`(m-5)/(2)-(m-3)/(5)=(1)/(2)`

If the straight lines (x-5)/(5m)=(2-y)/(5)=(1-z)/(-1)andx=(2y+1)/(4m)=(1-z)/(-3) are perpendicular to each other, find the value of m.

Simplify: (2)/(3)m-(4)/(5)n+(3)/(5)p+(-(3)/(4)m-(5)/(2)n+(2)/(3)p)+((5)/(2)m+(3)/(4)p-(5)/(6)n)

IfI_(m , n)=int_0^(pi/2)sin^m xcos^n xdx , Then show that I_(m , n)=(m-1)/(m+n)I_(m-2,n)(m ,n in N) Hence, prove that I_(m , n)=f(x)={((n-1)(n-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))pi/4 when both m and n are even ((m-1)(m-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))}

IfI_(m , n)=int_0^(pi/2)sin^m xcos^n xdx , Then show that I_(m , n)=(m-1)/(m+n)I_(m-2,n)(m ,n in N) Hence, prove that I_(m , n)=f(x)={((n-1)(n-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))pi/4 when both m and n are even ((m-1)(m-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))}

IfI_(m , n)=int_0^(pi/2)sin^m xcos^n xdx , Then show that I_(m , n)=(m-1)/(m+n)I_m-2n(m ,n in N) Hence, prove that I_(m , n)=f(x)={((n-1)(n-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))pi/4 when both m and n are even ((m-1)(m-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))

solve :(2m)/(3)-(m)/(5)=7

If the surm of the first ten terms of the series,(1(3)/(5))^(2)+(2(2)/(5))^(2)+(3(1)/(5))^(2)+4^(2)+(4(4)/(5))^(2)+ is (16)/(5)m, then m is equal to

If the sum of the first ten terms of the series (1(3)/(5))^(2)+(2(2)/(5))^(2)+(3(1)/(5))^(2)+4^(2)+(4(4)/(5))^(2)+.. is (16)/(5)m, then m is equal to: (1)102(2)101(3)100(4)99

(2m+5)/(3)=3m-10