how does mesa sine curve work?
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Do you mean the Porous Medium Equation? Or a Partial Differential Equation? If so I can link to a page on Mathworld which has plenty of formulae that are commonly used in mathematical physics.\n\nhttp://mathworld.wolfram.com/PartialDifferentialEquation.html\n\nThis however maybe a little difficult to comprehend for some people, so I can explain what my personal interpretation of a mesa curve is...although it may not be correct >>>\n\nA 'mesa' is described by www.dictionary.com as a broad, flat-topped elevation with one or more clifflike sides, common in the southwest United States.\n\nA sine curve is graphed from y = sin x making a snake like shape; lord I wish I could put pictures in here to help you :D\n\nSo, maybe a mesa sine curve is a sine curve that has it's apices(apexes) flattened and broadened...hope it's helped :)
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From the given data, with the foci located up and down and with an eccentricity greater than 1, the conic section is a hyperbola opening upward and downward.\n\nThe standard equation of this type of hyperbola (opening upward and downward) is:\n\n[(y - k)^2]/a^2 - [(x - h)^2]/b^2 = 1\nwhere:\nh = x-coordinate of the center of the hyperbola\nk = y-coordinate of the center of the hyperbola\na = center to vertex distance (semi-transverse axis)\nb = semi-conjugate axis\nc = center to focus distance\n\nRelationship among a, b, c:\n\nc^2 = a^2 + b^2\n\nRelationship among e (eccentricity), a, c:\n\ne = c/a\n\nFor c:\nFocus to focus distance = 2c\n\n7 - (-3) = 2c\n7 + 3 = 2c\n10 = 2c\nc = 5\n\nFor a:\n\ne = c/a\n\na = c/e\na = 5/1.25\na = 4\n\nFor b:\n\nc^2 = a^2 + b^2\n\n5^2 = 4^2 + b^2\n\n25 = 16 + b^2\n\nb^2 = 9\n\nb = 3\n\nFor center (h, k)\n\nh = 3\nk = [7 + (-3)]/2 = 4/2 = 2\n\n(h, k) = (3, 2)\n\nSTANDARD EQUATION IS:\n\n[(y - k)^2]/a^2 - [(x - h)^2]/b^2 = 1\n[(y - 2)^2]/4^2 - [(x - 3)^2]/3^2 = 1\n\n[(y - 2)^2]/16 - [(x - 3)^2]/9 = 1 ANSWER\n\nGENERAL EQUATION:\nIf you want the general equation, just expand the standard equation and get:\n\n[(y - 2)^2]/16 - [(x - 3)^2]/9 = 1\n9(y - 2)^2 - 16(x - 3)^2 = 144\n\n9(y^2 - 4y + 4) - 16(x^2 - 6x + 9) = 144\n9y^2 - 36y + 36 -16x^2 + 96x - 144 = 144\n-16x^2 + 96x + 9y^2 - 36y + 36 - 144 - 144 = 0\n\n-16x^2 + 96x + 9y^2 - 36y -252 = 0\n\n16x^2 - 96x - 9y^2 + 36y + 252 = 0 ANSWER
873733
In a right triangle every angle has a sine, it is the ratio of the side opposite the angle in question and the hypotenuse (the long side). A sine wave is just a name for a graph or chart of this value. If you take the sine of every angle from 1 through 360 degrees and plot them on a piece of graph paper you would get a circle, if you shift right one space for each value you will draw a sine wave. 60 cycle AC electric power is often referred to as being a Sine Wave because plotting the voltage of one complete cycle will produce the same graph.
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It is linear on intervals, on (- infinite, 0) and on (0, +infinite) but not on the whole R. \n\nTry plotting it, you get a reversed V, not a straight line.
443258
http://en.wikipedia.org/wiki/Sine_wave
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First off, what are the mechanics of your basic parabola?\nEvery parabola has several main parts:\n\n1. The vertex - essentially the point at the which the "curves" of the parabola begin\n2. The focus - the point (often seen as the satellite trans-miter) that all the waves the bounce off the satellite dish come into contact with\n3. The directrix - the line that is equidistant from the parabola as the vertex\n4. The focal diameter - the distance from the focus to the directrix\n5. The lattis rectum - the distance across from one side of the satellite to the other\n6. "P" - the distance from the focus to the vertex or the directrix to the vertex, the focal diameter is 2p  and the lattis rectum is 4p\n\nThe main reason is the nature of the parabolas. Satellites in space can see signals down to satellite dishes on Earth. No matter where on the inner dish the signals hit, they will always bounce off and come into contact with the focus (the trans-miter). The parabola is the most efficient design in accomplishing the goal of a satellite dish.
945543
A short element of the curve is dL=sqrt(dr^2+(r*dt)^2), r*dt elementary length of the arc with radius r and polar angle t (your theta), dr elementary increase of r for dt.\nThus dL=sqrt(r’^2+r^2)*dt.\nIf  r=a*(1-cost), then dL=a*sqrt((sint)^2+(1-cost)^2)=a*sqrt(2)*sqrt(1-cost)*dt. \nFortunately 1-cost=2*(sin(t/2))^2 or dL=2a*sin(t/2)*dt, L=-4a*cos(t/2) for t=0 until 2pi, thus L=-4*a*(-1-1)=8*a – Oh! check it poor kid!\nIf r=(sin(t/2))^2=0.5*(1-cost), then a=0.5 for t=0 until pi. It must be done likewise. Thus L=-4*0.5*(0-1)=2
869796
OK, first you have to find out the point(s) where both curves intersect. To do this, make both equations equal:\n\ny = x*sin(x) = y = cos(x)\n\nx*sin(x) = cos(x)\n\nx = cot(x)\n\nThe above equation gives us the locus of points where the two curves intersect. Say one point of the locus is:\n\nx1 = cot(x1)\n\n\nNow, to prove that both curves intersect at right angles to each other, we have to calculate the product of their slopes at the point of intersection & make sure they equal "-1". For our case:\n\nSlope of curve1 = dy/dx = d{x*sin(x)}/dx\n= x*cos(x) + sin(x)\n\nSlope of curve2 = d{cos(x)}/dx = - sin(x)\n\nProduct of their slopes at point x1:\n\n= {x1*cos(x1) + sin(x1)}*{-sin(x1)}\n= - { x1*cos(x1)*sin(x1) + sin^2(x1) }\n\nBut we already know that x1 = cot(x1), the point of intersection - plugging it into the above equation, we get:\n\n= - { cot(x1)*cos(x1)*sin(x1) + sin^2(x1) }\n= - { cos^2(x1) + sin^2(x1) }\n= -1\n\nThus, we get the product of the slopes equal to "-1" Thus, they intersect at right angles to each other.
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actually, you slolve each of the three parenthesis and that tells you when the equation equals zero...\n\nX=-2, x=1 and x=5.\n\nNow look at each interval to determine whether the curve is greater than or less than zero in that interval.  For example, \nless than -2: x=-3 is less than -2.  So substitute x=-3 and solve... (-1)(-4)(-8)=-24 which is less than 0.\nbetween -2 and 1: x=0 is between these numbers.  So substitute x=0 and solve...(2)(-1)(-5)=+10 which is greater than 0.\nbetween 1 and 5: x=2 is between these numbers.  So substitute x=2 and solve....(4)(1)(-3)=-12 which is less than 0. \ngreater than 5: use x=6: (8)(5)(1)=+40\n\nSo the number line should show an open circle at -2 and an arrow pointing left, and open circles at 1 and 5 with a line connecting the two circles at 1 and 5.
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Assuming you mean over R, solve the equation s*t + r*sin(t) = 0 for r and s for all t that is not the trivial solution (r,s)=(0,0). \nIn other words, if f(t)=sin(t) and g(t)=t were linearly dependent, then there is some non-zero slope s, s*g(t) = s*t and some non-zero amplitude r, r*f(t) = r*sin(t) such that the graphs of these functions completely coincide for all t. Since f is non-linear and g is, this is nonsense and the functions are linearly independent.
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Follow the previous answers to get the period. Once you obtain that, your equation will be y = sin(2pi*x/P), where P is the period. If you think about the regular sin curve, y = sin(x), this works out because it has a period of 2pi so you can see the cancellation.
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The graph of y = 1/x^2 can be graphed on a calculator and has even symmetry with the left half looking a lot like the left half of the hyperbola y = 1/x except it cuts upward more sharply.\n\nx = 1/y^2 is just this function's inverse which is found by exchanging the positive x and y axes and the negative x and y axes. \n\nImagine that you have a transparency with the graph on it with your right hand holding the top of the sheet and your left hand holding the bottom of the sheet. You flip the page over in such a way that your right hand is on the right side of the sheet and your left hand is on the left side of the sheet.\n\nSince the original graph has even symmetry, this process is also equivalent to rotating the graph of y = 1/x^2 clockwise by 90 degrees.\n\nSo it's the same kind of curved triangular pattern except about the x-axis rather than the y-axis.
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I guess my favorite is sin(x). The graph of sin(x) is pure and simple. Starting at the origin like many other famous functions, it curves up to a maximum, curves down to a negative minimum, and returns to the x-axis. This graph is reflected everywhere in nature, from wheels, pendulums, and other physics-related concepts. Also, the area enclosed by one half of a sin(x) curve and the x-axis is 2. How cool is that! Sin(x) is better than all the other trignometric functions because it is the easiest to use.
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Answering...\n\nBasic Equation:\n\nSine:.. y = a sin bx\nCosine: y = a cos bx\nwhere:\namplitude = absolute value of a (always positive)\nPeriod = 360 degrees/absolute value of b or 2pi/abs b\n\nEX: y = sin 4x\namplitude = abs a = 1\nPeriod = 360 deg./abs. b = 360/4 = 90 deg.\n\nEXPLANATION:\n\nSine Function\n1. The graph looks like a regular sea wave.\n2. For positive function, along the y-axis, the graph starts at the origin and then it goes up like a wave until it reaches the peak (called crest).\n3. Then it goes down until it reaches its lowest part (called trough).\n4. Then the cycle is repeated.\n5. For a negative sine function, from the origin, the graph goes down to its trough and then up again.\n\nCosine Function:\n1. The graph also looks like a regular sea wave.\n2. For a positive function, the graph (along the y-axis) starts at the its crest.\n3. Then it goes down until it reaches its trough.\n4. Then it goes up again until it reaches its crest again.\n5. The cycle is repeated.\n6. If the function is negative, along the y-axis, the graph starts at its trough first. Then it goes up.
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Simpson's Rule uses parabolas to approximate the curve, represented in diagrams by parabolas \nf1--f2--f3 and f3--f4--f5. Simpson's Rule can be expressed as:\n\n(f1/3 + 4f2/3 + 2f3/3 + 4f4/3 + ... + 2fN-2/3 + 4fN-1/3 + fN/3)*dx\n\nSimpson's Rule requires an even number of intervals (steps).
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Transverse electromagnetic waves (light,microwaves etc), the cosinewave shape is the same as calling something sinusoidal.\n\nSoundwave amplitudes can be sinusoidal.\n\nThe swing of a pendulum, simple harmonic motion.\n\nsinusoidal functions are solutions to many differential equations we find in nature.\n\nwaves on strings!
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This would be a function of vectors. Assuming you are reffering to sine waves the inverse of the sine gives you the angle. The total energy would be a function of Root Mean Square.