A rectangular prism has length that is twice its width and height that is 4 meters longer than its width. the volume of the rectangular prism is 48 cubic meters write a polynomial function to represent the volume of the rectangular prism
Let x-----------> is the length of a prism y-----------> is the width of a prism z-----------> is the height of a prism we know that [volume of a prism]=x*y*z------------> equation 1 x=2y-----------> equation 2 z=4+y---------> equation 3 V=48 m³
I substitute 2 and 3 in 1 V=x*y*z---------> V=(2y)*y*(4+y)--------> V=2y²*(4+y) V=2y³+8y²-----------> 48=2y³+8y²---------> 2y³+8y²-48=0
the answer is 2y³+8y²-48=0 (polynomial function)
using a graph tool see the attached figure
y=2 m x=2y------->x=2*2-----> x=4 m z=4+y-------> z=4+2-----> z=6 m
