✔ 最佳答案
Q1. Given that V varies directly as √h, find the percentage change in h if V is increased by5%.
let
V = k√h,where k is constant
(V/k)^2 = h
h = V^2 / f,wherefis constant
at beginning:
h[0] = (V[0])^2 / f
now,
h[1] = {(1 + 5%)V[0]}^2 / f
h[1] = 1.1025(V[0]^2) / f
percentage change:
{( h[1] - h[0] )/ h[0]} x 100%
= (1.1025 - 1) x 100%
= 10.25%
so,it is increased by 10.25%
Q2. Assume x varies directly as √y and inversely as z². Find the percentage change in x when y increases by44% and z decreases by20%.
let x = (k√y) / z² , where k is constant
at beginning:
x[0] = [k√(y[0]] / (z[0])²
now,
x[1] = {k√[(1 + 44%)y[0]]} / {(1 - 20%)z[0]}²
x[1] = 1.2{k√(y[0])} / 0.64 z[0]²
x[1] = 1.875 [{k√(y[0])} / z[0]²]
the percentage change:
{(x[1] - x[0]) / x[0]} x 100%
= (1.875 - 1) x 100%
= 87.5%
so,x is increased by 87.5%