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Kiek lygtis $$4\cdot cos(x)+\sqrt {6} = 6$$ turi sprendinių, priklausančių intervalui [-90; 360]?
Sprendimas.
4* cos(x)+saknis(
6) =
6
6) = 6
|
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4* cos(x)+saknis(6) = 6$$4\cdot cos(x)+\sqrt {6}$$ = $$6$$
6) = 6$$4\cdot cos(x)+\sqrt {6}$$ = $$6$$ 4* cos(x) = (6-saknis(6))$$4\cdot cos(x)$$ = $$(6-\sqrt {6})$$
6))$$4\cdot cos(x)$$ = $$(6-\sqrt {6})$$cos(x) =
$$cos(x)$$ = $$\frac{6-\sqrt {6}}{4}$$
| (6-saknis(6)) |
| / 4 |
$${\normalsize \sqrt {6}}$$ = $${\normalsize 2.45}$$
cos(x) =
$$cos(x)$$ = $$\frac{6-2.45}{4}$$
| (6-2.45) |
| / 4 |
$${\normalsize 6-2.45}$$ = $${\normalsize 3.55}$$
cos(x) =
$$cos(x)$$ = $$\frac{3.55}{4}$$
| (3.55) |
| / 4 |
$${\normalsize \frac{3.55}{4}}$$ = $${\normalsize \frac{3.55}{4}}$$
cos(x) =
$$cos(x)$$ = $$\frac{3.55}{4}$$
| 3.55 |
| / 4 |
$${\normalsize \frac{3.55}{4}}$$ = $${\normalsize 0.89}$$
cos(x) = 0.89$$cos(x)$$ = $$0.89$$
$$4\cdot cos(x)+\sqrt {6}$$ = $$6$$
$$cos(x)$$ = $$\frac{6-\sqrt {6}}{4}$$
$$cos(x)$$ = $$\frac{6-2.45}{4}$$
$$cos(x)$$ = $$\frac{3.55}{4}$$
$$cos(x)$$ = $$0.89$$
Brėžiame horizontalią tiesę y=0.89 ir kosinuso grafiką nuo -90 iki 360 laipsnių.
Grafikai intervale kertasi 3 kartus.
Atsakymas. 3