Question

Calculati media geometrica si media aritmetica a nr de mai jos.Comparati cele doua medii.
a) 320 si 80
b) 0,18 si 2
c) 3/4 si 3/25
d) 3/8 si 3/8
e) radical din 240 si 9 radical din 15

Answer 1

Răspuns

Explicație pas cu pas:

a)  

( 320 + 80 ) : 2 = 400 : 2 = 200 → media aritmetica

√(320×80) = √256 × √100 = 16 × 10 = 160 → media geometrica

Ma = 200 > Mg = 160

____________________

b)  

( 0,18 + 2 ) : 2 = 2,18 : 2 = 1,09 → media aritmetica ( Ma)

√(0,18×2) = √0,36 = 0,6 → media geometrica ( Mg)

Ma = 1,09  > Mg = 0,6

______________________________

c)

( 3 / 4 + 3 / 25 ) : 2 = ( 75 + 12 ) / 100  × 1 / 2 = 87 / 200 = 0,435 → Ma

√(3/4 × 3 / 25) = √(9/100 ) = 3 / 10 = 0,3 → Mg

Ma = 0,435 >  Mg = 0,3

_______________________

d)  

( 3/ 8 + 3 / 8 ) : 2 = 6 / 8  × 1 / 2 = 3 / 8 = 0,375 → Ma

√(3/8 × 3/8) = √9/64 = 3/ 8= 0,375 → Mg

Ma (3/8 ) =  Mg (3/8)

______________________________

e)

√240 = 4√15       si   9√15

( 4√15 + 9√15 ) : 2 = 13√15 / 2 = 6,5√15 → Ma

√(4√15×9√15) = √36 ×√15= 6√15 → Mg

Ma > Mg;  6,5√15 > 6√15