Prijemni ispit na Elektrotehničkom fakultetu u Beogradu
29. jun 2020.
1.Link zadatka Vrednost izraza [inline]\log_43\log_54\log_65\log_76\log_87\log_98[/inline] jednaka je:
[inline]\text{(A)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline] [inline]\text{(C)}[/inline] [inline]2[/inline] [inline]\text{(D)}[/inline] [inline]3[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle\frac{2}{3}\log_23[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\enclose{box}{\text{(A)}}[/inline] [inline]\displaystyle\frac{1}{2}[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline] [inline]\text{(C)}[/inline] [inline]2[/inline] [inline]\text{(D)}[/inline] [inline]3[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle\frac{2}{3}\log_23[/inline] [inline]\text{(N)}[/inline] Ne znam
2.Link zadatka Ako je površina kružnog isečka jednaka [inline]15\%[/inline] površine kruga, koliki je ugao tog kružnog isečka?
[inline]\text{(A)}[/inline] [inline]15^\circ[/inline] [inline]\text{(B)}[/inline] [inline]30^\circ[/inline] [inline]\text{(C)}[/inline] [inline]45^\circ[/inline] [inline]\text{(D)}[/inline] [inline]54^\circ[/inline] [inline]\text{(E)}[/inline] [inline]60^\circ[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]15^\circ[/inline] [inline]\text{(B)}[/inline] [inline]30^\circ[/inline] [inline]\text{(C)}[/inline] [inline]45^\circ[/inline] [inline]\enclose{box}{\text{(D)}}[/inline] [inline]54^\circ[/inline] [inline]\text{(E)}[/inline] [inline]60^\circ[/inline] [inline]\text{(N)}[/inline] Ne znam
3.Link zadatka Vrednost izraza [inline]\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt6\right)\sqrt{4-\sqrt{15}}[/inline] jednaka je:
[inline]\text{(A)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline] [inline]\text{(B)}[/inline] [inline]1[/inline] [inline]\text{(C)}[/inline] [inline]2[/inline] [inline]\text{(D)}[/inline] [inline]\sqrt2[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle\frac{\sqrt2}{2}[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline] [inline]\text{(B)}[/inline] [inline]1[/inline] [inline]\enclose{box}{\text{(C)}}[/inline] [inline]2[/inline] [inline]\text{(D)}[/inline] [inline]\sqrt2[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle\frac{\sqrt2}{2}[/inline] [inline]\text{(N)}[/inline] Ne znam
4.Link zadatka Inverzna funkcija funkcije [inline]f\colon[3,+\infty)\to[3,+\infty)[/inline] date sa [inline]f(x)=3\sqrt{x-3}+3[/inline] jeste funkcija [inline]g\colon[3,+\infty)\to[3,+\infty)[/inline] za koju važi:
[inline]\text{(A)}[/inline] [inline]\displaystyle g(x)=\frac{1}{9}x^2-\frac{2}{3}x+4[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle g(x)=\frac{1}{9}x^2+\frac{2}{3}x+4[/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle g(x)=\frac{1}{9}x^2+\frac{2}{3}x-2[/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle g(x)=\frac{1}{9}x^2-\frac{2}{3}x+2[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle g(x)=9\left(x^2-6x+\frac{28}{3}\right)[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\enclose{box}{\text{(A)}}[/inline] [inline]\displaystyle g(x)=\frac{1}{9}x^2-\frac{2}{3}x+4[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle g(x)=\frac{1}{9}x^2+\frac{2}{3}x+4[/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle g(x)=\frac{1}{9}x^2+\frac{2}{3}x-2[/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle g(x)=\frac{1}{9}x^2-\frac{2}{3}x+2[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle g(x)=9\left(x^2-6x+\frac{28}{3}\right)[/inline] [inline]\text{(N)}[/inline] Ne znam
5.Link zadatka Grafik funkcije [inline]f(x)=ax^2+bx+c[/inline], [inline]a,b,c\in\mathbb{R}[/inline], [inline]x\in\mathbb{R}[/inline], dat je na slici.
Vrednost izraza [inline]a(b+c)[/inline] jednaka je:
[inline]\text{(A)}[/inline] [inline]-1[/inline] [inline]\text{(B)}[/inline] [inline]5[/inline] [inline]\text{(C)}[/inline] [inline]7[/inline] [inline]\text{(D)}[/inline] [inline]-7[/inline] [inline]\text{(E)}[/inline] [inline]6[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]-1[/inline] [inline]\text{(B)}[/inline] [inline]5[/inline] [inline]\text{(C)}[/inline] [inline]7[/inline] [inline]\enclose{box}{\text{(D)}}[/inline] [inline]-7[/inline] [inline]\text{(E)}[/inline] [inline]6[/inline] [inline]\text{(N)}[/inline] Ne znam
6.Link zadatka Proizvod najmanjeg i najvećeg korena polinoma [inline]P(x)=x^4-9x^2+18[/inline] jeste:
[inline]\text{(A)}[/inline] [inline]3[/inline] [inline]\text{(B)}[/inline] [inline]-3[/inline] [inline]\text{(C)}[/inline] [inline]6[/inline] [inline]\text{(D)}[/inline] [inline]-6[/inline] [inline]\text{(E)}[/inline] [inline]-\sqrt{18}[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]3[/inline] [inline]\text{(B)}[/inline] [inline]-3[/inline] [inline]\text{(C)}[/inline] [inline]6[/inline] [inline]\enclose{box}{\text{(D)}}[/inline] [inline]-6[/inline] [inline]\text{(E)}[/inline] [inline]-\sqrt{18}[/inline] [inline]\text{(N)}[/inline] Ne znam
7.Link zadatka Realni deo kompleksnog broja [inline]\left(z-z^2+2z^3\right)\left(2-z+z^2\right)[/inline], za [inline]\displaystyle z=\frac{-1+i\sqrt3}{2}[/inline], [inline]i^2=-1[/inline], jednak je:
[inline]\text{(A)}[/inline] [inline]4\left(1+\text{Im }^2z\right)[/inline] [inline]\text{(B)}[/inline] [inline]0[/inline] [inline]\text{(C)}[/inline] [inline]4[/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline] [inline]\text{(E)}[/inline] [inline]-\text{Re }z+1[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\enclose{box}{\text{(A)}}[/inline] [inline]4\left(1+\text{Im }^2z\right)[/inline] [inline]\text{(B)}[/inline] [inline]0[/inline] [inline]\text{(C)}[/inline] [inline]4[/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline] [inline]\text{(E)}[/inline] [inline]-\text{Re }z+1[/inline] [inline]\text{(N)}[/inline] Ne znam
8.Link zadatka Neka je definisan niz funkcija [inline]f_n\colon\mathbb{R}\to\mathbb{R}[/inline] sa [inline]f_1(x)=2x+2020[/inline], [inline]f_{n+1}(x)=f_1\bigl(f_n(x)\bigr)[/inline], [inline]n\in\mathbb{N}[/inline]. Tada je [inline]f_{2020}(-2020)[/inline] jednako:
[inline]\text{(A)}[/inline] [inline]2^{2020}[/inline] [inline]\text{(B)}[/inline] [inline]-2^{2020}[/inline] [inline]\text{(C)}[/inline] [inline]2020[/inline] [inline]\text{(D)}[/inline] [inline]-2020[/inline] [inline]\text{(E)}[/inline] [inline]0[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]2^{2020}[/inline] [inline]\text{(B)}[/inline] [inline]-2^{2020}[/inline] [inline]\text{(C)}[/inline] [inline]2020[/inline] [inline]\enclose{box}{\text{(D)}}[/inline] [inline]-2020[/inline] [inline]\text{(E)}[/inline] [inline]0[/inline] [inline]\text{(N)}[/inline] Ne znam
9.Link zadatka Figura [inline]F_1[/inline] dobijena je tako što je iz jednakostraničnog trougla čija je površina [inline]P[/inline] izbačen trougao čija su temena središta stranica polaznog trougla. Figura [inline]F_1[/inline] se sastoji iz [inline]3[/inline] trougla. Figura [inline]F_2[/inline] dobijena je tako što su iz figure [inline]F_1[/inline] izbačena tri trougla čija su temena središta stranica tri trougla koji čine figuru [inline]F_1[/inline]. Figura [inline]F_2[/inline] se sastoji iz [inline]9[/inline] trouglova. Figura [inline]F_{n+1}[/inline] dobijena je tako što je iz figure [inline]F_n[/inline] izbačeno [inline]3^n[/inline] trouglova čija su temena središta stranica [inline]3^n[/inline] trouglova koji čine figuru [inline]F_n[/inline]. Zbir površina svih figura [inline]F_n[/inline], [inline]n\in\mathbb{N}[/inline], dobijenih na opisani način, jednak je:
[inline]\text{(A)}[/inline] [inline]\displaystyle\frac{3}{4}P[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle\frac{4}{3}P[/inline] [inline]\text{(C)}[/inline] [inline]4P[/inline] [inline]\text{(D)}[/inline] [inline]3P[/inline] [inline]\text{(E)}[/inline] [inline]+\infty[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]\displaystyle\frac{3}{4}P[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle\frac{4}{3}P[/inline] [inline]\text{(C)}[/inline] [inline]4P[/inline] [inline]\enclose{box}{\text{(D)}}[/inline] [inline]3P[/inline] [inline]\text{(E)}[/inline] [inline]+\infty[/inline] [inline]\text{(N)}[/inline] Ne znam
10.Link zadatka Broj svih realnih rešenja jednačine [inline]2x^2-6x+\sqrt{x^2-3x+6}+2=0[/inline] jeste:
[inline]\text{(A)}[/inline] [inline]2[/inline] [inline]\text{(B)}[/inline] [inline]1[/inline] [inline]\text{(C)}[/inline] [inline]3[/inline] [inline]\text{(D)}[/inline] [inline]4[/inline] [inline]\text{(E)}[/inline] Veći od [inline]4[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\enclose{box}{\text{(A)}}[/inline] [inline]2[/inline] [inline]\text{(B)}[/inline] [inline]1[/inline] [inline]\text{(C)}[/inline] [inline]3[/inline] [inline]\text{(D)}[/inline] [inline]4[/inline] [inline]\text{(E)}[/inline] Veći od [inline]4[/inline] [inline]\text{(N)}[/inline] Ne znam
11.Link zadatka Realno rešenje jednačine [inline]x+\log_{21}\left(3^x+1\right)=x\log_{21}7+\log_{21}756[/inline] pripada intervalu:
[inline]\text{(A)}[/inline] [inline](-\infty,-21][/inline] [inline]\text{(B)}[/inline] [inline](-21,0][/inline] [inline]\text{(C)}[/inline] [inline](0,21)[/inline] [inline]\text{(D)}[/inline] [inline][21,42)[/inline] [inline]\text{(E)}[/inline] [inline][42,+\infty)[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline](-\infty,-21][/inline] [inline]\text{(B)}[/inline] [inline](-21,0][/inline] [inline]\enclose{box}{\text{(C)}}[/inline] [inline](0,21)[/inline] [inline]\text{(D)}[/inline] [inline][21,42)[/inline] [inline]\text{(E)}[/inline] [inline][42,+\infty)[/inline] [inline]\text{(N)}[/inline] Ne znam
12.Link zadatka Dužina stranice kvadrata [inline]ABCD[/inline] jednaka je [inline]8\text{ cm}[/inline]. Kružnica prolazi kroz temena [inline]A[/inline] i [inline]D[/inline] i dodiruje stranicu [inline]BC[/inline]. Površina kruga koji određuje ta kružnica jeste:
[inline]\text{(A)}[/inline] [inline]16\pi\text{ cm}^2[/inline] [inline]\text{(B)}[/inline] [inline]25\pi\text{ cm}^2[/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle\frac{64}{25}\pi\text{ cm}^2[/inline] [inline]\text{(D)}[/inline] [inline]64\pi\text{ cm}^2[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle\frac{25}{64}\pi\text{ cm}^2[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]16\pi\text{ cm}^2[/inline] [inline]\enclose{box}{\text{(B)}}[/inline] [inline]25\pi\text{ cm}^2[/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle\frac{64}{25}\pi\text{ cm}^2[/inline] [inline]\text{(D)}[/inline] [inline]64\pi\text{ cm}^2[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle\frac{25}{64}\pi\text{ cm}^2[/inline] [inline]\text{(N)}[/inline] Ne znam
13.Link zadatka Koliko ima celobrojnih rešenja nejednačine [inline]\left(\sqrt{7+4\sqrt3}\right)^{\cos x}+\left(\sqrt{7-4\sqrt3}\right)^{\cos x}\le4[/inline] koja pripadaju intervalu [inline]\left[-2\pi,\;\sqrt3+\sqrt5\right][/inline]?
[inline]\text{(A)}[/inline] [inline]3[/inline] [inline]\text{(B)}[/inline] [inline]4[/inline] [inline]\text{(C)}[/inline] [inline]11[/inline] [inline]\text{(D)}[/inline] [inline]10[/inline] [inline]\text{(E)}[/inline] beskonačno mnogo [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]3[/inline] [inline]\text{(B)}[/inline] [inline]4[/inline] [inline]\text{(C)}[/inline] [inline]11[/inline] [inline]\enclose{box}{\text{(D)}}[/inline] [inline]10[/inline] [inline]\text{(E)}[/inline] beskonačno mnogo [inline]\text{(N)}[/inline] Ne znam
14.Link zadatka Skup rešenja nejednačine [inline]12\text{ arctg }^2x+\pi\text{ arctg }x-\pi^2\le0[/inline] je oblika (za neke realne brojeve [inline]a[/inline] i [inline]b[/inline] takve da je [inline]-\infty\lt a\lt b\lt\infty[/inline]):
[inline]\text{(A)}[/inline] [inline](-\infty,a]\cup[b,+\infty)[/inline] [inline]\text{(B)}[/inline] [inline][a,b][/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle\bigcup\limits_{k\in\mathbb{Z}}[a+2k\pi,\;b+2k\pi][/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle\bigcup\limits_{k\in\mathbb{Z}}[a+k\pi,\;b+k\pi][/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle\left(-\frac{\pi}{2},a\right]\cup\left[b,\frac{\pi}{2}\right)[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline](-\infty,a]\cup[b,+\infty)[/inline] [inline]\enclose{box}{\text{(B)}}[/inline] [inline][a,b][/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle\bigcup\limits_{k\in\mathbb{Z}}[a+2k\pi,\;b+2k\pi][/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle\bigcup\limits_{k\in\mathbb{Z}}[a+k\pi,\;b+k\pi][/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle\left(-\frac{\pi}{2},a\right]\cup\left[b,\frac{\pi}{2}\right)[/inline] [inline]\text{(N)}[/inline] Ne znam
15.Link zadatka Broj svih realnih rešenja jednačine [inline]\displaystyle\sin^2x+\frac{1}{\sin^2x}=\sin x[/inline] jeste:
[inline]\text{(A)}[/inline] [inline]0[/inline] [inline]\text{(B)}[/inline] [inline]1[/inline] [inline]\text{(C)}[/inline] [inline]2[/inline] [inline]\text{(D)}[/inline] [inline]3[/inline] [inline]\text{(E)}[/inline] veći od [inline]3[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\enclose{box}{\text{(A)}}[/inline] [inline]0[/inline] [inline]\text{(B)}[/inline] [inline]1[/inline] [inline]\text{(C)}[/inline] [inline]2[/inline] [inline]\text{(D)}[/inline] [inline]3[/inline] [inline]\text{(E)}[/inline] veći od [inline]3[/inline] [inline]\text{(N)}[/inline] Ne znam
16.Link zadatka Ako su tačke [inline]M[/inline], [inline]N[/inline], [inline]P[/inline] i [inline]Q[/inline] središta ivica [inline]DA[/inline], [inline]AB[/inline], [inline]BC[/inline] i [inline]CD[/inline] pravilnog tetraedra [inline]ABCD[/inline] ivice dužine [inline]a[/inline], onda je površina četvorougla [inline]MNPQ[/inline] jednaka:
[inline]\text{(A)}[/inline] [inline]\displaystyle\frac{a^2}{4}[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle\frac{a^2\sqrt3}{4}[/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle\frac{a^2\sqrt2}{2}[/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle\frac{a^2}{2}[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle\frac{a^2\sqrt3}{3}[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\enclose{box}{\text{(A)}}[/inline] [inline]\displaystyle\frac{a^2}{4}[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle\frac{a^2\sqrt3}{4}[/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle\frac{a^2\sqrt2}{2}[/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle\frac{a^2}{2}[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle\frac{a^2\sqrt3}{3}[/inline] [inline]\text{(N)}[/inline] Ne znam
17.Link zadatka Skup rešenja jednačine [inline]\displaystyle(\log_{\sin x}2)\left(\log_{\sin^2x}\frac{4}{3}\right)=2\log_\frac{4}{3}2[/inline] ima tačno tri zajednička elementa sa skupom [inline]S[/inline], ako je:
[inline]\text{(A)}[/inline] [inline]\displaystyle S=\left\{\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4},\frac{11\pi}{4},\frac{15\pi}{4}\right\}[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle S=\left\{\frac{\pi}{6},\frac{5\pi}{6},\frac{\pi}{3},\frac{2\pi}{3},\frac{7\pi}{6},\frac{11\pi}{6}\right\}[/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle S=\left\{\frac{\pi}{3},\frac{2\pi}{3},-\frac{\pi}{3},-\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}\right\}[/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle S=\left\{\frac{\pi}{3},\frac{7\pi}{3},\frac{13\pi}{3},\frac{19\pi}{3},\frac{25\pi}{3},\frac{31\pi}{3}\right\}[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle S=\left\{\frac{2\pi}{3},-\frac{4\pi}{3},-\frac{5\pi}{3},-\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}\right\}[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]\displaystyle S=\left\{\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4},\frac{11\pi}{4},\frac{15\pi}{4}\right\}[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle S=\left\{\frac{\pi}{6},\frac{5\pi}{6},\frac{\pi}{3},\frac{2\pi}{3},\frac{7\pi}{6},\frac{11\pi}{6}\right\}[/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle S=\left\{\frac{\pi}{3},\frac{2\pi}{3},-\frac{\pi}{3},-\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}\right\}[/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle S=\left\{\frac{\pi}{3},\frac{7\pi}{3},\frac{13\pi}{3},\frac{19\pi}{3},\frac{25\pi}{3},\frac{31\pi}{3}\right\}[/inline] [inline]\enclose{box}{\text{(E)}}[/inline] [inline]\displaystyle S=\left\{\frac{2\pi}{3},-\frac{4\pi}{3},-\frac{5\pi}{3},-\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}\right\}[/inline] [inline]\text{(N)}[/inline] Ne znam
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18.Link zadatka U tetivnom četvorouglu [inline]ABCD[/inline] dijagonala [inline]BD[/inline] je normalna na stranicu [inline]BC[/inline], uglovi [inline]\angle ABC[/inline] i [inline]\angle BAD[/inline] su jednaki [inline]120^\circ[/inline], a dužina stranice [inline]AD[/inline] jeste [inline]1\text{ cm}[/inline]. Proizvod dužine dijagonale [inline]BD[/inline] i dužine stranice [inline]CD[/inline] jednak je:
[inline]\text{(A)}[/inline] [inline]\displaystyle\frac{\sqrt3}{2}\text{ cm}^2[/inline] [inline]\text{(B)}[/inline] [inline]\sqrt3\text{ cm}^2[/inline] [inline]\text{(C)}[/inline] [inline]2\sqrt3\text{ cm}^2[/inline] [inline]\text{(D)}[/inline] [inline]6\sqrt3\text{ cm}^2[/inline] [inline]\text{(E)}[/inline] [inline]2\text{ cm}^2[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]\displaystyle\frac{\sqrt3}{2}\text{ cm}^2[/inline] [inline]\text{(B)}[/inline] [inline]\sqrt3\text{ cm}^2[/inline] [inline]\enclose{box}{\text{(C)}}[/inline] [inline]2\sqrt3\text{ cm}^2[/inline] [inline]\text{(D)}[/inline] [inline]6\sqrt3\text{ cm}^2[/inline] [inline]\text{(E)}[/inline] [inline]2\text{ cm}^2[/inline] [inline]\text{(N)}[/inline] Ne znam
19.Link zadatka Date su tačke [inline]A(2,2)[/inline], [inline]A'(-2,-2)[/inline], [inline]B(4,-4)[/inline] i [inline]B'(-4,4)[/inline]. Duži [inline]AA'[/inline] i [inline]BB'[/inline] su ose elipse [inline]\varepsilon[/inline]. Ako je [inline]Y(0,y_0)[/inline], [inline]y_0>0[/inline], tačka preseka [inline]y[/inline]-ose i elipse [inline]\varepsilon[/inline], onda je [inline]y_0[/inline] jednako:
[inline]\text{(A)}[/inline] [inline]\displaystyle\frac{8}{\sqrt5}[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle\frac{4\sqrt2}{\sqrt5}[/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle\frac{8\sqrt2}{\sqrt5}[/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle\frac{4}{\sqrt5}[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle\frac{32}{\sqrt5}[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\enclose{box}{\text{(A)}}[/inline] [inline]\displaystyle\frac{8}{\sqrt5}[/inline] [inline]\text{(B)}[/inline] [inline]\displaystyle\frac{4\sqrt2}{\sqrt5}[/inline] [inline]\text{(C)}[/inline] [inline]\displaystyle\frac{8\sqrt2}{\sqrt5}[/inline] [inline]\text{(D)}[/inline] [inline]\displaystyle\frac{4}{\sqrt5}[/inline] [inline]\text{(E)}[/inline] [inline]\displaystyle\frac{32}{\sqrt5}[/inline] [inline]\text{(N)}[/inline] Ne znam
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20.Link zadatka Vrednost izraza [inline]\text{tg }10^\circ-\text{tg }50^\circ+\text{tg }70^\circ[/inline] jeste:
[inline]\text{(A)}[/inline] [inline]\displaystyle\frac{\sqrt3}{3}[/inline] [inline]\text{(B)}[/inline] [inline]3\sqrt3[/inline] [inline]\text{(C)}[/inline] [inline]3[/inline] [inline]\text{(D)}[/inline] [inline]-1[/inline] [inline]\text{(E)}[/inline] [inline]\sqrt3[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}[/inline] [inline]\displaystyle\frac{\sqrt3}{3}[/inline] [inline]\text{(B)}[/inline] [inline]3\sqrt3[/inline] [inline]\text{(C)}[/inline] [inline]3[/inline] [inline]\text{(D)}[/inline] [inline]-1[/inline] [inline]\enclose{box}{\text{(E)}}[/inline] [inline]\sqrt3[/inline] [inline]\text{(N)}[/inline] Ne znam
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