19662 , 19668 , 19674 , 19680 , 19686 , 19692 , 19698 , 19704 , 19710 , 19716 , 19722 , 19728 , 19734 , 19740 , 19746 , 19752 , 19758 , 19764 , 19770 , 19776 , 19782 , 19788 , 19794 , 19800 , 19806 , 19812 , 19818 , 19824 , 19830 , 19836 , 19842 , 19848 , 19854 , 19860 , 19866 , 19872 , 19878 , 19884 , 19890 , 19896 , 19902 , 19908 , 19914 , 19920 , 19926 , 19932 , 19938 , 19944 , 19950 , 19956 , 19962 , 19968 , 19974 , 19980 , 19986 , 19992 , 19998 , 20004 , 20010 , 20016 , 20022 , 20028 , 20034 , 20040 , 20046 , 20052 , 20058 , 20064 , 20070 , 20076 , 20082 , 20088 , 20094 , 20100 , 20106 , 20112 , 20118 , 20124 , 20130 , 20136 , 20142 , 20148 , 20154 , 20160 , 20166 , 20172 , 20178 , 20184 , 20190 , 20196 , 20202 , 20208 , 20214 , 20220 , 20226 , 20232 , 20238 , 20244 , 20250 , 20256 , 20262 , 20268 , 20274 , 20280 , 20286 , 20292 , 20298 , 20304 , 20310 , 20316 , 20322 , 20328 , 20334 , 20340 , 20346 , 20352 , 20358 , 20364 , 20370 , 20376 , 20382 , 20388 , 20394 , 20400 , 20406 , 20412 , 20418 , 20424 , 20430 , 20436 , 20442 , 20448 , 20454 , 20460 , 20466 , 20472 , 20478 , 20484 , 20490 , 20496 , 20502 , 20508 , 20514 , 20520 , 20526 , 20532 , 20538 , 20544 , 20550 , 20556 , 20562 , 20568 , 20574 , 20580 , 20586 , 20592 , 20598 , 20604 , 20610 , 20616 , 20622 , 20628 , 20634 , 20640 , 20646 , 20652 , 20658 , 20664 , 20670 , 20676 , 20682 , 20688 , 20694 , 20700 , 20706 , 20712 , 20718 , 20724 , 20730 , 20736 , 20742 , 20748 , 20754 , 20760 , 20766 , 20772 , 20778 , 20784 , 20790 , 20796 , 20802 , 20808 , 20814 , 20820 , 20826 , 20832 , 20838 , 20844 , 20850 , 20856 , 20862 , 20868 , 20874 , 20880 , 20886 , 20892 , 20898 , 20904 , 20910 , 20916 , 20922 , 20928 , 20934 , 20940 , 20946 , 20952 , 20958 , 20964 , 20970 , 20976 , 20982 , 20988 , 20994 , 21000 , 21006 , 21012 , 21018 , 21024 , 21030 , 21036 , 21042 , 21048 , 21054 , 21060 , 21066 , 21072 , 21078 , 21084 , 21090 , 21096 , 21102 , 21108 , 21114 , 21120 , 21126 , 21132 , 21138 , 21144 , 21150 , 21156 , 21162 , 21168 , 21174 , 21180 , 21186 , 21192 , 21198 , 21204 , 21210 , 21216 , 21222 , 21228 , 21234 , 21240 , 21246 , 21252 , 21258 , 21264 , 21270 , 21276 , 21282 , 21288 , 21294 , 21300 , 21306 , 21312 , 21318 , 21324 , 21330 , 21336 , 21342 , 21348 , 21354 , 21360 , 21366 , 21372 , 21378 , 21384 , 21390 , 21396 , 21402 , 21408 , 21414 , 21420 , 21426 , 21432 , 21438 , 21444 , 21450 , 21456 , 21462 , 21468 , 21474 , 21480 , 21486 , 21492 , 21498 , 21504 , 21510 , 21516 , 21522 , 21528 , 21534 , 21540 , 21546 , 21552 , 21558 , 21564 , 21570 , 21576 , 21582 , 21588 , 21594 , 21600 , 21606 , 21612 , 21618 , 21624 , 21630 , 21636 , 21642 , 21648 , 21654 , 21660 , 21666 , 21672 , 21678 , 21684 , 21690 , 21696 , 21702 , 21708 , 21714 , 21720 , 21726 , 21732 , 21738 , 21744 , 21750 , 21756 , 21762 , 21768 , 21774 , 21780 , 21786 , 21792 , 21798 , 21804 , 21810 , 21816 , 21822 , 21828 , 21834 , 21840 , 21846 , 21852 , 21858 , 21864 , 21870 , 21876 , 21882 , 21888 , 21894 , 21900 , 21906 , 21912 , 21918 , 21924 , 21930 , 21936 , 21942 , 21948 , 21954 , 21960 , 21966 , 21972 , 21978 , 21984 , 21990 , 21996 , 22002 , 22008 , 22014 , 22020 , 22026 , 22032 , 22038 , 22044 , 22050 , 22056 , 22062 , 22068 , 22074 , 22080 , 22086 , 22092 , 22098 , 22104 , 22110 , 22116 , 22122 , 22128 , 22134 , 22140 , 22146 , 22152 , 22158 , 22164 , 22170 , 22176 , 22182 , 22188 , 22194 , 22200 , 22206 , 22212 , 22218 , 22224 , 22230 , 22236 , 22242 , 22248 , 22254 , 22260 , 22266 , 22272 , 22278 , 22284 , 22290 , 22296 , 22302 , 22308 , 22314 , 22320 , 22326 , 22332 , 22338 , 22344 , 22350 , 22356 , 22362 , 22368 , 22374 , 22380 , 22386 , 22392 , 22398 , 22404 , 22410 , 22416 , 22422 , 22428 , 22434 , 22440 , 22446 , 22452 , 22458 , 22464 , 22470 , 22476 , 22482 , 22488 , 22494 , 22500 , 22506 , 22512 , 22518 , 22524 , 22530 , 22536 , 22542 , 22548 , 22554 , 22560 , 22566 , 22572 , 22578 , 22584 , 22590 , 22596 , 22602 , 22608 , 22614 , 22620 , 22626 , 22632 , 22638 , 22644 , 22650 , 22656 , 22662 , 22668 , 22674 , 22680 , 22686 , 22692 , 22698 , 22704 , 22710 , 22716 , 22722 , 22728 , 22734 , 22740 , 22746 , 22752 , 22758 , 22764 , 22770 , 22776 , 22782 , 22788 , 22794 , 22800 , 22806 , 22812 , 22818 , 22824 , 22830 , 22836 , 22842 , 22848 , 22854 , 22860 , 22866 , 22872 , 22878 , 22884 , 22890 , 22896 , 22902 , 22908 , 22914 , 22920 , 22926 , 22932 , 22938 , 22944 , 22950 , 22956 , 22962 , 22968 , 22974 , 22980 , 22986 , 22992 , 22998 , 23004 , 23010 , 23016 , 23022 , 23028 , 23034 , 23040 , 23046 , 23052 , 23058 , 23064 , 23070 , 23076 , 23082 , 23088 , 23094 , 23100 , 23106 , 23112 , 23118 , 23124 , 23130 , 23136 , 23142 , 23148 , 23154 , 23160 , 23166 , 23172 , 23178 , 23184 , 23190 , 23196 , 23202 , 23208 , 23214 , 23220 , 23226 , 23232 , 23238 , 23244 , 23250 , 23256 , 23262 , 23268 , 23274 , 23280 , 23286 , 23292 , 23298 , 23304 , 23310 , 23316 , 23322 , 23328 , 23334 , 23340 , 23346 , 23352 , 23358 , 23364 , 23370 , 23376 , 23382 , 23388 , 23394 , 23400 , 23406 , 23412 , 23418 , 23424 , 23430 , 23436 , 23442 , 23448 , 23454 , 23460 , 23466 , 23472 , 23478 , 23484 , 23490 , 23496 , 23502 , 23508 , 23514 , 23520 , 23526 , 23532 , 23538 , 23544 , 23550 , 23556 , 23562 , 23568 , 23574 , 23580 , 23586 , 23592 , 23598 , 23604 , 23610 , 23616 , 23622 , 23628 , 23634 , 23640 , 23646 , 23652 , 23658 , 23664 , 23670 , 23676 , 23682 , 23688 , 23694 , 23700 , 23706 , 23712 , 23718 , 23724 , 23730 , 23736 , 23742 , 23748 , 23754 , 23760 , 23766 , 23772 , 23778 , 23784 , 23790 , 23796 , 23802 , 23808 , 23814 , 23820 , 23826 , 23832 , 23838 , 23844 , 23850 , 23856 , 23862 , 23868 , 23874 , 23880 , 23886 , 23892 , 23898 , 23904 , 23910 , 23916 , 23922 , 23928 , 23934 , 23940 , 23946 , 23952 , 23958 , 23964 , 23970 , 23976 , 23982 , 23988 , 23994 , 24000 . You're welcome, I'm sure.
What is 4635 plus 5463?
10098
How far is us from Britain?
10098 miles
What are the release dates for One Life to Live - 1968 1-10098?
One Life to Live - 1968 1-10098 was released on: USA: 9 January 2008
What are the release dates for Days of Our Lives - 1965 1-10098?
Days of Our Lives - 1965 1-10098 was released on: USA: July 2005 Belgium: 30 December 2009
What is the Club Penguin's gift card code?
7289-8900-10098-8890
What is the value of an H. Pieper single shot .32 rimfire rifle serial 10098 and when was it made?
10-100 USD; @ turn of the century give or take a few decades.
Who has more franchise wins - the Mets or the Phillies?
According to Baseball Reference, through the 2008 season the Phillies franchise record is 8945-10098 and the Mets franchise record is 3585-3889. if you are looking to find out which team is better, you must factor in the fact that the phillies have been around for 125 years and just won their 2nd championship in 2008. and the mets have been around for 46 years and have 2 championships also.
How many times have the Philadelphia Phillies made the Postseason?
The Philadelphia Phillies have reached the Postseason 13 times as of 20111. 1915 - Lost World Series (BOS 1-4)2. 1950 - Lost World Series (NYY 0-4)3. 1976 - Lost NLCS (CIN 0-3)4. 1977 - Lost NLCS (LA 1-3)5. 1978 - Lost NLCS (LA 1-3)6. 1980 - Won World Series (KC 4-2)7. 1983 - Lost World Series (BAL 1-4)8. 1993 - Lost World Series (TOR 2-4)9. 2007 - Lost NLDS (COL 0-3)10. 2008 - Won World Series (TB 4-1)11. 2009 - Lost World Series (NYY 2-4)12. 2010 - Lost NLCS (SF 2-4)13. 2011 - TBD
What are all the 5-digit multiples of 11?
-6
How would you work out the smallest surface area for a rectangular box with dimensions x plus y plus z equals 150cm?
This is a classic max min problem using Lagrange multipliers. We do this when we have a function of several variables that we want to maximize or minimize and a constraint. Now the equation for surface area of a box is the areas of all the sides added together Total Surface Area = 2(Areahxw) + 2(Areahxl) + 2(Areawxl) using x,y and z we have f(x,y,z) = 2(xy+xz+yz) we need the gradient of that which is <(partial derivative wrt x,), partial derivative wrt y,(partial derivative wrt z)> where wrt means with respect to and i am using <> for a vector. 2 = ∇f(x,y,z) remember that the gradient is a vector and is normal to the curve. now let g be the other function, the one we have constraints on. In this case x+y+z=150 so that sum is constant and we write g(x,y,z)=x+y+z-150=0 we know that ∇f(x,y,z)=2 now the gradient, ∇g(x,y,z) is <1,1,1> since the partial derivative of x+y+z-150 wrt to x is 1 etc. so we have 2=<1,1,1>λ in order for these to be equal, the components must be equal =λ/2<1,1,1> now we have several equations y+z=λ/2 x+z=λ/2 x+y=λ/2 x+y+z=150 so we have y+z=x+z so x=y we also have y+x=y+z so x=z this means x=z=y and using the last equation we have 3x=150 or x=50 so y=50 and z=50 the rectangular box must be 50x50x50 the surface area is 2(2500+2500+2500) check a few other values of x, y and z and see what surface area you get. Perhaps, 100x49x1? we've only got one solution we might be tempted to assume that these are the dimensions that will give the smallest surface area.. The method of Lagrange Multipliers will give a set of points that will either maximize or minimize a given function subject to the constraint, provided there actually are minimums or maximums. So the points 100,49,1 give us info if we found a max or a min 50x 50 x 50 box has a surface area of 15000 the 100x49x1 box has a surface area of 2(100x49+100x1+49x1)=10098 which is less than 15000 so we found a max not a min! since we have x+y+z=150 if one of them gets very small the others have to get very large to compensate, They cannot all get very big or they won't work with our constraint. So the fact that we have a max them seems to make sense. In others, take very small x and y say .01 each then z=149.98 we get a surface area of about 6 or so. (much less than 15000) So now we wonder, do we have a minim value? We looked at .01,.01,149,98 let's take that one more step. x=y=.001 z=150-.002=149.998 surface area is around 1/3 so it looks like we could keep making x and y smaller and smaller and the surface area would continue to shrink. So no matter what values you give me for x and y and z, I can find a box with smaller surface area. remember that a zero derivative may mean a max or min, or may be a saddle point, but a max or min always has a zero derivative. For constrained optimization problems, look and see if the constraint is bounded, for example a circle. The graph is x+y+x-150=0 is a plane in 3 space and is not bounded. This tells us about the existence of max and min.
What are the first 500 multiples of 22?
22, 44, 66, 88, 110, 132, 154, 176, 198, 220, 242, 264, 286, 308, 330, 352, 374, 396, 418, 440, 462, 484, 506, 528, 550, 572, 594, 616, 638, 660, 682, 704, 726, 748, 770, 792, 814, 836, 858, 880, 902, 924, 946, 968, 990, 1012, 1034, 1056, 1078, 1100, 1122, 1144, 1166, 1188, 1210, 1232, 1254, 1276, 1298, 1320, 1342, 1364, 1386, 1408, 1430, 1452, 1474, 1496, 1518, 1540, 1562, 1584, 1606, 1628, 1650, 1672, 1694, 1716, 1738, 1760, 1782, 1804, 1826, 1848, 1870, 1892, 1914, 1936, 1958, 1980, 2002, 2024, 2046, 2068, 2090, 2112, 2134, 2156, 2178, 2200, 2222, 2244, 2266, 2288, 2310, 2332, 2354, 2376, 2398, 2420, 2442, 2464, 2486, 2508, 2530, 2552, 2574, 2596, 2618, 2640, 2662, 2684, 2706, 2728, 2750, 2772, 2794, 2816, 2838, 2860, 2882, 2904, 2926, 2948, 2970, 2992, 3014, 3036, 3058, 3080, 3102, 3124, 3146, 3168, 3190, 3212, 3234, 3256, 3278, 3300, 3322, 3344, 3366, 3388, 3410, 3432, 3454, 3476, 3498, 3520, 3542, 3564, 3586, 3608, 3630, 3652, 3674, 3696, 3718, 3740, 3762, 3784, 3806, 3828, 3850, 3872, 3894, 3916, 3938, 3960, 3982, 4004, 4026, 4048, 4070, 4092, 4114, 4136, 4158, 4180, 4202, 4224, 4246, 4268, 4290, 4312, 4334, 4356, 4378, 4400, 4422, 4444, 4466, 4488, 4510, 4532, 4554, 4576, 4598, 4620, 4642, 4664, 4686, 4708, 4730, 4752, 4774, 4796, 4818, 4840, 4862, 4884, 4906, 4928, 4950, 4972, 4994, 5016, 5038, 5060, 5082, 5104, 5126, 5148, 5170, 5192, 5214, 5236, 5258, 5280, 5302, 5324, 5346, 5368, 5390, 5412, 5434, 5456, 5478, 5500, 5522, 5544, 5566, 5588, 5610, 5632, 5654, 5676, 5698, 5720, 5742, 5764, 5786, 5808, 5830, 5852, 5874, 5896, 5918, 5940, 5962, 5984, 6006, 6028, 6050, 6072, 6094, 6116, 6138, 6160, 6182, 6204, 6226, 6248, 6270, 6292, 6314, 6336, 6358, 6380, 6402, 6424, 6446, 6468, 6490, 6512, 6534, 6556, 6578, 6600, 6622, 6644, 6666, 6688, 6710, 6732, 6754, 6776, 6798, 6820, 6842, 6864, 6886, 6908, 6930, 6952, 6974, 6996, 7018, 7040, 7062, 7084, 7106, 7128, 7150, 7172, 7194, 7216, 7238, 7260, 7282, 7304, 7326, 7348, 7370, 7392, 7414, 7436, 7458, 7480, 7502, 7524, 7546, 7568, 7590, 7612, 7634, 7656, 7678, 7700, 7722, 7744, 7766, 7788, 7810, 7832, 7854, 7876, 7898, 7920, 7942, 7964, 7986, 8008, 8030, 8052, 8074, 8096, 8118, 8140, 8162, 8184, 8206, 8228, 8250, 8272, 8294, 8316, 8338, 8360, 8382, 8404, 8426, 8448, 8470, 8492, 8514, 8536, 8558, 8580, 8602, 8624, 8646, 8668, 8690, 8712, 8734, 8756, 8778, 8800, 8822, 8844, 8866, 8888, 8910, 8932, 8954, 8976, 8998, 9020, 9042, 9064, 9086, 9108, 9130, 9152, 9174, 9196, 9218, 9240, 9262, 9284, 9306, 9328, 9350, 9372, 9394, 9416, 9438, 9460, 9482, 9504, 9526, 9548, 9570, 9592, 9614, 9636, 9658, 9680, 9702, 9724, 9746, 9768, 9790, 9812, 9834, 9856, 9878, 9900, 9922, 9944, 9966, 9988, 10010, 10032, 10054, 10076, 10098, 10120, 10142, 10164, 10186, 10208, 10230, 10252, 10274, 10296, 10318, 10340, 10362, 10384, 10406, 10428, 10450, 10472, 10494, 10516, 10538, 10560, 10582, 10604, 10626, 10648, 10670, 10692, 10714, 10736, 10758, 10780, 10802, 10824, 10846, 10868, 10890, 10912, 10934, 10956, 10978, 11000.
What is zip code is new york?
New York City zip codes start at 10001 and go through 10048. They continue with 10055, 10060, 10065, 10069, 10072, 10075, and 10080 to 10292. The last set of nonsequential zip codes is 11101, 11217, 11220, 11375, 11411, 11416, 11417, 11429, 11570, 11692, 11766, 19809, 30005, and 91362.
