Recent content by votingmachine

You are assuming that there is only one way the triangles can be similar ... the drawing leads you there ... I suspect you need to evaluate the words and make your own drawings.

I suppose they might be asking you to go from: tan = sin / cos to x / y Then you would use a right triangle with sides x and y and hypotenuse z and the definitions of sin and cosine. But it seems a bit definitional to me.

When you are putting the bell into the starting position, You can raise and lower it freely, with the air going out-or-in the rubber tube. If you wanted to start with no air in the bell, I can think of 3 things that might go wrong. 1. You might squish some water into the rubber tube, and that...

It is an arbitrary scale. The counterweight balances the weight of the bell, so adding air to the trapped volume is perfectly against the atmospheric pressure. As long as the water is keeping a seal, it doesn't matter what your starting volume in the bell is. It matters that the bell has...

I'm puzzled by that statement the current "will split into the earth and the live" Current will divide based on the resistance across the appliance and the resistance to the ground (which is zero). That seems like the appliance gets no current. (My being puzzled is not the same as there being...

But the earth of the appliance connected to live pin of the plug is a miss-wiring of the appliance, not the plug. I see the circuit you are making, and why it would not trip the breaker. But the miss-wiring is specified as in the plug/cord: "A metal casing appliance's plug is created wrongly"...

There needs to be a wiring diagram for me. My first reading was that the hot AND the ground for a 3-prong plug are TOGETHER connected to the same terminal. That's a short that blows the fuse. If it is a 2-prong plug, then it is the same as if the plug was simply lugged in backwards (old plugs...

Taking that as: $$ x^5=\dfrac{5\sqrt{5}-11}{64} $$ note that the product of the right side by it's conjugate is 2^-10 So: X^5 times X^5 prime = 2^-10 by the product rule in comment #10, that is the same as: (X times X prime)^5 = 2^-10 raise both sides to the 5th power: X times X prime = 2^-2...

For the purpose of making the story scientifically valid, I would introduce some kind of random path crossing with the planets, and a gravity brake effect. Rather than the usual gravity assist, for instance, have the path be the reverse of the Voyager path. But I think as a class exercise...

I'm not familiar with the book, but it sounds like it is stuck in some orbit. My thought is that you exchange one problem for another. Any matter you suggest as present to reduce the speed so it doesn't fall in and then flyout ... that same matter will also KEEP slowing the orbiting ship until...

If you plot the numbers that can be squared to equal a result, you would have at X=1, two Y values, 1 and -1. At X=4 you would have two Y values, 2 and -2. At X=9 you would have two Y values, 3 and -3. At none of those is the positive number equal to the negative number. The "square root" of 4...

Fair enough. I saw the question "can Australia remove fire from their energy mix, if they've eliminated nuclear from the non-fire options?" and did not think it was being answered. I compared their aggregate energy demand to a single energy resource and that single resource appears far in...

I assume the per capita energy use includes industrial and commercial use, which dwarf home use. I googled: australia per capita energy consumption The "answer" in my search results is putatively from the World Bank. (5,483.82 kg of oil equivalent (2015)). Commercial power use HAS to be...

There are alternatives to batteries. I recall a project from the 70's where the TVA was planning to pump water to a reservoir on a mountain top, with energy recovery via hydroelectric generation. The efficiency is quite good, but the energy density is not great. Back of the envelope, say a...

Google says that Australians use about the energy equivalent of about 5500 kg of oil per year. It also tells me that oil is about 12 kWhr per kg. So an Australian needs roughly 66,000 kWhr of energy per year. If you were strictly relying on solar and storage, and make the assumption of 3000...