On a hot Saturday morning while people are working inside, the air conditioner keeps the temperature inside the building at 24 degreesC. At noon the air conditioner is turned off, and the people go home. The temperature outside is a constant 35 degreesC for the rest of the afternoon. If the time constant for the building is 5 hr, what will be the temperature inside the building at 4 : 00 font size decreased by 2 Upper P . font size decreased by 2 Upper M .

30.06 degree Celsius at 4:00 PM.

Step-by-step explanation:

We have been given that on a hot Saturday morning while people are working inside, the air conditioner keeps the temperature inside the building at 24 degrees C. At noon the air conditioner is turned off, and the people go home. The temperature outside is a constant 35 degrees C for the rest of the afternoon. The time constant for the building is 5 hr. We are asked to find the temperature inside the building at 4:00 PM.

We will use Newton's law of cooling to solve our given problem.

, where

= Temperature after t hours.

= Temperature of surrounding environment,

= Time constant.

Upon substituting our given values in Newton's cooling law, we will get:

To find the temperature at 4:00 pm, we will substitute in our formula as:

Therefore, the temperature inside building would be approximately 30.06 degree Celsius at 4:00 PM.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

quit

step-by-step explanation: