Rešenje - Osobine kružnica

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

$$d=2\cdot r$$

r=20,396078054371138

$$d=2\cdot 20,396078054371138$$

$$d=40,792156108742276$$

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

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

r=20,396078054371138

$$c=2\cdot 20,396078054371138\cdot \pi$$

$$c=40,792156108742276\cdot \pi$$

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

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

r=20,396078054371138

$$a=20,{396078054371138}^2\cdot \pi$$

$$a=416\cdot \pi$$

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:
$$x^2+y^2=416$$
$$h=0$$
$$k=0$$
Središte $$\left(0;0\right)$$

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 $$x$$:

$${\left(x+0\right)}^2+{\left(y+0\right)}^2=416$$

$${\left(x+0\right)}^2+{\left(0+0\right)}^2=416$$

$${\left(x+0\right)}^2+{\left(-0\right)}^2=416$$

$${\left(x+0\right)}^2+0=416$$

$${\left(x+0\right)}^2=416-0$$

$${\left(x+0\right)}^2=416$$

$$\sqrt{\left({\left(x+0\right)}^2\right)}=\sqrt{\left(416\right)}$$

$$x+0=\sqrt{\left(416\right)}$$

$$x=\pm \sqrt{\left(416\right)}-0$$

$$x_1=\left(\sqrt{\left(416\right)}-0,0\right),x_2=\left(-\sqrt{\left(416\right)}-0,0\right)$$

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 $$y$$:

$${\left(x+0\right)}^2+{\left(y+0\right)}^2=416$$

$${\left(0+0\right)}^2+{\left(y+0\right)}^2=416$$

$${\left(-0\right)}^2+{\left(y+0\right)}^2=416$$

$$0+{\left(y+0\right)}^2=416$$

$${\left(y+0\right)}^2=416-0$$

$${\left(y+0\right)}^2=416$$

$$\sqrt{\left({\left(y+0\right)}^2\right)}=\sqrt{\left(416\right)}$$

$$y+0=\sqrt{\left(416\right)}$$

$$y=\pm \sqrt{\left(416\right)}-0$$

$$y_1=\left(0,\sqrt{\left(416\right)}-0\right),y_2=\left(0,-\sqrt{\left(416\right)}-0\right)$$