MATHS......

1.
1 / 2 mv^2 = hf -hfo (f)
mv^2 / 2 = f(h-ho)
mv^2(h-ho) / 2 = f
f = hmv^2(1-o) / 2

or

1 / 2mv^2 = hf-hfo (f)
1 / 2mv^2 = f(h-ho)
(h-ho) / 2mv^2 = f
f = h(1-o) / (2mv^2)

2.
k = x+y / x-y (x)
k(x-y) = x+y
kx-ky = x+y
kx-x = ky+y
x(k-1) = y(k+1)
x = y(k+1) / (k-1)

3.
h = ut+1 / 2at^2 (a)
h(2at^2) = ut+1
2aht^2 = ut+1
a(2ht^2) = ut+1
a = (ut+1) / (2ht^2)

4.
c-b = a(c+b) (b)
c-b = ac+ab
c-ac = ab+b
c(1-a) = b(a+1)
c(1-a) / (a+1) = b
b = c(1-a) / (a+1)

5.
1/a+1/b = -2 (a)
b/ab + a/ab = -2
(b+a)/ab = -2
b+a = -2ab
b = -2ab-a
b = a(-2b-1)
b/(-2b-1) =a
a = -[ b/(2b+1) ]

6.
k = 4/ab-1/c (b)
k = 4c/abc-ab/ abc
k = (4c-ab)/abc
abck = 4c- ab
abck+ab = 4c
b(ack+a) = 4c
b = (4c)/[a(ck+1)]