Question

The temperature inside a certain industrial machine at time t seconds after startup, for 0 < t < 10, is given by h(t) = 42t + 1 – 4t + 2 degrees Celsius. How many seconds after startup is the temperature inside the machine equal to 128 degrees Celsius?

Answer 1

Answer:

$t= \frac{125}{38} s$

Step-by-step explanation:

We are given the temperature inside the machine from startup until 10 seconds later, the formula is:

$h(t)= 42 \cdot t +1 - 4\cdot t +2 (degrees \, C)$

We want to know at what time t the temperature inside the machine will be equal to 128 °C.

So we set:

$h(t)=128$

$42\cdot t+1-4\cdot t+2=128$

Now, we rearrange the equation to keep terms with t on the left hand side and terms without t on the right hand side

$42\cdot t-4\cdot t=128-1-2$

and we simplify:

$(42-4)\cdot t= 128-2-1= 125$

$38 \cdot t = 125$

now it's easy to solve for t:

$t=\frac{125}{38}$

And thus we arrive to the solution.