Длина прямоугольника 10 дм а ширина 4 дм чему равен его периметр, его площадь?

Площадь= 4дм*10дм=40дм
периметр=10дм+10дм+4дм+4дм=28дм

10 +4=14 см ширина
10+14=24 см периметр
10*14=140 см площадь

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Даны 3 точки плоскости А(2,-3) В(-1,4) С(1,-2) , необходимо:

а) создать уравнение прямой АВ, найти её угловой коэффициент.

Вектор АВ = (-3; 7), к = Δу/Δх = -7/3.

Уравнение: (х - 2)/(-3) = у + 3)/7 или 7х + 3у - 5 = 0.

б) составить уравнение прямых, которые проходят через точку С параллельно и перпендикулярно к прямой АВ.

У параллельной прямой коэффициенты перед переменными сохраняются: 7х + 3у + С = 0, подставим координаты точки С:

7*1 + 3*(-2) + С = 0, отсюда С = 6 - 7 = -1.

Уравнение 7х + 3у - 1 = 0.

У перпендикулярной прямой коэффициенты А и В меняются на -В и А.

Уравнение -3х + 7у + С = 0. Подставим координаты точки С.

-3*1 + 7*(-2) + С = 0, отсюда С = 14 + 3 = 17.

Уравнение -3х + 7у + 17 = 0.

в) Найти угол между прямыми АВ и ВС.

Вектор ВА = -АВ = (3; -7), модуль равен √(9 + 49) = √58.

вектор ВС = (2; -6), модуль равен √(4 + 36) = √40.

cos B = (3*2 + (-7)*(-6))/(√58*√40) = 48/√(58*40) = 12/√145 = 0,996546.

Угол равен 0,083141 радиан или 4,763642 градусов

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