if a polyhedron has a volume of 35 cm^3 and is dilated by a factor of 5/2, what will be the volume of the dilated polyhedron? Ro
und your answer to the nearest thousandth if necessary.
1 answer:
If a polyhedron has a volume of 35 cm cube and is dilated by a factor of 5/2 then the volume of dilated polyhedron will be 50.6 cm cube.
Given Volume of polyhedron=35 cm cube . Factor from which is dilated 5/2.
If the polyhedron is dilated by factor 5/2 then the volume of the polyhedron will change by the cube of that factor because when it is dilated by factor its material also increases.
Volume =35
After dilation
Volume=35+
=35+15.625
=50.625
After Rounding nearest to thousand we will get 50.6 .
Hence after dilation the volume which is 35 cm cube will change from 35 to 50.6.
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1) The solution for m² - 5m - 14 = 0 are x=7 and x=-2.
2)The solution for b² - 4b + 4 = 0 is x=2.
<u>Step-by-step explanation</u>:
The general form of quadratic equation is ax²+bx+c = 0
where
- a is the coefficient of x².
- b is the coefficient of x.
- c is the constant term.
<u>To find the roots :</u>
- Sum of the roots = b
- Product of the roots = c
1) The given quadratic equation is m² - 5m - 14 = 0.
From the above equation, it can be determined that b = -5 and c = -14
The roots are -7 and 2.
- Sum of the roots = -7+2 = -5
- Product of the roots = -7
2 = -14
The solution is given by (x-7) (x+2) = 0.
Therefore, the solutions are x=7 and x= -2.
2) The given quadratic equation is b² - 4b + 4 = 0.
From the above equation, it can be determined that b = -4 and c = 4
The roots are -2 and -2.
- Sum of the roots = -2-2 = -4
- Product of the roots = -2
The solution is given by (x-2) (x-2) = 0.
Therefore, the solution is x=2.