Answered

Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

The data table shows how the amplitude of a mechanical wave varies with the energy it carries. Analyze the data to identify the mathematical relationship between amplitude and energy. Use your equation to find the energy if the amplitude is 9 units.

\begin{tabular}{|l|l|}
\hline
Amplitude & Energy \\
\hline
1 unit & 2 units \\
\hline
2 units & 8 units \\
\hline
3 units & 18 units \\
\hline
4 units & 32 units \\
\hline
\end{tabular}

A. 54 units
B. 98 units
C. 324 units
D. 162 units

Sagot :

GinnyAnswer
To determine the relationship between amplitude and energy, we will analyze the provided data. The table shows measurements of amplitude and corresponding energy values:

[tex]\[ \begin{array}{|c|c|} \hline \text{Amplitude (A)} & \text{Energy (E)} \\ \hline 1 & 2 \\ \hline 2 & 8 \\ \hline 3 & 18 \\ \hline 4 & 32 \\ \hline \end{array} \][/tex]

We will fit these data points to a polynomial of the form [tex]\( E = a \cdot A^2 + b \cdot A + c \)[/tex]. Solving the regression for the quadratic polynomial, we find the coefficients [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex]. In our case, this relationship simplifies to primarily a quadratic dependence:

[tex]\[ E \approx 2 \cdot A^2 \][/tex]

Given this relationship, we'll now use it to find the energy when the amplitude is 9 units:

[tex]\[ E = 2 \cdot A^2 \][/tex]

Substituting [tex]\( A = 9 \)[/tex]:

[tex]\[ E = 2 \cdot (9)^2 \][/tex]
[tex]\[ E = 2 \cdot 81 \][/tex]
[tex]\[ E = 162 \][/tex]

Therefore, if the amplitude is 9 units, the energy is 162 units.

The correct answer is:
D. 162 units
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.