The sum of two warrants is 180 and the MS of those warrants is 12. If so, how many additional possibilities are there like reservation?
To find the sum of two numbers, we can set up a system of equations to represent the given conditions:
Let's assume the two warrants are represented by the variables x and y.
The sum of two warrants is 180:
x + y = 180
The mean square (MS) of those warrants is 12:
((x^2 + y^2)/2)^(1/2) = 12
To find additional possibilities similar to a reservation, we need to determine how many pairs of (x, y) satisfy these conditions.
One way to solve this system of equations is by substitution:
From the first equation, we can express x as 180 - y and substitute it into the second equation:
((180 - y)^2 + y^2)/2)^(1/2) = 12
Expanding and simplifying the equation:
((32400 - 360y + y^2 + y^2)/2)^(1/2) = 12
(2y^2 - 360y + 32400)/2 = 144
Simplifying further:
y^2 - 180y + 16200 = 144
Bringing all terms to one side of the equation:
y^2 - 180y + 16056 = 0
Now, we can use the quadratic formula to find the values of y that satisfy this equation:
y = (-b ± √(b^2 - 4ac)) / (2a)
a = 1, b = -180, and c = 16056
Plugging in these values:
y = (-(-180) ± √((-180)^2 - 4(1)(16056))) / (2(1))
Simplifying within the square root:
y = (180 ± √(32400 - 64224)) / 2
y = (180 ± √(-31824)) / 2
As the square root of a negative number results in an imaginary number, there are no real solutions for y that satisfy the given conditions. Therefore, there are no additional possibilities like a reservation.