Given f(x) = V(3 x – 12) +2, what is the range in set notation?
2 answers:
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Answer:
1279.3 cubic inches (Rounded to the nearest tenth)
Step-by-step explanation:
Side of a cubic box = 12 inches
volume of cubic box = (since side is equal to 12 inches)
= = 1,728 cubic inches
It means that box can be filled with 1,728 cubic inches of any material
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But, it is given that it has one basketball placed in it.
hence we need to find the volume of basketball .
Since basket ball is spherical in shape
formula to calculate its volume will be same as that of formula to calculate volume of sphere
volume of sphere = where r is the radius of sphere
radius of basketball = diameter/2 = 9.5/2 in = 4.75 inches
therefore volume of basket ball is given by
volume of basketball =
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In box with volume 1,728 cubic inches,, 448.693 cubic inches is occupied by basketball.
It means rest is empty which can be filled with foam.
To calculate the empty space, we subtract volume of basket ball from volume of box
volume of empty space = volume of box - volume of basket
= 1728 - 448.693 = 1279.307 cubic inches
1279.307 cubic inches in nearest tenth will be 1279.3 cubic inches.
Hence, 1279.3 cubic inches of foam are needed to fill the rest of the box