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Prove (a) cosh2(x) ā sinh2(x) = 1 and (b) 1 ā tanh 2(x) = sech 2(x). solution (a) cosh2(x) ā sinh2(x) = ex + eāx 2 2 ā 2 = e2x + 2 + eā2x 4 ā = 4 = . (b) we start with the identity proved in part (a): cosh2(x) ā sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 ā sinh2(x) cosh2(x) = 1 or 1 ā tanh 2(x) = .
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When george started his current job, his employer told him that at the end of the first year, he would receive two vacation days. after each year worked, his number of vacation days will double up to five work weeks (25days) of payed vacation. how many vacation days will he have in 4 years
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Igure 1 and figure 2 are two congruent parallelograms drawn on a coordinate grid as shown below: 4 quadrant coordinate grid showing two parallelograms. figure 1 has vertices at negative 5, 2 and negative 3, 4 and negative 4, 7 and negative 6, 5. figure 2 has vertices at 5, negative 2 and 7, negative 4 and 6, negative 7 and 4, negative 5. which two transformations can map figure 1 onto figure 2? reflection across the y-axis, followed by reflection across x-axis reflection across the x-axis, followed by reflection across y-axis reflection across the x-axis, followed by translation 10 units right reflection across the y-axis, followed by translation 5 units down
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