X-6y=11 pls solve for y in a fraction or decimal
1 answer:
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408.454 cubic inches of air is surrounding the ball in the box
Step-by-step explanation:
When a sphere is inscribed in a cube and touching all of its faces, then
- The diameter of the sphere = the side of the cube
- The empty volume of the cube is the difference between the volume of the cube and the volume of the sphere
∵ The basketball is shaped a sphere
∵ The box is shaped a cube
∵ The ball touching every wall of the box
∴ The diameter of the ball = the side of the box
∵ The length of one side of the cube = 9.5 inches
∴ The diameter of the ball = 9.5 inches
∵ The diameter of the ball = 2 r, where r is the radius of the ball
∴ 9.5 = 2 r
- Divide both sides by 2
∴ r = 4.75 inches
∵ The volume of the air that surrounded the ball in the box =
volume of the box - volume of the ball
∵ Volume box (cube) = s³
∵ s = 9.5 inches
∴ Volume of the box = (9.5)³
∴ Volume of the box = 857.375 inches³
∵ Volume the ball (sphere) = π r³
∵ r = 4.75
∴ Volume the ball = (π)(4.75)³
∴ Volume the ball = 448.921 inches³
Substitute the values of the volumes of the box and the ball in the rule above
∴ The volume of the air = 857.375 - 448.921
∴ The volume of the air = 408.454 inches³
408.454 cubic inches of air is surrounding the ball in the box
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Answer:
Coordinate of 4th vertex of the rectangle is ( 8 , -8 ).
Step-by-step explanation:
Given Vertices of Rectangle are ( 5 , -3 ) , ( 5 , -8 ) , ( 8 , -3 )
To find: Coordinate of Fourth Vertex of the rectangle.
First, Plot all given three points on the graph.
Graph is attached.
We know that Opposite sides of the rectangle are equal and parallel.
Also All angles of rectangles are right angle.
So to satisfy these properties of rectangle.
4th coordinate must be on line x = 8 and y = -8.
⇒ Fourth coordinate = ( 8 , -8 )
Therefore, Coordinate of 4th vertex of the rectangle is ( 8 , -8 ).
