Write a program that reads a string from the keyboard and tests whether it contains a valid date. Display the date and a message that indicates whether it is valid. If it is not valid, also display a message explaining why it is not valid. The input date will have the format mm/dd/. A valid month value mm must be from 1 to 12 (January is 1). The day value dd must be from 1 to a value that is appropriate for the given month. February has 28 days except for leap years when it has 29. A leap year is any year that is divisible by 4 but not divisible by 100 unless it is also divisible by 400.

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For positive constants a and b, the force between two atoms in a molecule is given f(r) = −a r2 + b r3 , where r > 0 is the distance between the atoms. note: a and b are upper case letters. (a) find f '(r) = (b) find the critical point for f(r). r = (c) find f ''(r) = (d) find the value of r so that f ''(r) = 0.

Write a program that performs a simple n-body simulation, called "jumping leprechauns." this simulation involves n leprechauns, numberd 1 to n. it maintains a gold value g_i for each leprechaun i, which begins with each leprechaun starting out with a million dollars worth of gold, that is, g_i = 1000000 for each i = 1,. in addition, the simulation also maintains, for each leprachaun,i, a place on the horizon, which is represented as a double-precision floating point number, x_i. in each iteration of the simulation, the simulation processes the leprachauns in order. processing a leprachaun i during its iteration begins by computing a new place on the horizon for i, which is determined by the assignment: