Question

am nevoie de ajutor la problema 2 va rog

Answer 1

1997 + 2 * (1+ 2 + 3 +.......+ 1996) =

1997 + 2 * (1996 * 1997 / 2) = 1997 + 1996 * 1997 =

1997 (1 + 1996) = 1997 * 1997   este patrat perfect

Answer 2

apotema piramidei este inaltimea unei fete laterale
Fie O piciorul inaltimii piramidei
In trg dr VOA (< O=90 grd)aplic T Pitagora ⇒AO^2=VA^2-VO^2=144*3-18^2=108=3*6^2⇒
AO=6V3
6V3 reprezinta 2 treimi din mediana bazei AM ⇒ AM=6V3*3/2=9V3
latura bazei o aflu din trg dr AMB unde AB=l, MB=l/2  ⇒aplic T Pitagora 
$l^{2}$=$\frac{ l^{2} }{4}$+($9 \sqrt{3}) ^{2}$ ⇒
4 l^2= l^2+4*81*3 ⇒ 3 *l^2=3*4*81 ⇒ l^2=81*4 ⇒ l=18
apotema o aflu din trg VMB (dr in M) unde MB= 9 ,aplic T Pitagora ⇒VM^2=VB^2-MB^2⇒
VM^2=144*3-81=351=3^3*13⇒ VM=3V39
b) Al= Pb*VM/2=18*3*3V39/2=81V39
c) V= Ab*h/3=l*AM/2*VO/3=18*9V3/2*18/3=486V3
d) in trg VOA (dr in O) tg VAO=VO/AO=3/V3=V3 , < A=60 grd