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Calculate [tex]\Delta L[/tex] using the formula:

[tex]\Delta L = 90 \cdot \left(11 \cdot 10^{-6}\right) \cdot 39.3[/tex]

Then, compute [tex]\Delta L = 90[/tex].

Answer :

Sure! Let's solve the problem step-by-step:

We're tasked with calculating the change in length, [tex]\(\Delta L\)[/tex], using the formula:

[tex]\[
\Delta L = L_0 \times \alpha \times \Delta T
\][/tex]

Where:
- [tex]\(L_0\)[/tex] is the initial length, given as 90 (unspecified units, but the calculation is unitless).
- [tex]\(\alpha\)[/tex] is the coefficient of linear expansion, given as [tex]\(11 \times 10^{-6}\)[/tex].
- [tex]\(\Delta T\)[/tex] is the change in temperature, given as 39.3 degrees.

Now, let's perform the calculation:

1. Start by writing down the formula:

[tex]\[
\Delta L = 90 \times (11 \times 10^{-6}) \times 39.3
\][/tex]

2. Multiply the initial length ([tex]\(L_0\)[/tex]), the coefficient of linear expansion ([tex]\(\alpha\)[/tex]), and the temperature change ([tex]\(\Delta T\)[/tex]):

[tex]\[
\Delta L = 90 \times 0.000011 \times 39.3
\][/tex]

3. Calculate the result:

- First, multiply [tex]\(90 \times 0.000011 = 0.00099\)[/tex].
- Then, multiply [tex]\(0.00099 \times 39.3 = 0.038907\)[/tex].

Thus, the change in length, [tex]\(\Delta L\)[/tex], is approximately 0.038907.

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