Răspuns:
Explicație pas cu pas:
1)
a = ( 2,3)² x ( 2.3)⁵: (2,3)⁵
-> se scrie baza ( 2,3) si se aduna exponentii la inmultire, iar la impartire se scad
a = ( 2,3)⁽²⁺⁵⁻⁵⁾
a = (2,3)² -> putere cu baza 2,3
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b -> este incomplet, deoarece apare semnul impartirii, dupa (2,3)^15 : (2,3)^13 : ?
Voi afla valoarea lui ,,b" in forma postata:
b = (2,3)¹⁵ : (2,3)¹³
b = (2,3)⁽¹⁵⁻¹³⁾
b = (2,3)² (1)
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Daca b = (2,3)¹⁵ : (2,3)¹³ : (2,3)¹, atunci valoarea lui b era:
b = (2,3)¹⁵⁻¹³⁻¹
b = (2,3)¹
b = 2,3 (2)
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c = [ (2,3)⁵]²
c = (2,3)⁵ˣ²
c = (2,3)¹⁰
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c > a = b => (2,3)¹⁰ > (2,3)² = (2,3)² (1)
c > a > b: (2,3)¹⁰ > (2,3)² > 2,3 (2)
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2). Calculeaza:
(1 - 0,4 : 0,8 + 3 : 1,2 ) : [ (2,6 - 7/3 × 42/49 ) × 10/7 ] =
7/3 × 42/49 = (7/49) × 42/3 = (1/7) × 14 = 14/7 = 2
= ( 1 - 4/10 : 8/10 + 3 : 12/10 ) : [ ( 26/10 - 2 ) × 10/7 ] =
= ( 1 - 4/10 × 10/8 + 3 × 10/12 ) : [ ( 26/10 - 20/10 ) × 10/7] =
= ( 1 - 1/2 + 10/4 ) : ( 6/10 × 10/7 ) =
= ( 2/2 - 1/2 + 5/2 ) : (6/7) =
= (6/2) × (7/6) =
= (6/6) × 7/2 =
= 7/2 =
= 3,5
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3)
( a + b )/2 = 72 → media aritmetica a numerelor a si b
a + b = 2 × 72
a + b = 144 → suma numerelor a si b
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( b + c ) /2 = 78 → media aritmetica a numerelor b si c
b + c = 2 × 78
b + c = 156 → suma numerelor b si c
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( a + c ) / 2 = 64 → media aritmetica a numerelor a si c
a + c = 2 × 64
a + c = 128 → suma numerelor a si c
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deduc:
a + b = 144
b + c = 156
a + c = 128
_______________ adun sumele
2 × a + 2 × b + 2 × c = 144 + 156 + 128
2 × ( a + b + c ) = 428 → dublul sumei celor trei numere
a + b + c = 428 : 2
a + b + c = 214 → suma celor trei numere
Media aritmetica a celor trei numere este:
( a + b + c ) / 3 = 214 / 3 = 71,(3)
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(1/2) din 71,(3) = 35,(6) →jumatate din media aritmetica a celor trei numere
(1/2) × ( 214)/3 = 107/3 = 35,(6)
