Mathematics, 03.11.2020 01:00 joejoefofana
Gavin's science class is learning how space vehicles protect themselves from debris and meteoroids including small rocks. He learns that these objects, although usually very small, can be moving at speeds of up to 8,000 meters per second in outer space. At such high speeds, even small pebbles can damage and possibly puncture the sides of space vehicles.
Using an empty shoe box, a sheet of paper towel, and tape, Gavin and his class build a model of a spacecraft. Gavin's teacher asks him to shoot peas at the paper towel part of the model using a straw pea shooter. The peas will represent meteoroids. The class' model is illustrated below.
First, Gavin shoots a 3.0-gram pea at the model. Its speed is measured at 12 meters per second as it leaves the straw. The pea does not break through the paper towel.
For Gavin's next trial, he decides to use a different pea and shoot it at a different speed. Which of the peas illustrated below is most likely to break through the paper towel?
Answers: 3
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Prove (a) cosh2(x) β sinh2(x) = 1 and (b) 1 β tanh 2(x) = sech 2(x). solution (a) cosh2(x) β sinh2(x) = ex + eβx 2 2 β 2 = e2x + 2 + eβ2x 4 β = 4 = . (b) we start with the identity proved in part (a): cosh2(x) β sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 β sinh2(x) cosh2(x) = 1 or 1 β tanh 2(x) = .
Answers: 3
Gavin's science class is learning how space vehicles protect themselves from debris and meteoroids i...
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