The differential equation below models the temperature of a 91°C cup of coffee in a 17°C room, where it is known that the coffee cools at a rate of 1°C per minute when its temperature is 70°C. Solve the differential equation to find an expression for the temperature of the coffee at time t. dy dt = − 1 53 (y − 17)\

Step-by-step explanation:

This differential equation is a first order linear differential equation with separable variables, whose solution is found as follows:

The solution of the differential equation is:

Where:

- Temperature, measured in °C.

- Time, measured in minutes.

The time when the cup of coffee has the temperature of 70 °C is:

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

faster, im not sure why but i know it is faster