Answer: 3.66 cm
Step-by-step explanation: Given a rectangular casing BCDE with segment DE = 3 cm and segment BE = 3.5 cm.
The area A of a rectangle is length multiply by width.
Where length L = 3.5 cm and
width W = 3 cm
Area A = 3.5 × 3 = 10.5 cm^2
The pipe that will fit the fiber optic line is in cylindrical shape. Where area of a cylinder = πr^2.
But area A = 10.5. Substitute the values for the area of the cylinder
10.5 = πr^2
10.5 = 3.143 × r^2
Make r^2 the subject of formula
r^2 = 10.5/3.143
r = sqrt ( 3.34225 )
r = 1.828
Diameter = 2 × radius
Diameter = 2 × 1.829
Diameter = 3.656 cm
Therefore, the smallest diameter of pipe that will fit the fiber optic line is 3.66 cm approximately.
That would be Option C (Answer).
Well the line is straight so it will always have the same slope no matter what points you use but to solve it mathematically you do change in y/change in x
(3.5-(-1))/(4-(-5))
4.5/9 = 0.5
So the slope is 0.5
Now pick 2 random points on the line
(-3,0) and (5,4)
Now do the same thing for these 2 points
(4-0)/5-(-3)
4/8 = 0.5
So no matter what points the slope is always 0.5
<span>Simplifying
2x + 5 + 6x + -1 = 120
Reorder the terms:
5 + -1 + 2x + 6x = 120
Combine like terms: 5 + -1 = 4
4 + 2x + 6x = 120
Combine like terms: 2x + 6x = 8x
4 + 8x = 120
Solving
4 + 8x = 120
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + 8x = 120 + -4
Combine like terms: 4 + -4 = 0
0 + 8x = 120 + -4
8x = 120 + -4
Combine like terms: 120 + -4 = 116
8x = 116
Divide each side by '8'.
x = 14.5
Simplifying
x = 14.5</span>
