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3 years ago

11

In a hydroelectricity production, water falls from a dam into a turbine wheel 49 m below. What is the velocity of water at the t

urbine?
A) 0 m/s
B) 15.5 m/s
C) 31 m/s
D) 46.5 m/s

1 answer:

ozzi3 years ago

7 0

Answer:

C: 31 m/s

Step-by-step explanation:

It falls from a dam.

Thus;

Initial velocity; u = 0 m/s

Height; h = 49 m

Acceleration due to gravity is 9.8 m/s²

To solve for the final velocity this, we will use Newton's third equation of motion;

v² = u² + 2gh

v² = 0² + 2(9.8 × 49)

v = √960.5

v ≈ 31 m/s

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The system of hypothesis on this case are:

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Where $\mu_1$ and $\mu_2$ represent the percentages that we want to test on this case.

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$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c | } \\ \bf{Part \: A} & \bf \footnotesize{The \: decimal \: form \: of \: the \: rational \: number \: \dfrac{3}{40} \: is \: \gray{ \normalsize{ 0.075 }}} \\ \\ \hline \\ \bf{Part \: B}& \: \bf \footnotesize{The \: value \: of \: \dfrac{1}{ \sqrt[4]{(9)^{ - 2} } } \: is \: \normalsize 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \\ \hline \\ { \bf Part \:C \: }& \: { \bf\footnotesize{On \: simplifying \: \: (5+3 \sqrt{7} ) + (12 - 3 \sqrt{7}) \: we \: get \: \normalsize{ 17 }. \: \: \: \: \: \: \: \: }} \\ \\ \end{array}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

$\bf \underline{Answer-} \\$

${ \bf{Part \: A \: | \: \footnotesize{The \: decimal \: form \: of \: the \: rational \: number \: \dfrac{3}{40} \: is \: \gray{ \normalsize{ 0.075 }}}}}$

${ \bf{Part \: B \: | \: \footnotesize{The \: value \: of \: \dfrac{1}{ \sqrt[4]{(9)^{ - 2} } } \: is \: \normalsize 3 }}}$

$\bf \underline{Step \:by \:step\: Explanation-} \\$

${ \sf \: \: \: \: \: : \: \: \implies\dfrac{1}{ \sqrt[4]{(9)^{ - 2} } }}$

${ \sf \: \: \: \: \: : \: \: \implies\dfrac{1}{ \sqrt[ \cancel4]{(9)^{ \cancel{ - 2}} } }}$

${ \sf \: \: \: \: \: : \: \: \implies\dfrac{1}{ \sqrt{9^{ - 1} } }}$

${ \sf \: \: \: \: \: : \: \: \implies\dfrac{1}{ {3}^{ - 1 } }}$

${ \sf \: \: \: \: \: : \: \: \implies\dfrac{1}{ \dfrac{1}{3} }}$

${ \sf \: \: \: \: \: : \: \: \implies3}$

${ \bf Part \:C \: } | \: { \bf\footnotesize{On \: simplifying \: \: (5+3 \sqrt{7} ) + (12 - 3 \sqrt{7}) \: we \: get \: \normalsize{ 17 }. }}$

${~~~\sf ~~:~~\implies (5+3 \sqrt{7} ) + (12 - 3 \sqrt{7})}$

${~~~~\sf ~:~~\implies 5+ \cancel{3 \sqrt{7}} + 12 \cancel{ - 3 \sqrt{7}}}$

${~\sf ~~~~:~~\implies 17}$

$\underline{\rule{200pt}{2.5pt}}$

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2 years ago