Определи значение x, соответствующее значению y=0 для линейного уравнения 7x+12y=35.

S3: which kind of sports is your favourite?
S1: Oh, I lobe hockey. I know everything about it. It's a winter sport, but simetimes people play it even when it's summer or autumn.
S3: and you, S2?
S2: well, I hate hockey. It's very dangerous to play in it, though sometimes games can be quite interesting. I love swimming. It's great to swim and relax in the same time. I love this feeling of relaxing and training [in the same time].
S1: oh, and you, S3? Which kind of sports do you prefer?
S3: Frankly speaking, I like sport(s) but I didn't really know what I should choose. Can you help with that choice?
S1: Yes, of course. Let's talk about it a bit later.
S3+S2: Ok. See you then(,)guys. Bye.

а) a1 = 30, a2 = 24, d = 24 — 30 = -6

Формула n-ого члена: a(n) = 36 — 6n

b) Найдем количество положительных чисел в этой прогрессии

{ a(n) = 36 — 6n > 0

{ a(n+1) = 36 — 6(n+1) < 0

Раскрываем скобки

{ a(n) = 36 — 6n >= 0

{ a(n+1) = 36 — 6n — 6 = 30 — 6n  < 0

Переносим n направо и делим неравенства на 6

{ 6 >= n

{ 5 < n

Очевидно, n = 5

a(5) = 36 — 6*5 = 6

a(6) = 36 — 6*6 = 0

c) Определим количество чисел, если их сумма равна -150.

S = (2a1 + d*(n-1))*n/2 = -150

(2*30 — 6*(n-1))*n = -150*2 = -300

(66 — 6n)*n = -300 = -6*50

Сокращаем на 6

(11 — n)*n = -50

n^2 — 11n — 50 = 0

(n — 25)(n + 2) = 0

Так как n > 0, то n = 25

Объяснение: