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1 year ago

A right triangular prism is shown.What is the lateral surface area?

Mathematics

1 answer:

makkiz [27]1 year ago

5 0

The general formula for the lateral surface area of a right prism is

L = ph

where p represents the perimeter of the base and h represents the height of the prism.

In our case, the perimeter is the sum of the bases.

p = 5 + 5.6 + 2.5 = 13.1 cm

now, the height of the prism is 8 cm

then L = 13.1 cm x 8 cm = 104.8cm^2

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Write a formula for the function g(x) obtained when the graph of f(x)= square root x is shifted up 1 unit and to the left 9 unit

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$\bf ~~~~~~~~~~~~\textit{function transformations}
\\\\\\
f(x)= A( Bx+ C)+ D
\\\\
~~~~y= A( Bx+ C)+ D
\\\\
f(x)= A\sqrt{ Bx+ C}+ D
\\\\
f(x)= A(\mathbb{R})^{ Bx+ C}+ D
\\\\
f(x)= A sin\left( B x+ C \right)+ D
\\\\[-0.35em]
~\dotfill\\\\
\bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\
\bullet \textit{ flips it upside-down if } A\textit{ is negative}\\
~~~~~~\textit{reflection over the x-axis}
\\\\
\bullet \textit{ flips it sideways if } B\textit{ is negative}$

$\bf ~~~~~~\textit{reflection over the y-axis}
\\\\
\bullet \textit{ horizontal shift by }\frac{ C}{ B}\\
~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\
~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\
\bullet \textit{ vertical shift by } D\\
~~~~~~if\ D\textit{ is negative, downwards}\\\\
~~~~~~if\ D\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{ B}$

with that template in mind, let's take a peek.

$\bf f(x)=\sqrt{x}~\hspace{7em}\stackrel{\textit{up by 1}}{D=1}\qquad \stackrel{\textit{left by 9}}{C=9}
\\\\[-0.35em]
~\dotfill\\\\
g(x)=\stackrel{A}{1}\sqrt{\stackrel{B}{1}x+\stackrel{C}{0}}+\stackrel{D}{0}\implies \stackrel{\textit{shifted}}{g(x)=\stackrel{A}{1}\sqrt{\stackrel{B}{1}x+\stackrel{C}{9}}+\stackrel{D}{1}}\implies \blacktriangleright g(x)=\sqrt{x+9}+1 \blacktriangleleft$

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