n a morning walk, three persons step off together. Their steps measure 80 cm, 85 cm and 90 cm respectively. - id1449035620201111 от сас001 11.11.2020 13:59

Question

Алгебра: n a morning walk, three persons step off together. Their steps measure 80 cm, 85 cm and 90 cm respectively. What is the minimum distance each should walk so that all can cover the same distance in complete steps?

сас001 · Accepted Answer

А) sin²x+2sinxcosx+cos²x=0
sin²x+cos²x+sin2x=0
1+sin2x=0
sin2x=-1
2x=3π/2+2πn, n∈Z
x=3π/4+πn, n∈Z
ответ: x=3π/4+πn, n∈Z
б) 5sin²x-3cos²x=0
5(1-cos²x)-3cos²x=0
5-5cos²x-3cos²x=0
5-8cos²x=0
8cos²x=5
cos²x=5/8
cosx=+-√(5/8)
x1=arccos(√5/8) + 2πn, n∈Z
x2=(π-arccos(√5/8)) + 2πn, n∈Z
ответ: x1=arccos(√5/8) + 2πn, n∈Z
x2=(π-arccos(√5/8)) + 2πn, n∈Z

в)6cos²x-2sin²x=5
6cos²x-2(1-cos²x)=5
6cos²x-2+2cos²x=5
8cos²x-7=0
8cos²x=7
cos²x=7/8
cosx=+-√(7/8)
x1=arccos(√(7/8))+2πn,n∈Z
x2=(π-arccos(√(7/8)))+2πn,n∈Z

г) sin²2x-3sin2x+2=0
Пусть z=sin2x (-1≤z≤1)
z²-3z+2=0
z1=(3+√(9-8))/2=(3+1)/2=2 - не удовлетворяет условию
z2=(3-√(9-8))/2=(3-1)/2=1
sin2x=1
2x=π/2+2πn, n∈Z
x=π/4+πn, n∈Z

n a morning walk, three persons step off together. Their steps measure 80 cm, 85 cm and 90 cm respectively. What is the minimum distance each should walk so that all can cover the same distance in complete steps?

MOGZ ответил