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garri49 [273]
3 years ago
6

Two parallel lines are _____ coplanar.

Mathematics
2 answers:
dimulka [17.4K]3 years ago
8 0

Answer:

1. always

2. sometimes

Step-by-step explanation:

Two lines are coplanar if they lie in the same plane or in parallel planes. There is  ALWAYS a plane which contains two parallel lines (see first attached image for details).

Two lines that lie in parallel planes are sometimes parallel. For example, see at second image. Planes \alpha and \beta are parallel. Consider pair of lines a and a_1 - they are parallel, but if you consider the pair of lines a and b_1, you can see they are not parallel.

Lapatulllka [165]3 years ago
4 0

Answer:

always

sometimes

Step-by-step explanation:

By definition parallel lines are lines in a plane which do not meet, that means, they have to be coplanar. Coplanar means they are included in the same plane. Then, two parallel lines are always coplanar (imagine two parallel lines in a 3d space, there is always a plane that can contain them).

Two lines that lie in parallel planes are sometimes parallel. As stated before, if there is a third plane which contains the two lines, they can be parallel or cannot, but if there is no plane which contains them, they are not parallel.

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A rectangular enclosure is to be created using 82m rope.
atroni [7]
Let
x-----> the length of rectangle
y-----> the width of rectangle

we know that 
perimeter of rectangle=2*[x+y]
perimeter of rectangle=82 m
82=2*[x+y]---> divide by 2 both sides---> 41=x+y--> y=41-x---> equation 1

Area of rectangle=x*y
substitute equation 1 in the area formula
Area=x*[41-x]----> 41x-x²

using a graph tool
see the attached figure

the vertex is the point (20.5,420.25)
that means
 for x=20.5 m ( length of rectangle)
the area is 420.25 m²

y=420.25/20.5----> 20.5 m

the dimensions are
20.5 m x 20.5 m------> is a square

the answer part 1) 
<span>the dimensions of the rectangular with Maximum area is a square with length side 20.5 meters
</span>
Part 2)<span>b) Suppose 41 barriers each 2m long, are used instead. Can the same area be enclosed?
</span>divide the length side of the square by 2
so
20.5/2=10.25--------> 10 barriers
the dimensions are 10 barriers x 10 barriers
10 barriers=10*2---> 20 m

the area enclosed with barriers is =20*20----> 400 m²

400 m² < 420.25 m²
so

the answer Part 2) is 
<span>the area enclosed by the barriers is less than the area enclosed by the rope
</span>
Part 3)<span>How much more area can be enclosed if the rope is used instead of the barriers
</span>
area using the rope=420.25 m²
area using the barriers=400 m²

420.25-400=20.25 m²

the answer part 3) is
20.25 m²

6 0
3 years ago
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