Question

to dig a well of x dcm deep. one part of the total expenses varies direcly with x and other part varies directly with x^2. if the expenses of digging wells of 100dcm and 200 dcm depth are rs5000 and rs12000 respectively, let us writeby calculating the expenses of digging a well of 250dcm depth​

Answer 1

Answer:

Given:

Acc. To given condition:

First part of expense (t1) ∝ x

Where x is the depth of well.

t1 = kx

second part of expense (t2) ∝ x2

t2 = mx2

total expense (t) = t1 + t2

It can be written as:

t = k x + m x2

First depth = 100 dcm and first expense = Rs.5000

5000 = k 100 + m(100)2)

5000 = 100k + 10000m …(1)

First depth = 200 dcm and first expense = Rs.12000

12000 = k 200 + m(200)2)

12000 = 200k + 40000m …(2)

Multiply (1) by 2 :

10000 = 200k + 20000m …..(3)

Subtract (3) from (2)

2000 = 20000m

Put m in (1)

5000 = 100k + 1000

100k = 5000 – 1000

100k = 4000

⇒ k = 40

For x = 250 dcm

⇒ t = 10000 + 6250

t = Rs16250

So total expene will be Rs. 16250