(with steps ) find the inverse laplace transform, f(t), of the function: (7s^2 - 15s + 50)/(s(s^2 + 25))

R=

Step-by-step explanation:

Using partial fraction decomposition to get a simpler denominator for the inverse transform:

Multiple  both sides by

Separate in equations by grouping by the degree of the s:

Solving for A and C:

Substitute the value of A in the first separated equation to find the value of B:

Returning to the partial fraction decomposition:

Applying the inverse Laplace transform:

Using the next formulas:

the answer is: the length is 5/6 yards.

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step-by-step explanation:

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.