1.Link zadatka Vrednost izraza [inline]\displaystyle\left[\left(0.75\right)^{-4}:\left(1\frac{7}{9}\right)^{\frac{3}{2}}+\left(-3\right)^2:\left(\frac{2}{3}\right)^{-3}\right]^{\frac{1}{2}}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]16[/inline]; [inline]\text{B)}[/inline] [inline]8[/inline]; [inline]\text{C)}[/inline] [inline]4[/inline]; [inline]\text{D)}[/inline] [inline]1[/inline]; [inline]\text{E)}[/inline] [inline]2[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]16[/inline]; [inline]\text{B)}[/inline] [inline]8[/inline]; [inline]\text{C)}[/inline] [inline]4[/inline]; [inline]\text{D)}[/inline] [inline]1[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]2[/inline]; [inline]\text{N)}[/inline] Ne znam.
2.Link zadatka Ako kompleksan broj [inline]z[/inline] zadovoljava jednačinu [inline]\displaystyle\left(z+i\right)^2-z\cdot\overline z=\frac{i-1}{2}[/inline], [inline]i^2=-1[/inline], onda je [inline]\text{Re}\left(z\right)+\text{Im}\left(z\right)[/inline] jednako:
[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\sqrt2}{2}[/inline]; [inline]\text{C)}[/inline] [inline]0[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{E)}[/inline] [inline]-1[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\sqrt2}{2}[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]0[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{E)}[/inline] [inline]-1[/inline]; [inline]\text{N)}[/inline] Ne znam.
3.Link zadatka Tokom takmičenja u skoku u dalj jedna atletičarka je u prvoj seriji preskočila [inline]6\text{ m}[/inline], dok je u drugoj seriji preskočila za [inline]5\%[/inline] veću dužinu u odnosu na prvu seriju. Ako je skok iz druge serije bio za [inline]10\%[/inline] kraći od skoka iz treće serije, onda je u trećoj seriji ova atletičarka preskočila:
[inline]\text{A)}[/inline] [inline]7.3\text{ m}[/inline]; [inline]\text{B)}[/inline] [inline]7.2\text{ m}[/inline]; [inline]\text{C)}[/inline] [inline]6.8\text{ m}[/inline]; [inline]\text{D)}[/inline] [inline]6.9\text{ m}[/inline]; [inline]\text{E)}[/inline] [inline]7\text{ m}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]7.3\text{ m}[/inline]; [inline]\text{B)}[/inline] [inline]7.2\text{ m}[/inline]; [inline]\text{C)}[/inline] [inline]6.8\text{ m}[/inline]; [inline]\text{D)}[/inline] [inline]6.9\text{ m}[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]7\text{ m}[/inline]; [inline]\text{N)}[/inline] Ne znam.
4.Link zadatka Ako je [inline]f\left(x+2\right)=2x-1[/inline] i [inline]f\bigl(g\left(x\right)-2\bigr)=2x+1[/inline], onda je:
[inline]\text{A)}[/inline] [inline]g\left(x\right)=x+1[/inline]; [inline]\text{B)}[/inline] [inline]g\left(x\right)=x+5[/inline]; [inline]\text{C)}[/inline] [inline]g\left(x\right)=2x+3[/inline]; [inline]\text{D)}[/inline] [inline]g\left(x\right)=2x+6[/inline]; [inline]\text{E)}[/inline] [inline]g\left(x\right)=x+3[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]g\left(x\right)=x+1[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]g\left(x\right)=x+5[/inline]; [inline]\text{C)}[/inline] [inline]g\left(x\right)=2x+3[/inline]; [inline]\text{D)}[/inline] [inline]g\left(x\right)=2x+6[/inline]; [inline]\text{E)}[/inline] [inline]g\left(x\right)=x+3[/inline]; [inline]\text{N)}[/inline] Ne znam.
5.Link zadatka Ako je [inline]ab>0[/inline], onda je izraz [inline]\displaystyle\frac{\left(a+\sqrt{ab}+b\right)^2-\left(a-\sqrt{ab}+b\right)^2}{a^3+b^3}\cdot\left(\left(a-b\right)^2+ab\right)[/inline] identički jednak izrazu:
[inline]\text{A)}[/inline] [inline]4ab[/inline]; [inline]\text{B)}[/inline] [inline]2ab[/inline]; [inline]\text{C)}[/inline] [inline]4\sqrt{ab}[/inline]; [inline]\text{D)}[/inline] [inline]2\sqrt{ab}[/inline]; [inline]\text{E)}[/inline] [inline]2\left(a+b\right)[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]4ab[/inline]; [inline]\text{B)}[/inline] [inline]2ab[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]4\sqrt{ab}[/inline]; [inline]\text{D)}[/inline] [inline]2\sqrt{ab}[/inline]; [inline]\text{E)}[/inline] [inline]2\left(a+b\right)[/inline]; [inline]\text{N)}[/inline] Ne znam.
6.Link zadatka Ako su [inline]x_1[/inline] i [inline]x_2[/inline] realna rešenja jednačine [inline]2x^2+2\left(m-1\right)x+m^2+m+2=0[/inline], [inline]m\in\mathbb{R}[/inline], onda je najveća vrednost izraza [inline]\left|x_1-x_2\right|[/inline] jednaka:
[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline]; [inline]\text{C)}[/inline] [inline]2[/inline]; [inline]\text{D)}[/inline] [inline]4[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline]; [inline]\text{C)}[/inline] [inline]2[/inline]; [inline]\text{D)}[/inline] [inline]4[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{N)}[/inline] Ne znam.
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7.Link zadatka Neka su [inline]a[/inline] i [inline]b[/inline] vrednosti za koje je polinom [inline]P\left(x\right)=x^{2016}+27x^{2013}+ax+b[/inline] deljiv sa [inline]x+1[/inline], a pri deljenju sa [inline]x+3[/inline] daje ostatak [inline]16[/inline]. Tada je vrednost izraza [inline]\sqrt{a+b}[/inline] jednaka:
[inline]\text{A)}[/inline] [inline]6[/inline]; [inline]\text{B)}[/inline] [inline]2[/inline]; [inline]\text{C)}[/inline] [inline]8[/inline]; [inline]\text{D)}[/inline] [inline]5[/inline]; [inline]\text{E)}[/inline] [inline]4[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]6[/inline]; [inline]\text{B)}[/inline] [inline]2[/inline]; [inline]\text{C)}[/inline] [inline]8[/inline]; [inline]\text{D)}[/inline] [inline]5[/inline]; [inline]\text{E)}[/inline] [inline]4[/inline]; [inline]\text{N)}[/inline] Ne znam.
8.Link zadatka Ako je [inline]\log_38=a[/inline] i [inline]\log_925=b[/inline], onda je vrednost [inline]\log_{20}81[/inline] jednaka:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{6}{2a+3b}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{12}{3a+2b}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{12}{3a+4b}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{12}{2a+3b}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{6}{3a+2b}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{6}{2a+3b}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{12}{3a+2b}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{12}{3a+4b}[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\displaystyle\frac{12}{2a+3b}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{6}{3a+2b}[/inline]; [inline]\text{N)}[/inline] Ne znam.
9.Link zadatka Realno rešenje jednačine [inline]\sqrt{x-\sqrt{x+8}}+1=\sqrt{x+1}[/inline] pripada intervalu:
[inline]\text{A)}[/inline] [inline]\left(-1,2\right)[/inline]; [inline]\text{B)}[/inline] [inline]\left[5,8\right)[/inline]; [inline]\text{C)}[/inline] [inline]\left[11,14\right)[/inline]; [inline]\text{D)}[/inline] [inline]\left[2,5\right)[/inline]; [inline]\text{E)}[/inline] [inline]\left[8,11\right)[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\left(-1,2\right)[/inline]; [inline]\text{B)}[/inline] [inline]\left[5,8\right)[/inline]; [inline]\text{C)}[/inline] [inline]\left[11,14\right)[/inline]; [inline]\text{D)}[/inline] [inline]\left[2,5\right)[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\left[8,11\right)[/inline]; [inline]\text{N)}[/inline] Ne znam.
10.Link zadatka Broj različitih realnih rešenja jednačine [inline]3^{3x+1}-3^{2x}\cdot4^{x+1}-3^{x+1}\cdot4^{2x}+4^{3x+1}=0[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] veći od [inline]3[/inline]; [inline]\text{C)}[/inline] [inline]2[/inline]; [inline]\text{D)}[/inline] [inline]0[/inline]; [inline]\text{E)}[/inline] [inline]3[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] veći od [inline]3[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]2[/inline]; [inline]\text{D)}[/inline] [inline]0[/inline]; [inline]\text{E)}[/inline] [inline]3[/inline]; [inline]\text{N)}[/inline] Ne znam.
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11.Link zadatka Skup svih rešenja nejednačine [inline]\log_{x-1}\left(x+1\right)>\log_{\sqrt{x-1}}\left(x-1\right)[/inline] je:
[inline]\text{A)}[/inline] [inline]\left(3,5\right)[/inline]; [inline]\text{B)}[/inline] [inline]\left(2,3\right)[/inline]; [inline]\text{C)}[/inline] [inline]\left(1,2\right)[/inline]; [inline]\text{D)}[/inline] [inline]\left(1,3\right)[/inline]; [inline]\text{E)}[/inline] [inline]\left(2,5\right)[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\left(3,5\right)[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\left(2,3\right)[/inline]; [inline]\text{C)}[/inline] [inline]\left(1,2\right)[/inline]; [inline]\text{D)}[/inline] [inline]\left(1,3\right)[/inline]; [inline]\text{E)}[/inline] [inline]\left(2,5\right)[/inline]; [inline]\text{N)}[/inline] Ne znam.
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12.Link zadatka U razvoju [inline]\left(\sqrt[6]5+\sqrt[8]7\right)^{2016}[/inline] broj članova koji su celi brojevi jednak je:
[inline]\text{A)}[/inline] [inline]84[/inline]; [inline]\text{B)}[/inline] [inline]43[/inline]; [inline]\text{C)}[/inline] [inline]42[/inline]; [inline]\text{D)}[/inline] [inline]85[/inline]; [inline]\text{E)}[/inline] [inline]169[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]84[/inline]; [inline]\text{B)}[/inline] [inline]43[/inline]; [inline]\text{C)}[/inline] [inline]42[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]85[/inline]; [inline]\text{E)}[/inline] [inline]169[/inline]; [inline]\text{N)}[/inline] Ne znam.
13.Link zadatka Ako je zbir prva tri člana rastućeg geometrijskog niza jednak [inline]26[/inline], a zbir trećeg, četvrtog i petog člana jednak [inline]234[/inline], onda je proizvod prvog i petog člana tog niza jednak:
[inline]\text{A)}[/inline] [inline]324[/inline]; [inline]\text{B)}[/inline] [inline]196[/inline]; [inline]\text{C)}[/inline] [inline]256[/inline]; [inline]\text{D)}[/inline] [inline]400[/inline]; [inline]\text{E)}[/inline] [inline]144[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]324[/inline]; [inline]\text{B)}[/inline] [inline]196[/inline]; [inline]\text{C)}[/inline] [inline]256[/inline]; [inline]\text{D)}[/inline] [inline]400[/inline]; [inline]\text{E)}[/inline] [inline]144[/inline]; [inline]\text{N)}[/inline] Ne znam.
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14.Link zadatka U trouglu [inline]ABC[/inline] je [inline]\left|AB\right|=2\text{ cm}[/inline], [inline]\left|AC\right|=3\text{ cm}[/inline] i [inline]\displaystyle\cos\alpha=\frac{1}{3}[/inline], gde je [inline]\alpha[/inline] unutrašnji ugao kod temena [inline]A[/inline]. Dužina poluprečnika upisane kružnice trougla [inline]ABC[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{3}{4}\text{ cm}[/inline]; [inline]\text{B)}[/inline] [inline]1\text{ cm}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\sqrt2}{2}\text{ cm}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{2}\text{ cm}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{\sqrt3}{2}\text{ cm}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{3}{4}\text{ cm}[/inline]; [inline]\text{B)}[/inline] [inline]1\text{ cm}[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\displaystyle\frac{\sqrt2}{2}\text{ cm}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{2}\text{ cm}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{\sqrt3}{2}\text{ cm}[/inline]; [inline]\text{N)}[/inline] Ne znam.
15.Link zadatka Vrednost izraza [inline]\displaystyle\frac{\sin10^\circ+\cos40^\circ}{\cos10^\circ-\cos130^\circ}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{\sqrt3}{2}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\sqrt2}{2}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{\sqrt3}{3}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{\sqrt3}{2}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\sqrt2}{2}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle\frac{\sqrt3}{3}[/inline]; [inline]\text{N)}[/inline] Ne znam.
16.Link zadatka Ako je prava [inline]3y-4x=0[/inline] asimptota, a prava [inline]8x+\sqrt{11}y=20[/inline] tangenta hiperbole [inline]\displaystyle\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/inline], [inline]a,b\in\mathbb{R}[/inline], onda je vrednost izraza [inline]b^2-a^2[/inline] jednaka:
[inline]\text{A)}[/inline] [inline]21[/inline]; [inline]\text{B)}[/inline] [inline]35[/inline]; [inline]\text{C)}[/inline] [inline]28[/inline]; [inline]\text{D)}[/inline] [inline]7[/inline]; [inline]\text{E)}[/inline] [inline]14[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]21[/inline]; [inline]\text{B)}[/inline] [inline]35[/inline]; [inline]\text{C)}[/inline] [inline]28[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]7[/inline]; [inline]\text{E)}[/inline] [inline]14[/inline]; [inline]\text{N)}[/inline] Ne znam.
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17.Link zadatka Neka je [inline]n[/inline] broj svih šestocifrenih brojeva čije su prve tri cifre parni brojevi, a poslednje tri cifre različiti neparni brojevi. Broj svih delilaca broja [inline]n[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]60[/inline]; [inline]\text{B)}[/inline] [inline]30[/inline]; [inline]\text{C)}[/inline] [inline]20[/inline]; [inline]\text{D)}[/inline] [inline]40[/inline]; [inline]\text{E)}[/inline] [inline]32[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]60[/inline]; [inline]\text{B)}[/inline] [inline]30[/inline]; [inline]\text{C)}[/inline] [inline]20[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]40[/inline]; [inline]\text{E)}[/inline] [inline]32[/inline]; [inline]\text{N)}[/inline] Ne znam.
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18.Link zadatka Zbir svih rešenja jednačine [inline]\cos^23x+\sin^24x=1[/inline] koja pripadaju intervalu [inline]\displaystyle\left(0,\frac{\pi}{2}\right)[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{5\pi}{7}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{6\pi}{7}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{4\pi}{7}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{3\pi}{7}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{8\pi}{7}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{5\pi}{7}[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\displaystyle\frac{6\pi}{7}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{4\pi}{7}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{3\pi}{7}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{8\pi}{7}[/inline]; [inline]\text{N)}[/inline] Ne znam.
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19.Link zadatka Osnova prave piramide je paralelogram sa stranicama dužina [inline]10\text{ cm}[/inline] i [inline]18\text{ cm}[/inline] i površinom [inline]90\text{ cm}^2[/inline]. Ako je zapremina piramide [inline]180\text{ cm}^3[/inline], onda je površina omotača date piramide (u [inline]\text{cm}^2[/inline]) jednaka:
[inline]\text{A)}[/inline] [inline]192[/inline]; [inline]\text{B)}[/inline] [inline]200[/inline]; [inline]\text{C)}[/inline] [inline]196[/inline]; [inline]\text{D)}[/inline] [inline]224[/inline]; [inline]\text{E)}[/inline] [inline]248[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]192[/inline]; [inline]\text{B)}[/inline] [inline]200[/inline]; [inline]\text{C)}[/inline] [inline]196[/inline]; [inline]\text{D)}[/inline] [inline]224[/inline]; [inline]\text{E)}[/inline] [inline]248[/inline]; [inline]\text{N)}[/inline] Ne znam.
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20.Link zadatka U polukrug poluprečnika [inline]r=\sqrt5\text{ cm}[/inline] upisan je pravougaonik maksimalnog obima tako da jedna stranica pravougaonika pripada prečniku polukruga. Dužina dijagonale tog pravougaonika je:
[inline]\text{A)}[/inline] [inline]2\sqrt5\text{ cm}[/inline]; [inline]\text{B)}[/inline] [inline]\sqrt{18}\text{ cm}[/inline]; [inline]\text{C)}[/inline] [inline]\sqrt{19}\text{ cm}[/inline]; [inline]\text{D)}[/inline] [inline]\sqrt{17}\text{ cm}[/inline]; [inline]\text{E)}[/inline] [inline]4\text{ cm}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]2\sqrt5\text{ cm}[/inline]; [inline]\text{B)}[/inline] [inline]\sqrt{18}\text{ cm}[/inline]; [inline]\text{C)}[/inline] [inline]\sqrt{19}\text{ cm}[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\sqrt{17}\text{ cm}[/inline]; [inline]\text{E)}[/inline] [inline]4\text{ cm}[/inline]; [inline]\text{N)}[/inline] Ne znam.
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Napomena: Ukoliko vam treba pomoć oko rešavanja nekog od zadataka koji dosad nije obrađivan ni na jednoj temi, slobodno zatražite pomoć na forumu „Matemanija“, naravno uz poštovanje forumskih pravila.