Answer:
[tex]t= \frac{125}{38} s[/tex]
Step-by-step explanation:
We are given the temperature inside the machine from startup until 10 seconds later, the formula is:
[tex]h(t)= 42 \cdot t +1 - 4\cdot t +2 (degrees \, C)[/tex]
We want to know at what time t the temperature inside the machine will be equal to 128 °C.
So we set:
[tex]h(t)=128[/tex]
[tex]42\cdot t+1-4\cdot t+2=128[/tex]
Now, we rearrange the equation to keep terms with t on the left hand side and terms without t on the right hand side
[tex]42\cdot t-4\cdot t=128-1-2[/tex]
and we simplify:
[tex](42-4)\cdot t= 128-2-1= 125[/tex]
[tex]38 \cdot t = 125[/tex]
now it's easy to solve for t:
[tex]t=\frac{125}{38}[/tex]
And thus we arrive to the solution.
