16t2 + vt - S = 0 This is in the general form of the quadratic equation, and the general quadratic solution can be applied directly. t = [ (-v) plus or minus the square root of (v2 + 64S) ] all divided by 32.
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S equals -10t2 plus vt plus k This is one of the three formulae for motion. The standard form is S = ut + 1/2ft2. S = distance, u = initial velocity, f = acceleration, t = time, k is unknown. The equation in the question could thus be written, S = ut - 10t2 +k. This would imply that the acceleration is -10.
By the Way, guys, this is based on the equation H= -16t2+vt+s
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I assume that the "speed" equation is velocity equals distance divided by time (v=d/t). To get 't' on the left side, we'll multiply both sides by 't': (vt=dt/t) and the two 't's on the right side cancel out (because t divided by t is 1): (vt=d). Now we move the v to the right side by dividing both sides by 'v': (vt/v=d/v). Just the 't's in the step before, now we have a v divided by a v on the left side, so they cancel out, and our final equation is time equals distance divided by velocity: t=d/v
GARCH processes are used to model the conditional volatility of financial returns in discrete time. There are many many different types of GARCH, the most popular and simplest being the GARCH(1,1), where returns have mean mu and conditional variance vt (t indexes time): returnt = mu + sqrt(vt)et where et is a standardized innovation.Conditional variance follows a first order autoregressive process: vt= a + b* vt-1 + c* vt-1*et-1^2