1) ¹⁵√ 5 *5 * ¹⁰√5 = 5 ^ ( 1/15 + 1 + 1/10 ) = 5 ^ ( 2/30 + 30/30 + 3/30 ) =
= 5 ^ 35/30 = 5 ^ 7/6
2) ⁶ √ 5 = 5 ^ 1/6
3) 5 ^ 7/6 : 5 ^ 1/6 = 5 ^ ( 7/6 - 1/6 ) = 5 ^ 6/6 = 5 ^ 1 = 5
Ответ 5
100,200,300,400,500,600,700,800,900-это сотни
1) sinx = -1/2;
x = (-1)^(n+1)* arcsin(|-1/2|) + pi*n;
x = (-1)^(n+1)* pi/6) + pi*n; n ∈ Z
n = 0; x = -pi/6 ∉[0;3p]
n = 1; x = pi/6 + pi = 7pi/6 ∈<span>[0;3p]
</span>n = 2; x = -pi/6 + 2pi = 11pi/6 ∈<span>[0;3p]
</span>n = 3; x = pi/6 + 3pi ∉<span>[0;3p]
</span>Ответ: x = 7pi/6 ∪ x = 11pi/6
2) sinx = 1/2;
x = (-1)^(n)* arcsin1/2) + pi*n;
x = (-1)^(n)* pi/6)+ pi*n; n ∈ Z
n = -1; x = -pi/6 - pi ∉ [-p/2;3p/2]
n = 0; x = pi/6 ∈[-p/2;3p/2]
n = 1; x = -pi/6 + pi = 5pi/6 ∈[-p/2;3p/2]
n = 2; x = pi/6 + 2pi ∉[-p/2;3p/2]
Ответ: x = pi/6 ∪ x = 5pi/6
3) sinx = -√2/2;
x = (-1)^(n+1)* arcsin(|-√2/2|) + pi*n;
x = (-1)^(n+1)* pi/4) + pi*n; n ∈ Z
n = -4; x = -pi/4 - 4pi ∉[-3p;0]
n = -3; x = pi/4 - 3pi = -11pi/4 ∈[-3p;0]
n = -2; x = -pi/4 -2pi = -9pi/4 ∈[-3p;0]
n = -1; x = pi/4 - pi = - 3pi/4 ∈[-3p;0]
n = 0; x = -pi/4 ∈[-3p;0]
n = 1; x = pi/4 + pi ∉[-3p;0]
Ответ: x = -11pi/4 ∪ x = -9pi/4 ∪ x = pi/4 - pi ∪ x = -pi/4
4) sinx = √2/2;
x = (-1)^(n)* arcsin(√2/2) + pi*n;
x = (-1)^(n)* pi/4)+ pi*n; n ∈ Z
n = -2; x = pi/4 - 2pi = -7pi/4 ∉[-3p/2;5p/2]
n = -1; x = -pi/4 - pi = - 5pi/4 ∈[-3p/2;5p/2]
n = 0; x = pi/4 ∈[-3p/2;5p/2]
n = 1; x = -pi/4 + pi = 3pi/4 ∈<span>[-3p/2;5p/2]
</span>n = 2; x = pi/4 + 2pi = 9pi/4 ∈<span>[-3p/2;5p/2]
</span>n = 3; x = -pi/4 + 3pi ∉[-3p/2;5p/2]
Ответ: x = -5pi/4 ∪ x = pi/4 ∪ x = 3pi/4 ∪ x = 9pi/4
5) sinx = -√3/2;
x = (-1)^(n+1)* arcsin(|-√3/2|) + pi*n;
x = (-1)^(n+1)* pi/3) + pi*n; n ∈ Z
n = -2; x = -pi/3 - 2pi ∉[-2p;2p]
n = -1; x = pi/3 - pi = -2pi/3;
n = 0; x = -pi/3 ∈[-2p;2p]
n = 1; x = pi/3 + pi = 4pi/3 ∈[-2p;2p]
n = 2; x = -pi/3 + 2pi = 5pi/3 ∈[-2p;2p]
n = 3; x = pi/3 + 3pi ∉[-2p;2p]
Ответ: x = -2pi/3 ∪ x = -pi/3 ∪ x =4pi/3 ∪ x = 5pi/3
Прямоугольник с периметром 8 см квадрат P=4a 4a=P 4a=8 a=8:4=2 Сторона этого квадрата равна 2см ,следовательно,2 стороны прямоугольника с периметром 14 см равны 2 см P=2(a+b) P=2a+2b 2a+2b=P 2*2+2b=14 2b=14-4 2b=10 b=5 =>2 другие стороны прямоугольника равны по 5 см, DC=AB=2+5=7
2 стороны прямоугольника с периметром 18см равны 5 см P=2(a+b) P=2a+2b 2a+2b=P 2*5+2b=18 2b=18-10=8 b=8:2 b=4 см . AD= BC=2+4=6
DC=AB=2+5=7
AD= BC=2+4=6
P=2(a+b)=2(6+7)=2*13=26
7x^2 - 4x + 1 >0
7x^2 - 4x + 1 = 0
D = 16 - 4*7 <0
x ∈ ( - ∞; + ∞)
