The path of a launched missile can be modeled by a quadratic function. explain how you would use the function to determine the greatest height the rocket reaches and the horizontal distance it travels before reaching the ground. answer in complete sentences.

The highest point is at witch the rocket stops to going up and starts to going down, this point will is the vertex of the quadratic equation, this point is the zero of the first derivate of the quadratic equation, so if the quadratic equation is:

y = a*x^2 + b*x + c

the first derivate will be:

v = 2a*t + b

now we find the x in which v = 0

x = -b/2a

Now, we replace this time in the first equation and find the max height.

Y = a*(-b/2a)^2 + b*-b/2a + c

if it is trhowed from the ground, then c = 0, the horizontal distance will be when Y is zero again:

Y = a*x^2 + b*x

is zero at x = 0, we must find the other root.

Y = (a*x + b)*x

so x = -b/a

Then the horizontal distance traveled is x = -b/a, that is the horizontal distance at which the rocket hits the ground again.

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.