Distance formulas

In addition to guess and check, this solution will create a table to organize the guesses. The key word train indicates the use of the distance formula, D = RxT. The answer will be the time when the total miles equal 440, since the trains are that many miles apart. If the first guess is six hours, the table will be ... 

Depending on which distance formula you re using, the input is quite different. One distance formula inputs the rate and time. The second distance formula inputs coordinates of points. And the third formula inputs just time. In all three cases, the output is a distance measure. 

The distance formula s = -16/2 + v0t + sa gives you the height of an object when you know how much time has elapsed. You determine the input, the amount of time, by solving the quadratic equation for t. 

In this problem, the distances aren t really equal. You have to add on x number of meters to represent the additional distance that the runner from Kenya must cover. The rates are also different, but the times will be the same, if they start at the same time and finish at the same time. Take the distance formula, d = rt and solve for t, giving you t = —. Now set the time it takes the runner from Kenya equal to the time for the runner from Ethiopia. Then change the times to distances and rates. 

What if two jets leave at different times, and you want to determine the speed at which a particular jet is traveling Use the distance formula and the Pythagorean theorem. 

Find the two distances along the hypotenuses (in terms of x) using the Pythagorean theorem. After finding the distances, use the distance formula d = rt, and solve for t, t = y. The time it took for each part of the trip along a hypotenuse was the same, so the two distances divided by their respective rates are equal to one another. Because Katie paddles more quickly than she walks, let the rate at which she walks be r and the rate at which she paddles be 2.5r. 

Using the distance formula in Cartesian coordinates to measure sides... 

Circles, rectangles, and squares are easily described using the coordinate axes and some points and equations. The distance formula for the coordinate plane allows you to solve for lengths of segments if you have the values of the coordinates at either end. 

The trigonometric functions in the distance formula for the 4 distances between the 4 equivalent top nuclei... 

Other distance formulas may involve ranking [1] followed by a distance calculation or generalized distances of the type ... 

TABLE 3.2 Interplanar distance formulas for the seven crystal systems... 

Then, the radius of curvature, R between the center of curvature and the tangent points (for example Ra in Figure 4.4 b) can be found from the simple distance formula of analytical geometry ... 

Table 8-3 K-factor of the safety distance formula according to official regulations in Germany, from [35]... 

A more general procedure can be derived by applying a distance formula as introduced by Lance und Williams ... 

Table 5.5 Parameters for hierarchical cluster analysis by means of the general distance formula after Lance and Williams in Eq. (5.101).

In Image, the pixel coordinates of the center of the melted calibration regions are recorded and the distances between them are calculated using the Cartesian distance formula see Note 8). If several equivalent distances can be calculated between the various calibration points, the variations in these distances are averaged see Note 9). 

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