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mazolethrin3461
27.11.2021 •
Mathematics
SUBIECTUL I
1. 1p Să se determine primul termen al unei progresii aritmetice (an
)n≥1 știind că rația este
egală cu 5 și suma primilor zece termeni ai progresiei este egală cu 245.
2. 1p Să se determine punctele de intersecție ale graficului funcției
f: R → R, f (x) = x
2 − 7x + 12, cu axele de coordonate.
3. 1p Să se determine numărul real a pentru care vectorii
u⃗ = (a − 2)i + (3a − 1)j și v = 2i +4j sunt coliniari.
4. 1p Să se calculeze ctg x, știind că sin x =
√3
2
, x ∈ (0, 90°
).
5. 1p Să se determine soluțiile reale ale ecuației 49x+2 = 7
x
2+5
.
6. 1p Să se rezolve ecuația : Ax
2+Cx
2 = 0, x∈ N , x≥ 2.
SUBIECTUL II
1 Se consideră matricea A(a) = (
1 0 √a
1 0 1
a 1 1
), unde a ∈ (0, ∞).
a) 0.5p Arătați că det(A(4)) = 1.
b) 0.5p Demonstrați că det(A(a) ∙ A(1) − A(a + 1)) > 0, pentru orice a ∈ (0, ∞).
2. Pe mulțimea de numere reale se definește legea de compoziție asociativă
x ∘ y = √3(xy + 4) − 3(x + y).
a) 0.5p Arătați că √3 ∘ 2 = √3.
b) 0.5pDemonstrați că x ∘ y = √3(x − √3)(y − √3) + √3, pentru orice numere reale x și y.
SUBIECTUL III
1 0.5p Se consideră funcția f: R → R, f(x) = e
2x
(x − 5).
Arătați că f
′
(x) = e
2x
(2x − 9), x ∈ R .
2. 0.5p Se consideră funcția f: R → R, f(x) =
x
√x
2+1
.
Arătați că ∫ f(x)√x
2 + 1
2
0
dx = 2.
Solved
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Ответ:
there was a tipikal answers of this question
Ответ:
huh? wait, di ko po maintindihan
Ответ:
Each wall are transformed objects from the start. Keep going you got it!
Step-by-step explanation: