The X-43 is an unmanned experimental hypersonicaircraft design with multiple planned scale variations meant to test different aspects of highly supersonic flight. It is part of NASA's Hyper-X program.It is said that it can travel at a speed of Mach-10.
http://en.wikipedia.org/wiki/X-43
9.8 Mach
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If f' (x) = x43, then f(x) = (1/44) x44 + C.
You can solve this using Newton's Method. First, solve the equation for zero, and use it to define the function f(x): Let f(x) = x3 - x - 20 It's derivative then would be: f'(x) = 3x2 - 1 Now let's take a rough guess at what x would be - we'll go with three - and plug it into the system xn+1 = xn - f(xn) / f'(xn): x0 = 3 x1 = x0 - (x03 - x0 - 20) / (3 * x02 - 1) = 2.8461538461538461539 x2 = x1 - (x13 - x1 - 20) / (3 * x12 - 1) = 2.8371684181740047662 x3 = x2 - (x23 - x2 - 20) / (3 * x22 - 1) = 2.8371386689493412305 x4 = x3 - (x33 - x3 - 20) / (3 * x32 - 1) = 2.8371386686239233464 x5 = x4 - (x43 - x4 - 20) / (3 * x42 - 1) = 2.8371386686239233464 So x is approximately equal to 2.8371386686239233464. If we plug that into the original equation, we can see that it is correct: 2.83713866862392334643 = 22.8371386686239233464 22.8371386686239233464 - 2.8371386686239233464 = 20
The probability of rolling a number divisible by three on a fair die (3 and 6) is 2 in 6, or 1 in 3, or about 0.3333. Since there are 36 permutations of rolling two dice, the probability, then, of rolling (at least one) number divisible by three on two rolls of a die is 19 in 36, or about 0.5278. Simply count the number of desired results, and divide by the number of possible results, as I have done below.111213 x141516 x212223 x242526 x31 x32 x33 x34 x35 x36 x414243 x444546 x515253 x545556 x61 x62 x63 x64 x65 x66 xIf, on the other hand, you are looking at the probability of rolling a sum divisible by three, consider ...11 212 3 x13 414 515 6 x16 721 3 x22 423 524 6 x25 726 831 432 533 6 x34 735 836 9 x41 542 6 x43 744 845 9 x46 1051 6 x52 753 854 9 x55 1056 1161 762 863 9 x64 1065 1166 12 x... which is 12 in 36, or 1 in 3, or about 0.3333.
The answer is absolutely! Secondary market products are readily available for a conversion such as this. A plastic, resin, or fiberglass track is installed just under the top edge of the coping around the swimming pool. The track is usually attached with some sort of stainless steel screw. Rolled Wall foam can be cut into long sheets and attached to the existing plaster walls--usually with spray adhesive. The foam evens out the surface and also provides a nice "shock absorbant" pad in between the liner and the wall. Complete measurements of the existing structure need to be taken--and they need to be extremely accurate. Some of these measurements include the height of the wall, angle of slope, depth and step areas. For 99% of these conversions, a liner must be custom manufactured. I say this because you might hear an installer give you a quote for a "stock liner"--a mass-produced liner made based upon general measurements--carried in quantity at the local distributor. Conversions are rarely exact, so don't be alarmed if you have a small wrinkle or two. Expect to spend 25-50% over what a traditional liner replacement would cost. There's not too much of a difference in materials, so the cost will be mainly in the skilled labor. Definately find someone that has performed these conversions before. Don't just take their word for it. Go see the jobs--without the installer present!!!! Talk with the customers, and ask them how the installer performed. Best wishes on your project!!