An engineer is building a bridge that should be able to hold a maximum weight of 1 ton. He builds a model of the bridge that is
1 answer:
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Answer:
Suppose you want to assess student attitudes about the new campus center by surveying 100 students at your school. In this example, the group of 100 students represents the Sample, and all of the students at your school represent the Population.
Step-by-step explanation:
Previous concepts
The term sample represent a set of observations or individuals selected from a population. And we can have a random sample (when all the individuals have the same probability of being selected) or a non random sample (when not all the individuals have probability of inclusion into the sample)
The term population represent the total of observations or individuals with a common characteristic.
If N represent the sample of the population and n the sample size we have always this inequality:
Solution to the problem
Suppose you want to assess student attitudes about the new campus center by surveying 100 students at your school. In this example, the group of 100 students represents the Sample, and all of the students at your school represent the Population.
Answer:
distance: 320.624 miles
direction: 43.576°
Step-by-step explanation:
The speed and direction can be found by adding the given vectors.
... 320∠40° + 20∠130°
... = (320·cos(40°), 320·sin(40°)) + (20·cos(130°), 20·sin(130°))
... = (245.134, 205.692) +(-12.856, 15.321) = (232.278, 221.013)
The magnitude of the vector with these components is found using the Pythagorean theorem. The direction is found using the arctangent function.
... = √(232.278² +221.013²)∠arctan(221.013/232.278)
... = 320.624∠43.576°
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A suitable vector or graphing calculator can do this easily. In the screenshot of a TI-84 app below, the variable D has the value π/180. The display mode is set to degrees.
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<em>Comment on coordinate systems</em>
Navigation directions are generally measured clockwise from North. Angles in the usual x-y coordinate plane are measured counterclockwise from +x (effectively, East). You can consider the geometry of the navigation coordinate system to be a reflection across the line y=x of the geometry of the usual x-y coordinate system.
Reflection does not change lengths or angles within a given geometry. Hence, we can use all the usual tools of vector calculation using navigation coordinates, without bothering to translate them back and forth to x-y coordinates.
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Problems like this generally can be worked using the Law of Cosines and the Law of Sines, too. It generally helps to draw a diagram so you can find the values of the angles betwee the various vectors more easily.
