The cost of a square slab is proportional to its thickness and also proportional to the square of its length. What is the cost of a square slab that is 3 meters long and 0.1 meter thick?
(1) The cost of a square slab that is 2 meters long and 0.2 meter thick is $160 more than the cost of a square slab that is 2 meters long and 0.1 meter thick. ?
(2) The cost of a square slab that is 3 meters long and 0.1 meter thick is $200 more than the cost of a square slab that is 2 meters long and 0.1 meter thick.
選D 算這題要算很久 有戰友知道快的解法嗎??
作者: yzg1236 时间: 2010-8-3 06:08
你是咋算的呢？作者: hijenny 时间: 2010-8-4 06:40
根據這題意 : 因為是square, 所以long and width是一樣的. 1. a square slab is proportional to its thickness 假設thickness = T => T * k1 2. also proportional to the square of its length 假設length = L => L * k2 成本C = T * k1 * L^2 * k2^2 => C = T * L^2 * (k1*k2^2) 由於不管length or thickness怎樣變動, 常數(constant)都不會變, 因為他是成比例的, 因此簡化為 (k1*k2^2) = K => T * L^2 * K
C=cost, k=constant, T=thickness, L =length C= k * T * L^2
so when T=0.1, L=3, C=? (we need to know the value of k)
(1) The cost of a square slab that is 2 meters long and 0.2 meter thick --> C= k * 0.2 * 2^2 the cost of a square slab that is 2 meters long and 0.1 meter thick --> C= k * 0.1 * 2^2 difference of two costs=160 (given) --> (k * 0.2 * 2^2) - (k * 0.1 * 2^2) =160 so you can get the value of k=400 ---> sufficient (2) The cost of a square slab that is 3 meters long and 0.1 meter thick --> C= k * 0.1 * 3^2 the cost of a square slab that is 2 meters long and 0.1 meter thick --> C= k * 0.1 * 2^2 difference of two costs=200 (given) --> (k * 0.1 * 3^2) - (k * 0.1 * 2^2) =200 so you can get the value of k=400 ---> sufficient