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@ПавелВишняков
September 2021
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m11m
Вариант 1.
1. (3 ⁴/₅ + 1 ⁵/₆) *3= (¹⁹/₅ + ¹¹/₆)*3 =(
19*6+11*5)
* 3 =
30
=
114+55
= 169/10 = 16,9
10
2.
2^(0.48)
=
2^(0.48)
= 2⁻² = 1/4
4^(1.24) 2^(2.48)
3. (9x²+4y²-(3x-2y)²) : xy = (9x²+4y²-9x²+12xy-4y²) : xy =
= (12xy): xy = 12
4.
a²·³⁵
=
a²·³⁵
= a⁻²
a²·⁹⁷ * a¹·³⁸ a⁴·³⁵
(2.5)⁻² = (5/2)⁻² = (2/5)² = 4/25 = 0.16
5. 3^(2+log₃ 5) = 3² * 3^(lg₃ 5) = 9 *5=45
6. log₂ log₂ 256 = log₂ log₂ 2⁸ = log₂ 8 = log₂ 2³ = 3
7.
18(sin² 36° - cos² 36°)
=
-18(cos² 36° - sin² 36°)
=
cos 72° cos 72°
= -18 cos(2*36°) =
- 18cos 72°
= -18
cos72° cos 72°
8.
sinα (5cosα+2)
=
sinα
*
5cosα +2
= tgα * (1/2)= 5 * (1/2)=
(10cosα+4) cosα cosα 2(5cosα+2)
= 2.5
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Answers & Comments
1. (3 ⁴/₅ + 1 ⁵/₆) *3= (¹⁹/₅ + ¹¹/₆)*3 =(19*6+11*5) * 3 =
30
= 114+55 = 169/10 = 16,9
10
2. 2^(0.48) = 2^(0.48) = 2⁻² = 1/4
4^(1.24) 2^(2.48)
3. (9x²+4y²-(3x-2y)²) : xy = (9x²+4y²-9x²+12xy-4y²) : xy =
= (12xy): xy = 12
4. a²·³⁵ = a²·³⁵ = a⁻²
a²·⁹⁷ * a¹·³⁸ a⁴·³⁵
(2.5)⁻² = (5/2)⁻² = (2/5)² = 4/25 = 0.16
5. 3^(2+log₃ 5) = 3² * 3^(lg₃ 5) = 9 *5=45
6. log₂ log₂ 256 = log₂ log₂ 2⁸ = log₂ 8 = log₂ 2³ = 3
7. 18(sin² 36° - cos² 36°) = -18(cos² 36° - sin² 36°) =
cos 72° cos 72°
= -18 cos(2*36°) = - 18cos 72° = -18
cos72° cos 72°
8. sinα (5cosα+2) = sinα * 5cosα +2 = tgα * (1/2)= 5 * (1/2)=
(10cosα+4) cosα cosα 2(5cosα+2)
= 2.5