emilyhoang12121
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you are building a birdhouse that will have a volume of 128 in^3. the birdhouse will have the dimensions shown

a. write a polynomial that represents the volume of the birdhouse

b. what are the dimensions of the birdhouse ?

show your work please

you are building a birdhouse that will have a volume of 128 in3 the birdhouse will have the dimensions shown a write a polynomial that represents the volume of class=


Answer :

kate200468
[tex]a.\\V-the\ volume\\\\V(w)=4\cdot w\cdot (w+4)=4w^2+16w\ [in^3]\\\\b.\\V=128\ in^3\ \ \ \Rightarrow\ \ \ 4w^2+16w=128\ \ \ \Rightarrow\ \ \ 4w^2+16w-128=0\ /:4\\\\w^2+4w-32=0\\\\w^2+4w+4-36=0\ \ \ \Leftrightarrow\ \ \ (w+2)^2=36\\\\w+2=6\ \ \ \ \ or\ \ \ \ \ w+2=-6\\\\w=4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ w=-8\ \ \ \ (and\ \ \ w>0)\\\\w=4\ \ \ \Rightarrow\ \ \ w+4=8\\\\Ans.\ the\ dimensions\ of\ the\ birdhouse:\ \ 4\ in,\ 4\ in,\ 8 \ in[/tex]

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