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Задать вопрос экспертам

Консультация № 184175

08.10.2011, 20:11

51.74 руб.

08.10.2011, 20:54

0 3 1

Образование

Здравствуйте, уважаемые эксперты! Прошу вас, помогите!!! https://rfpro.ru/upload/6374

Обсуждение

давно

Орловский Дмитрий

Мастер-Эксперт
319965
1463

08.10.2011, 21:28

общий

это ответ

Здравствуйте, Ольга Никанова!
5) подставляя x=rcos[$966$], y=rsin[$966$] в уравнение кривой, находим
r⁴=a²r²(3cos²[$966$]+2sin²[$966$])
сокращая на r² и подставляя cos²[$966$]=(1+cos2[$966$])/2, sin²[$966$]=(1-cos2[$966$])/2, находим
r([$966$])=a[$8730$](5/2+1/2cos2[$966$])
эта функция всюду положительна, поэтому [$966$] меняется от 0 до 2pi
S=[$8747$][$8747$]dxdy=[$8747$][$8747$]rdrd[$966$]=[$8747$]₀^2pid[$966$][$8747$]₀^r([$966$])rdr=
=[$8747$]₀^2pid[$966$](r²/2)|₀^r([$966$])=(1/2)[$8747$]₀^2pir²([$966$])d[$966$]=(a²/4)[$8747$]₀^2pi(5+cos2[$966$])d[$966$]=
=(a²/4)(5[$966$]+sin2[$966$]/2)|₀^2pi=5*pi*a²/2

давно

Орловский Дмитрий

Мастер-Эксперт
319965
1463

09.10.2011, 00:21

общий

Решение 6 в присоединенном файле.

Прикрепленные файлы:

094d6b995d855c19b7dbaee0a9c6c4c7.jpg

скачать (380.00 кБ)

Неизвестный

09.10.2011, 01:49

общий

Адресаты:

Спасибо Вам огромное,Дмитрий!!! Вы как всегда на высоте!!!

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