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zhannawk [14.2K]
3 years ago
9

A scientist finds the temperature of a sample at the beginning of an experiment is t degrees celcius. After 1 hour, the temperat

ure is t^2 degrees celcius. If the temperature after 1 hour is 81 degrees celcius, what are two possible original temperatures? What is the difference between the possible original temperatures?
Mathematics
2 answers:
ale4655 [162]3 years ago
6 0
So the two possible original temperatures would be either -9 or 9.
KATRIN_1 [288]3 years ago
3 0
The possible temperatures are 9 degrees or -9 degrees as t^2 means t squared so the square root of 81 is t, however -9 x -9 and 9x9 is 81 so they're both possible answers.

as for the second part I'm not sure what they specifically want. sorry
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Cerrena [4.2K]
The fourth or the D) Option is correct.

To find the new induced matrix via a scalar quantified multiplication we have to multiply the scalar quantity with each element surrounded and provided in a composed (In this case) 3×3 or three times three matrix comprising 3 columns and 3 rows for each element which is having a valued numerical in each and every position.

Multiply the scalar quantity with each element with respect to its row and column positioning that is,

Row × Column. So;

(1 × 1) × 7, (2 × 1) × 7, (3 × 1) × 7, (1 × 2) × 7, (2 × 2) × 7, (3 × 2) × 7, (1 × 3) × 7, (2 × 3) × 7 and (3 × 3) × 7. This will provide the final answer, that is, the D) Option.

To interpret and make it more interesting in LaTeX form. Here is the solution with LaTeX induced matrix.

\mathcal{A = \begin{bmatrix}1 & 0 & 3 \\ 2 & -1 & 2 \\ 0 & 2 & 1 \\ \end{bmatrix}}

\mathbf{\therefore \quad 7A = 7 \times \begin{bmatrix}1 & 0 & 3 \\ 2 & - 1 & 2 \\ 0 & 2 & 1 \\ \end{bmatrix}}

\mathbf{\therefore \quad \begin{bmatrix}7 \times 1 & 7 \times 0 & 7 \times 3 \\ 7 \times 2 & 7 \times -1 & 7 \times 2 \\ 7 \times 0 & 7 \times 2 & 7 \times 1 \\ \end{bmatrix}}

\therefore \quad \begin{\bmatrix}7 & 14 & 0 \\ 0 & -7 & 14 \\ 21 & 14 & 7 \end{bmatrix}

Hope it helps.
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