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When a chemical called DCA reaches 33 °C, it explodes.
A chemist heats a sample of DCA so that its temperature rises by 2°C every minute, as shown in the table below. After how many minutes will the sample explode?
Minutes passed
Temperature of DCA (°C)

When a chemical called DCA reaches 33 C it explodes A chemist heats a sample of DCA so that its temperature rises by 2C every minute as shown in the table below class=


Answer :

Answer:

The sample will explode after 45 minutes passed.

Step-by-step explanation:

We can find the total minutes the sample will explode by using the arithmetic sequence:

[tex]\boxed{U_n=U_1+(n-1)d}[/tex]

where:

  • [tex]U_n[/tex] = the n-th term
  • [tex]U_1[/tex] = the 1st term
  • [tex]n[/tex] = total number of terms
  • [tex]d[/tex] = difference

Given:

  • [tex]U_1[/tex] = -55
  • [tex]d[/tex] = 2
  • [tex]U_n[/tex] = 33

[tex]U_n=U_1+(n-1)d[/tex]

[tex]33=-55+(n-1)(2)[/tex]

[tex]2(n-1)=33+55[/tex]

[tex]n-1=88\div2[/tex]

[tex]n=44+1[/tex]

[tex]\bf n=45[/tex]

Therefore, the sample will explode after 45 minutes passed.

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