Дано
$$frac{1}{100} sqrt{- 100 x^{2} – 80 x + 84} – frac{47}{50} {asin}{left (frac{1}{200} left(- 200 x – 80right) right )}$$
Подстановка условия
$$frac{1}{100} sqrt{- 100 x^{2} – 80 x + 84} – frac{47}{50} {asin}{left (frac{1}{200} left(- 200 x – 80right) right )}$$
sqrt(-100*(1/2)^2 – 80*(1/2) + 84)/100 – 47*asin((-200*(1/2) – 80)/200)/50
$$frac{1}{100} sqrt{- 100 (1/2)^{2} – 80 (1/2) + 84} – frac{47}{50} {asin}{left (frac{1}{200} left(- 200 (1/2) – 80right) right )}$$
sqrt(-25 – 80/2 + 84)/100 – 47*asin((-100 – 80)/200)/50
$$frac{1}{100} sqrt{- 40 – 25 + 84} – frac{47}{50} {asin}{left (frac{1}{200} left(- 100 – 80right) right )}$$
sqrt(19)/100 + 47*asin(9/10)/50
$$frac{sqrt{19}}{100} + frac{47}{50} {asin}{left (frac{9}{10} right )}$$
Степени
$$frac{1}{100} sqrt{- 100 x^{2} – 80 x + 84} + frac{47}{50} {asin}{left (x + frac{2}{5} right )}$$
Численный ответ
0.01*(84.0 – 80.0*x – 100.0*x^2)^0.5 – 0.94*asin((-200*x – 80)/200)
Рациональный знаменатель
$$frac{1}{100} left(sqrt{- 100 x^{2} – 80 x + 84} + 94 {asin}{left (x + frac{2}{5} right )}right)$$
Объединение рациональных выражений
$$frac{1}{50} left(sqrt{5 x left(- 5 x – 4right) + 21} + 47 {asin}{left (- frac{1}{5} left(- 5 x – 2right) right )}right)$$
Общее упрощение
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/ 21 – 25*x – 20*x 47*asin(2/5 + x)
———————- + —————-
50 50
$$frac{1}{50} sqrt{- 25 x^{2} – 20 x + 21} + frac{47}{50} {asin}{left (x + frac{2}{5} right )}$$
Общий знаменатель
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/ 2
/ 21 – 25*x – 20*x 47*asin(2/5 + x)
———————- + —————-
50 50
$$frac{1}{50} sqrt{- 25 x^{2} – 20 x + 21} + frac{47}{50} {asin}{left (x + frac{2}{5} right )}$$
Комбинаторика
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/ 2
/ 21 – 25*x – 20*x + 47*asin(2/5 + x)
—————————————–
50
$$frac{1}{50} left(sqrt{- 25 x^{2} – 20 x + 21} + 47 {asin}{left (x + frac{2}{5} right )}right)$$
