One way to do this would be with Newton's method: Let: f(x) = 709 - x2 f'(x) = -2x We'll start with 27 as an approximation: x0 = 27 x1 = x0 - f(x0) / f'(x0) = 27 - (709 - 729) / -2(27) = 27 - 10/27 ≈ 26.629629 x2 = x1 - f(x1) / f'(x1) ≈ 26.629629 - (709 - 709.137174) / -2(26.629629) ≈ 26.627053 x3 = x2 - f(x2) / f'(x2) ≈ 26.627053 - (709 - 708.999951) / -2(26.627053) ≈ 26.627053 So we know that the square root is approximately 26.627053. You can check this of course by squaring our answer: 26.6270532 = 708.999951
The end part of the question does not seem to make sense. The equation has three real roots, a single root at x = -1 and a double root at x = 1
x0 = 1 because any number raised to the power of 0 is always equal to 1
The integral of e-2x is -1/2*e-2x + c but I am not sure what "for x0" in the question means.
That would besqrt[ (x80 - x0)2 + (y80 - y0)2 ) at an angle of tan-1 (y80 - y0) / (x80 - x0)or(x80 - x0) i + (y80 - y0) j
If x is 0, the square root is 0 also.
The general equation for a linear approximation is f(x) ≈ f(x0) + f'(x0)(x-x0) where f(x0) is the value of the function at x0 and f'(x0) is the derivative at x0. This describes a tangent line used to approximate the function. In higher order functions, the same concept can be applied. f(x,y) ≈ f(x0,y0) + fx(x0,y0)(x-x0) + fy(x0,y0)(y-y0) where f(x0,y0) is the value of the function at (x0,y0), fx(x0,y0) is the partial derivative with respect to x at (x0,y0), and fy(x0,y0) is the partial derivative with respect to y at (x0,y0). This describes a tangent plane used to approximate a surface.
For a quadratic function, there is one minimum/maximum (the proof requires calculus) and also it is either always convex or concave (prove is also calculus) it is continuous every where, hence, it can have a maximum of 2 roots. Graph it. If there is more than 2 roots, by Intermediate Value Theorem, it cannot be convex/concave everywhere. It will HAVE to have two intervals of increasing or decreasing. It can be easily proven that given any quadratic function f(x), if x = x0 is a minimum/maximum, and x=a != x0 is a root, then 2x0-a is also a root. It is still true that a = x0 as 2x0-x0=x0 implying it is the only root. But the concept of min/max requires Calculus to prove existence. So, this is Calculus, not algebra.
It's a method used in Numerical Analysis to find increasingly more accurate solutions to the roots of an equation. x1 = x0 - f(x0)/f'(x0) where f'(x0) is the derivative of f(x0)
Use the Newton-Raphson method. Let f(x) = x2 - 350 and let f'(x) = 2*x Then start with any guess, x0. The next estimate is x1 = x0 - f(x0)/f'(x0). Continue iterations with xn+1 = xn - f(xn)/f'(xn). If you start with x0 = 15 (quite a long way off, given that 152 is only 225), x2 is accurate to 6 decimal places (error = 8 in 10 million) and x3 to 13 dp (2 in 100 trillion).
The answer is -13 1/3ohere is the detailed calculation for the problem:Let x0 be the angle, then;(180 - x0) - 2[180 - (90 - x0)] =40(180 -x0) - 2[90+x0]=40180 -x0 - 180 - 2x0=40-3x0=40hencex0= -13 1/3oAny comments are welcome
One way to do this would be with Newton's method: Let: f(x) = 709 - x2 f'(x) = -2x We'll start with 27 as an approximation: x0 = 27 x1 = x0 - f(x0) / f'(x0) = 27 - (709 - 729) / -2(27) = 27 - 10/27 ≈ 26.629629 x2 = x1 - f(x1) / f'(x1) ≈ 26.629629 - (709 - 709.137174) / -2(26.629629) ≈ 26.627053 x3 = x2 - f(x2) / f'(x2) ≈ 26.627053 - (709 - 708.999951) / -2(26.627053) ≈ 26.627053 So we know that the square root is approximately 26.627053. You can check this of course by squaring our answer: 26.6270532 = 708.999951
0! You said x0! anything x0=0!
The end part of the question does not seem to make sense. The equation has three real roots, a single root at x = -1 and a double root at x = 1
On a transformer connection H1 and H2 are the primary connections. X1 and X2 are the secondary connections. If your transformer has a split secondary that is grounded, that terminal is X0. The sequence is X1 - X0 - X2. The X0 usually indicates that there is a connection to a neutral wire along with the ground wire.
The only "formula" is 54741155041/9 However, you can calculate the value iteratively, using the Newton-Raphson method as follows: Define f(x) = x9 - 547411504 and solve for f(x) = 0 The first derivative is f'(x) = 9*x8 So take a guess at x, say x0. Calculate x1 = x0 - f(x0)/f'(x0) Continue: calculate x2 = x1 - f(x1)/f'(x1). If you started with a reasonably good estimate you will find that the the estimates converge to the answer. In this case, the answer is 12.079 (approx).
x0 = 1 because any number raised to the power of 0 is always equal to 1