The differential equation below models the temperature of a 91°c cup of coffee in a 21°c room, where it is known that the coffee cools at a rate of 1°c per minute when its temperature is 71°c. solve the differential equation to find an expression for the temperature of the coffee at time t. (let y be the temperature of the cup of coffee in °c, and let t be the time in minutes, with t = 0 corresponding to the time when the temperature was 91°c.) dy/dt =(− 1/50)(y − 21)

Explanation:

We start from:

Separating variables:

Integrating with initial conditions:

Isolating T:

You may note that when t is zero the temperature is 91 ºC, as is specified by the problem. As well, when t is bigger (close to infinite), the temperature tends to be the room temperature (21 ºC)

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases . this process does not change the mass number.

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as -decay. in this the mass number remains same.

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.

it is a negative acceleration