There are two main things in high school maths, being, calculus and trigonometry. let us gloss over them quickly? Calculus is about finding the value of the accumulation of quantities, rates of change and slopes and curves. this is then calculated as if it were a function, where the function or slope and all known quantities are placed on a diagram. so, if it were a curve that grows because of angles getting greater, then it would be there to work that out. let us take a example for [1] differential calculus and [2] integral calculus? [1] If you need to find the function of a curve that is; f[x] = [x^2]? typically, we would use quadratic equations to find the values, but, there is an easier way. the easier way to do it is to work out the exact value from the [x^2 =] 4x. then you may say that f = 4, yes? [2] If you are doing integral calculus (d / dx [x + a] [ft] [dt] = f[x]), (d / d) is one times by x, leaving [one x]. that is where the equations regarding x end, so that is the answer for x, being, if there are two [x] on the left, and one on the right, then the rest of the equation is minus one [x], to realize the one [x] on the right. With trigonometry, you merely need to measure the ratio of 0.6, as that goes 600 times into 360 degrees, yes? so, for every 0.6 degrees you count one percent, and then can use a calculator.
Uncle Ferd wantin' to know... ... can ya express dat as an... ... algebraic equation? He didn't take trig or calculus... ... an' barely passed geometry.
Well, if there is [x] blah blah blah [x] on the one side, and one [x] on the other side, then all that other stuff must equal 2[x], so, half is [x] and the other half is [f].
With quadratic equations, you find that there is often lots of stuff over other stuff, then another one of those 'split sums.' let us take an example; x = [d^3x/b+x] * [2bx/d] This will mean that [x] is listed thrice on the other side of the [equals] sign, yes? this would mean that all the equations equal [3x] and the answer to all those things is equal to [3], where you take the sum and say that the whole sum equals [3x], so, [3x] equals [d + b], [x] = ([d + b] / 3).
Parabola is a very complicated field of what i refer to as geometry or trigonometry being an upscaled geometry, with parabola being an 'offshoot' of these types of things, yet they are all related. If you are given a circle and asked what it's properties are, you take the two positive fields, being the right and top sides of the cross section, and then calculate the degrees of the circle with only the right angle in mind. this right angle will be equal to, as the remainder, half of the sum of the positive integers minus, well, the negative integers.
Polar form is a science dedicated to, as far as i can tell, screws and swivels and cogs. this is because they use a circle, which is very popular in maths, it seems, and make pretty patterns on the circle for the benefit of the connection to the other, in computer or circuit board side of things, terms to connect two things. if you are a biologist, you might understand this as muscles and joints, that are, instead of twisted around each other for strength, combined to provide a strong connection to the rest of the body. if you are a artist, this is like a fractal too, yes? Anyway, if you were to observe that there needs to be structure here, a repeated pattern for the sake of continuity, you might get smart and think you can devise your own 'connections to things?' this you might think you can do with an oddly shaped connection, to hold it together better, but, due to the standards set by engineering, you need to make it continuous and circular, or triangular or squared, as these are the shapes used by engineers to do things they want to keep to a standard. but, even pentacles are considered in engineering, in the form of screw drivers or things that have, due to size and such, five 'grooves' to the apparatus. So, the polar form is found by taking the pressure on the device, found by taking the stress levels of the material, potential too, found by taking 'pressure versus strength.' you can find the pressure of the apparatus by taking the size of the groove, minus the frequency of angles to grooves, relating to the strength of the materials. this means the strength of the materials is placed against the frequency of this strength being tested, of course. you would take the angle of the groove, remembering each groove takes away from stress on each 'branch of the tree.' the more grooves there are the less materials there are to hold the parts together of course. In maths language, we take the angles, and find how long the route is to the design. the designs range from [1] circle, [2] rose, [3] line, [4] spiral and [5] conic sections. these are all related in that they have areas, angles and a curves yes? so, the more area you have [a], the more curves you may have and therefore the more potential angles you may have [c]. If you were to observe that we need to find the radius, we could take the [a] area times the [c] angles equals [c] or so, with [c] being found by multiplying by the angles , you will find this very easy, yes?
This looks hard; https://wikimedia.org/api/rest_v1/media/math/render/svg/bc7a51eb75e0c27509daae52547e2d5fe17a37c3 If you were to observe all the sums involved in this, obviously you want the quickest way to get to the answer reliably, yes? this means you want to find the geometric progression of the equation, and, that means working most of the sum out. In our example, [infinity] plus [k = 0] is equal to infinity, and, multiplying this by [a] equals [1a] * [inf]. then, multiplying this [1a * inf] by [r^k] = [1a * inf * krr]. this does not leave us with the information we need though, so, we need to move along to the other side of the equals sign to look for more constants. If we were to take the limit to be n into infinity, then we could take [infinity] / [n] / [limit], yes? this means, infinity is defined as the limit, and you divide the limit into [n]. if infinity is what you seek, it is the limit of the sum, and, if [n] is what you seek, then the [limit] divided by [n] equals [x], i would presume.
Define X = Y = 1 X=Y -> X[SUP]2[/SUP] = Y[SUP]2[/SUP] -> X[SUP]2[/SUP]-1 = Y[SUP]2[/SUP]-1 -> (X-1)(X+1) = Y[SUP]2[/SUP] - 1 [by the difference of two perfect squares] Since X = Y = 1, X-1 = Y[SUP]2[/SUP] - 1 So X+1 = 1 [divide by sides by X-1] And X = 0 But X is defined to be 1 Therefore 1 = 0
Why? You have 100 lbs of potatoes, which are 99 percent water by weight. You let them dehydrate until they're 98 percent water. How much do they weigh now?
When you got x+1=1, it should have been x+1=y+1. (because you divided (x-1) from both sides right?) So the original claim still holds. - - - Updated - - - Argh what did I do wrong?
What is the value of x-1? - - - Updated - - - .99p=100 lbs... you need to think about the setup more carefully. The answer is quite surprising!
0 but to balance out the equation you would have needed y-1 on the other side right? - - - Updated - - - Hmm... I think I remember how to do it now. Let p= weight of potatoes. Let x=weight of dried out potatoes. .99p-.98p=x Is this the right set up?
And before I forget, this is a surprising one too! You wrap a string around the earth at the equator amd pull it tight [assume the earth is perfectly smooth[. You then add one foot to the length of the string. What would be the uniform gap between the string, all the way around the earth, due to the extra one foot of length.
Closer! . X[SUB]i[/SUB] = total weight [initial] = 100 Lbs P = weight of dry potatoes W[SUB]i[/SUB] = weight of water [initial] = .99 X[SUB]i[/SUB] = 0.99 x 100 = 99 Lbs P + W[SUB]i[/SUB] = X[SUB]i[/SUB] = P + 99 = 100, so P = 1 Lbs of dry potato After dehydration to 98% water... .98 X[SUB]f[/SUB] + 1 Lb = X[SUB]f[/SUB]... Finish the math. The answer is surprising. The string problem is really cool. The answer still messes with my head. It just doesn't seem possible!
Do you know the problem with the firing a bullet on a train traveling at the speed of light? the formula says the bullet goes faster inside the train towards the target, yes? Now, imagine you are on a jet ski, and you throw a beach ball from the front of it, in front of you... the beach ball bounces against you, yes? I always found that funny...
Not quite. Nothing with a rest mass can travel at the speed of light. If you are driving a car with a helium-filled balloon floating around inside, when you accelerate, it moves to the front of the car. When you hit the brakes, it moves to the back of the car. Why?
As the car accelerates, the air is forced to accelerate together with the car. Due to the inertia of the air (its resistance to a change in speed), more air molecules remain in the back of the car, where the pressure becomes slightly higher than in the front of the car. The same happens to the helium inside the balloon, but because helium is lighter than air, the pressure difference between the front and back of the balloon is smaller. This results in a net force that pushes the balloon forward relative to the air. Another way to look at this is to treat it like buoyancy. The forward acceleration of the car is similar to an acceleration due to gravity. The light helium balloon displaces heavy air and comes to float on top (or here front). The mathematical link between those two views (surface vs volume) is called the divergence theorem. F = ac (dair - dHe) V ab = F / (dHe V) = ac (dair - dHe) / dHe = 6.2 ac dair: density of air (1.29 kg/m^3) dHe: density of helium (0.18 kg/m^3) ac: acceleration of the car ab: acceleration of the balloon relative to the air/car I was surprised to find out that the balloon accelerates about 6 times faster than the car. It won't accelerate that quickly for long though, because even a small amount of drag as it moves through the air will slow a very light balloon down substantially.
