z=y+x2–√,w=y−x2–√.(1)(1)z=y+x2,w=y−x2. Plugging (1) into the z,wz,w-space equation of your parabola and simplifying, we get the x,yx,y-space equation y−x−1=−(x+y−1)2.(2)(2)y−x−1=−(x+y−1)2. The ...
Imaginary numbers are numbers we sometimes need but do not really exist. For example, take the following equation: x² + 1 = 0 Here we know that x has to be -1, since -1 + 1 = 0, but… How much is x worth? normally for this we use the square root, but here we are going...
解析 C Points A (−2,0) and B (0,4) are on the line y=2x+4. After the rotation, we can get A1 (0,2) and B1 (4,0). Assume that the equation of the line after the rotation is y=kx+b, 4k+b=0 and b=2, ∴k=−0.5, ∴y=−0.5x+2. When x=6, y=−1....
You can rotate a three-dimensional plot for different points of view.Rotate a Plot Interactively Entering Values of Angles Directly Rotate a Plot Interactively 1. Generate a three-dimensional plot in your worksheet. For example, execute plot3d(sin(x)*sin(y),x=-Pi..Pi,y=-Pi..Pi);....
Here is the equation expanded out into scalar math and simplified: It is important to note that the only difference between these two equations is that we're multiplying by Axis 1's x coordinate at the end of the first equation and we're multiplying by Axis 1's y coordinate at the end...
ordinary differential equationpoint transformationequivalence problemdifferential invariantWe introduce the Wigner operator $widehat{Delta} _theta (x,,p)$ for the rotated quadrature phases and use the technique of integration within an ordered product of operators to derive its explicitly simpler form. ...
Thus, the equation of the Earth's shape is: x2/a2+y2/b2+z2/c2=1 where (for the Earth): a=b=6,378,137.0 meters c=6,356,752.3142 meters Applying geometric methods yields the formula for the radius of the circle of latitude: Rlat=a*cos(lat)/(1-e2sin2(lat))1/2 where:...
A region in the plane can be bounded laterally by two vertical lines, superiorly by a function and inferiorly by the x-axis. If this region rotates around the x-axis, the volume of the solid that it defines is calculated by applying the dis...
An ellipse of center in the origin and the axis rotated by an angle θθ has equation: (xcosθ+ysinθ)2a2+(ycosθ−xsinθ)2b2=1(xcosθ+ysinθ)2a2+(ycosθ−xsinθ)2b2=1 that can be write as: Ax2+Bxy+Cy2=1Ax2+Bxy+Cy2=1 with B2−4AC<0B2−4AC<...
The general form of the equation of a circle is x^2 + y^2 + 2x - 6y + 1= 0. What are the coordinates of the center of the circle? The general form of the equation of a circle is x^2 + y^2 + 2 x - 6 y + 1 = 0. What are the coordinates of the center of the circ...