Rešenje - Osobine kružnica

Prečnik $$\left(d\right)$$ ima dvostruku vrednost radijusa:

$$d=2\cdot r$$

r=49,39635614091387

$$d=2\cdot 49,39635614091387$$

$$d=98,79271228182775$$

Opseg $$\left(c\right)$$ ima dvostruku vrednost radijusa pomnoženo sa π:

$$c=2\cdot r\cdot \pi$$

r=49,39635614091387

$$c=2\cdot 49,39635614091387\cdot \pi$$

$$c=98,79271228182775\cdot \pi$$

Površina $$\left(a\right)$$ ima vrednost kvadrata radijusa pomnoženo sa π:

$$a=r^2\cdot \pi$$

r=49,39635614091387

$$a=49,{39635614091387}^2\cdot \pi$$

$$a=2440\cdot \pi$$

Koordinate središta kružnice se obično, ali ne uvek, prikazuju sa $$h$$ i $$k$$ u standardnoj jednačini kružnice: $${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$$
Otkrijte $$h$$ i $$k$$ u jednačini:
$$x+{50}^2+y^2=2440$$
$$h=-50$$
$$k=0$$
Središte $$\left(-50;0\right)$$

Da biste našli $$x$$ -presek(e), supstitucirajte $$0$$ za $$y$$ u standardnoj formi jednačine kruga
$${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$$
i rešite kvadratnu jednačinu za $$x$$:

$${\left(x+50\right)}^2+{\left(y+0\right)}^2=2440$$

$${\left(x+50\right)}^2+{\left(0+0\right)}^2=2440$$

$${\left(x+50\right)}^2+{\left(-0\right)}^2=2440$$

$${\left(x+50\right)}^2+0=2440$$

$${\left(x+50\right)}^2=2440-0$$

$${\left(x+50\right)}^2=2440$$

$$\sqrt{\left({\left(x+50\right)}^2\right)}=\sqrt{\left(2440\right)}$$

$$x+50=\sqrt{\left(2440\right)}$$

$$x=\pm \sqrt{\left(2440\right)}-50$$

$$x_1=\left(\sqrt{\left(2440\right)}-50,0\right),x_2=\left(-\sqrt{\left(2440\right)}-50,0\right)$$

Da bi se pronašli odsečci na osi $$y$$, zameni $$0$$ za $$x$$ u standardnoj jednačini kružnice $${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$$ i reši kvadratnu jednačinu za $$y$$:

$${\left(x+50\right)}^2+{\left(y+0\right)}^2=2440$$

$${\left(0+50\right)}^2+{\left(y+0\right)}^2=2440$$

$${\left(50\right)}^2+{\left(y+0\right)}^2=2440$$

$$2500+{\left(y+0\right)}^2=2440$$

$${\left(y+0\right)}^2=2440-2500$$

$${\left(y+0\right)}^2=-60$$

$$\sqrt{\left({\left(y+0\right)}^2\right)}=\sqrt{\left(-60\right)}$$

$$y+0=\sqrt{\left(-60\right)}$$

$$y=\pm \sqrt{\left(-60\right)}-0$$

Nema odsečaka na osi y