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Консультация № 187336
14.05.2013, 15:26
90.68 руб.
0
3
3
Обсуждение
14.05.2013, 15:46
общий
это ответ
Здравствуйте, Илья!
5.
Точка A отвечает t=0, а точка B отвечает t=pi/2. Элемент длины дуги
dl=([x'(t)]2+[y'(t)]2)1/2dt=(9cos4tsin2t+9sin4tcos2t)1/2dt=3sintcost(cos2t+sin2t)1/2dt=3sintcostdt
Искомый интеграл
I=[$8747$]0pi/2y(t)dl=[$8747$]0pi/2sin3t*3sintcostdt=3[$8747$]0pi/2sin4tcostdt=3[$8747$]0pi/2sin4td(sint)
После замены u=sint получаем
I=3[$8747$]01u4du=(3u5/5)|01=3/5
5.
Точка A отвечает t=0, а точка B отвечает t=pi/2. Элемент длины дуги
dl=([x'(t)]2+[y'(t)]2)1/2dt=(9cos4tsin2t+9sin4tcos2t)1/2dt=3sintcost(cos2t+sin2t)1/2dt=3sintcostdt
Искомый интеграл
I=[$8747$]0pi/2y(t)dl=[$8747$]0pi/2sin3t*3sintcostdt=3[$8747$]0pi/2sin4tcostdt=3[$8747$]0pi/2sin4td(sint)
После замены u=sint получаем
I=3[$8747$]01u4du=(3u5/5)|01=3/5
14.05.2013, 16:08
общий
это ответ
Здравствуйте, Илья!
7
Абсцисса центра тяжести:
Ордината центра тяжести равна 0 по причине симметричности пластины.
7
Абсцисса центра тяжести:
Ордината центра тяжести равна 0 по причине симметричности пластины.
14.05.2013, 17:22
общий
это ответ
Здравствуйте, Илья!
8.
grad U = (Ux', Uy', Uz') = (2xyz2, x2z2, 2x2yz),
grad U|M = (2[$183$]2[$183$](1/3)[$183$](3/2), 4[$183$](3/2), 2[$183$]4[$183$](1/3)[$183$][$8730$](3/2)) = (2, 6, 4[$8730$]6/3).
grad V = (Vx', Vy', Vz') = (3x, 6y, -4z),
grad V|M = (3[$183$]2, 6[$183$](1/3), -4[$183$][$8730$](3/2)) = (6, 2, -2[$8730$]6).
Пусть [$966$] - угол между градиентами полей U и V.
cos [$966$] = (grad U[$183$]grad V)/(|grad U|[$183$]|grad V|).
В точке М имеем:
Искомый угол равен
8.
grad U = (Ux', Uy', Uz') = (2xyz2, x2z2, 2x2yz),
grad U|M = (2[$183$]2[$183$](1/3)[$183$](3/2), 4[$183$](3/2), 2[$183$]4[$183$](1/3)[$183$][$8730$](3/2)) = (2, 6, 4[$8730$]6/3).
grad V = (Vx', Vy', Vz') = (3x, 6y, -4z),
grad V|M = (3[$183$]2, 6[$183$](1/3), -4[$183$][$8730$](3/2)) = (6, 2, -2[$8730$]6).
Пусть [$966$] - угол между градиентами полей U и V.
cos [$966$] = (grad U[$183$]grad V)/(|grad U|[$183$]|grad V|).
В точке М имеем:
Искомый угол равен
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