The value of z is calculated from the following formula:
z=(12a+5b)/(11a+19b)
a is increased by 2.2%
b is increased by 1.2% of a
Using partial differentiation, find an expression for the percentage change in z in terms of a and b.
b is measured as 11.
What non-zero value of a would result in a zero percentage change in z?
2007-11-30 07:56:10 · 3 answers · asked by ozi 1 in Science & Mathematics ➔ Mathematics
The general formula is
Δz = za*Δa + zb*Δb
where za = partial dz/da
zb = partial dz/db
b = 11
Δa = 0.022*a
Δb = 0.012*a
za = [12*(11a+19b) - 11*(12a+5b)] / (11a+19b)^2
= (12*19 - 55)*b / (11a+19b)^2
zb = [5*(11a+19b) - 19*(12a+5b)] / (11a+19b)^2
= (55 - 12*19)*a / (11a+19b)^2
Sub these values and solve.
We require Δz = 0, or
(12*19 - 55)*b*0.022*a + (55 - 12*19)*a*0.012*a = 0
Simplify:
0.022b - 0.012a = 0
a = 22/12 * 11 = 121/6 = 20.16667
2007-11-30 09:54:24 · answer #1 · answered by Dr D 7 · 0⤊ 0⤋
get a math tutor
2007-11-30 15:59:12 · answer #2 · answered by NeNe 1 · 0⤊ 0⤋
Depends what z is.
2007-11-30 15:59:54 · answer #3 · answered by Anonymous · 0⤊ 0⤋