When (1+x)^n is expanded in increasing powers of x?
1) When (1+x)^n is expanded in increasing powers of x, the ratios of three consecutive coefficients are 9:24:42. Find the value of n 2) in the expansion of (1+x)^n. the coefficients of x, x^2, x^3 form an arithmetic progression. Find the value of n. 3) In the expansion of (1+x)^n, the coefficients of x^4, x^5 and x^6 form an arithmetic progression (i) explain why 2 x nC5 = nC4+nC6 and hence show that n^2 - 21n +98 = 0 (ii) and hence find the two possible values of n please help me! i have no idea how to do it. Thanks so much for your time if you can't do all of them, you can do one :) thanks!
Can someone list me Gandalf the whites powers?
It really depends on the source; non-canon stuff (like video games) have expanded on his powers a lot from either the books or movies.
Why is steam from the turbine condensed to water then again converted into steam to run turbine? Why cant we just super heat the lower temp steam to run the turbine again in power plants.?
All the heating does is cause a phase change and add energy, not produce the pressure needed to run the turbine. Boiling water into steam doesn't raise its pressure unless it's confined, and that's not how turbine-based engines work. In a continuous-flow process in a power plant where steam is constantly produced in the boiler and spun through a turbine, the steam can't be at any higher pressure than the feed water supply. If it did, how could the feed water get into the boiler? Thus, the fluid entering the boiler must be high pressure to start with -- ie pumped or compressed.I think the key piece of missing information here is that it is energetically easier to pump a liquid than to compress a vapor or gas. Consider:work = force * distanceandpressure = force / areafor an ideal pump:stroke distance = pumped volume / piston areathus the areas cancel out and you get this equation for pumping liquids:work = pressure * pumped volumeNote that mass and density don't even appear in this equation. Gases are a lot more complicated because they heat up when compressed and cool when expanded -- but it's still true that the energy required to raise the pressure of a fluid is basically insensitive to that fluid's density. Mass flow rate doesn't matter! Volume flow rate is what counts. So which would you rather pump -- a whole of of diffuse steam, or a small amount of dense water? Likewise, energy extracted is related to volume flow and pressure drop through the turbine. So you extract a lot of energy by expanding low-density steam, and then use a small amount of energy pumping water back to complete the loop. That's why most power plants have boilers and condensers instead of using a single phase throughout.Yes, technically, you can compress low-temp steam, reheat it, and run a turbine that way. It's just not as energetically efficient.
What is the relationship between MW and GWh (in a power plant)?
1 gigawatt = 1000 megawatts 1 MW of electrical power is different GWh in a year according to how long the power can be used through the year. 1 year = 8760 hours. So at 100%, a power plant of 1 MW will produce 8760 MWh, or 8.76 GWh With a nuclear power plant that usually runs 80% of the time you have: 1 MW = 7 GWh in a year ..... 7,008 = 80% of 8760
How do you convert 256 to hexadecimal manually (I wonder because hexadecimal notation is in powers of 16 and 256 = 16^2)?
It is helpful to note that talking about numbers such as 256 or 1,543 or 2 or 17 means we're using positional notation, where a digit's position within a number denotes which power of the base the digit is a coefficient for.This makes more sense when you think of a number in terms of its expansion. Here's what 256 looks like in base 10 in expanded form:[math]256 = 2*10^2 + 5*10^1 + 6*10^0[/math] So, in a less-than-formally-correct way, converting a number from base 10 (aka decimal) to base 16 (aka hexadecimal) means you're trying to sum to 256 using only powers of 16 with non-negative integer coefficients that are each less than the base. For example, any number expressed in hexadecimal expansion in base 16 looks something like this: [math]sum = ... a*16^2 + b*16^1 + c*16^0[/math]Where [math]a, b, c < 16[/math] For 256, [math]256 = 1*16^2 + 0*16^1 + 0*16^0[/math]So [math]a = 1, b = 0, c = 0[/math]. And you get your positional notation (numbers as most people know them) by concatenating those coefficients, starting with higher powers first. a + b + c is 100 in this case, which is hexadecimal for 256.
Whats difference between scientific notation and standard form?
scientific notation is just a short way of writing a long number standard form is just the number written out Example: standard form)5,000,000,000 scientific notation) 5 x 10^9 for 133 the standard form is just 133 but the scientific notation is 1.33 x 10^2 to turn a # into scientific notation u have to make it between 0 and 10 [no more, no less] by moving the decimal to the right or left then when u get the # more then zero and less then ten, multiply it by 10 to the power of how many places u moved the decimal so 1.33 is more then 0 but less 10 and to get from 133 to 1.33 i moved the decimal twice so it's 1.33 x 10^2 *when the # is like 0.0000164 u have to move the decimal to the right 5 times so it would be 1.64 x 10^5 in scientific notation but since u move the decimal to the right the exponent [5] is negative to the final answer to writing 0.0000164 n scientific notation is 1.64 x 10^(-5)