# Uncertainties in calculated results Determine the uncertainties in results. Uncertainties in graphs

## Uncertainties in calculated results Determine the uncertainties in results. Uncertainties in graphs

Friedman, Gabe, Federal Litigation Reporter has reference to this Academic Journal, PHwiki organized this Journal Uncertainties in calculated results Uncertainties. Absolute uncertainty is the value of r in addition to om uncertainty reported in a measurement (the larger of the reading error or the st in addition to ard deviation of the measurements). This value carries the same units as the measurement. Fractional uncertainty equals the absolute error divided by the mean value of the measurement (it has no units). Percentage uncertainty is the fractional uncertainty multiplied by 100 to make it a percentage (it has no units). Determine the uncertainties in results. A simple approximate method rather than root mean squared calculations is sufficient to determine maximum uncertainties For functions such as addition in addition to subtraction absolute uncertainties may be added When adding or subtracting measurements, the uncertainty in the sum is the sum of the absolute uncertainty in each measurement taken An example: suppose the length of a rectangle is measured as 26 ± 3 cm in addition to the width is 10 ± 2 cm. The perimeter of the rectangle is calculated as L + L + W + W = (26 + 26 + 10 + 10) ± (3 + 3 + 2 + 2) = 72 ± 10 cm

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Trans as long as m equations into generic straight line as long as m (y = mx + b) in addition to plot the corresponding graph To use the slope, intercept, or area under a graph to determine the value of physical quantities, it is easiest to work with a straight-line graph. Most graphs can be trans as long as med from a curved trend to a linear trend by calculating new variables. If the relationship between two variables is known in theory, then the known relationship can be used to trans as long as m a graph into a straight-line graph. An example: Suppose that the speed of a falling ball is measured at various distances as the ball falls from a height of 10 m toward the ground on the moon. From energy conservation, we can predict that the speed of the ball is related to the height above the ground as v2 = 2gh. If we were to plot v vs. h we would get a sideways facing parabola. How can we make this a linear equation If we calculate a new quantity (call it w) so that w = v2, then our relationship becomes w = 2gh. If we plot w vs. h, we will get a straight line. (see the graphs below). This straight line can be used to find g on the moon (the slope of the graph = 2g). Analyze a straight-line graph to determine the equation relating the variables Once the straight-line graph has been achieved, using the intercept in addition to slope the equation of the trend line can be written (y = mx + b). Then substitute into the linear equation as long as the quantity that was used as the y in addition to /or x variable to produce the straight-line graph. In our example, the equation of the trend line is y = 3.2x. This means that our relationship is v2 = 3.2h. And, the slope of the trend line (3.2) should be twice the acceleration of gravity on the moon, so 2g = 3.2, or g on the moon = 1.2 ms-2.

Graph of Y vs. X, we would get a straight line. AND, the slope of that line is equal to n, the exponent in our original relationship. The vertical intercept (b) = log k. The value of the vertical intercept, b, can be used to find the constant k: b = log k, so 10b = 10log k = k. Simply substitute the values of n in addition to k determined from the trans as long as med log-log graph into the original relationship to get the equation relating the two variables, y in addition to x. y = kenx Again, this will produce a curved graph in addition to we can use logs (this time it has to be ln) to trans as long as m the graph into a straight line. Let’s see what logs will do as long as us this time. take the ln of both sides of the equation: ln y = ln (kenx) used the properties of ln to simplify: ln y = ln k + (nx)ln e = ln k + nx substitue ln y = Y Y = ln k + nx. if we were to make a graph of Y vs x, we would get a straight line. AND, the slope of that line is equal to n (the constant in the exponent of our relationship). The vertical intercept (b) = ln k. The value of the vertical intercept, b, can be used to find the constant k: b = ln k, so eb = eln k = k. This type of graph is called a semi-log graph because we only had to use the ln function to trans as long as m one of the variables. Semi-log graphs will trans as long as m exponential relationships into straight-line graphs. Simply substitute the values of n in addition to k determined from the trans as long as med semi-log graph into the original relationship to get the equation relating the two variables, y in addition to x.

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## Friedman, Gabe Federal Litigation Reporter

Friedman, Gabe is from United States and they belong to Los Angeles Daily Journal and they are from  Los Angeles, United States got related to this Particular Journal. and Friedman, Gabe deal with the subjects like Government Regulatory Agencies; Law; Securities & Exchange Commission

## Journal Ratings by ECPI University-Innsbrook

This Particular Journal got reviewed and rated by ECPI University-Innsbrook and short form of this particular Institution is VA and gave this Journal an Excellent Rating.