Find expressions for the possible dimensions of the rectangular prism. V = 12y3 + 13y2 + 3y

Mathematics

2 answers:

jok3333 [9.3K]2 years ago

7 0

Answer:

Step-by-step explanation:

The dimensions of a rectangular prism are length, width, and depth.

Volume = length * width * depth

Here, V = 3y3 + 16y2 + 5y. If you can factor that into three terms, those could be the dimensions of the prism.

How do you factor it? Do all three terms have something in common? Sure, they all have a y, so factor a y out of each term.

V = y(3y2 + 16y + 5)

Then, factor what's left.

V = y(3y + 1)(y + 5)

The dimensions of the prism are y, (3y + 1), and (y + 5).

fenix001 [56]2 years ago

7 0

Answer:

The dimensions of a rectangular prism are length, width, and depth.

Volume = length * width * depth

Here, V = 3y3 + 16y2 + 5y. If you can factor that into three terms, those could be the dimensions of the prism.

How do you factor it? Do all three terms have something in common? Sure, they all have a y, so factor a y out of each term.

V = y(3y2 + 16y + 5)

Then, factor what's left.

V = y(3y + 1)(y + 5)

The dimensions of the prism are y, (3y + 1), and (y + 5).

Step-by-step explanation:

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the lateral area of a cone is 574 pi cm2. The radius is 19.6 cm. What is the slant height to the nearest tenth of a centimeter?

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$\bf \textit{lateral area of a cone}\\\\
LA=\pi r\sqrt{r^2+h^2}~~
\begin{cases}
r=radius\\
\sqrt{r^2+h^2}=slant~height\\
-----------\\
LA=574\pi \\
r=19.6
\end{cases}
\\\\\\
574\pi =\pi (19.6)\sqrt{r^2+h^2}\implies \cfrac{574\pi }{19.6\pi }=\sqrt{r^2+h^2}
\\\\\\
\cfrac{574}{19.6}=\sqrt{r^2+h^2}$