StudentAidUnit 4: Functions and Graphs — Exercise 4 3
10th Class Mathematics · Unit 4: Functions and Graphs
4.3.1.A function B(t) = 5,000 + 200t represents the total balance (in rupees) after t months. What will be the balance after 6 months?
Given
Function
B(t) = 5000+200t,quad t=6
Working
B(6) = 5000+200(6)
= 5000+1200
Result
Balance after 6 months
B(6) = Rs. 6{,}200
4.3.2.A function f(k) = 150 + 20k represents the total fare (in rupees) for k kilometres. How much will the fare be for a 12 kilometres ride?
Given
Function
f(k) = 150+20k,quad k=12
Working
f(12) = 150+20(12)
= 150+240
Result
Fare for 12 km
f(12) = Rs. 390
4.3.3.The cost of manufacturing fancy sofa set would be fixed charges Rs. 5500 which is modeled as f(n) = 5500/n, where n is the number of sofa sets. Find the cost of 50 sofa sets.
Given
Function
f(n) = 5500n,quad n=50
Working
f(50) = 550050
= 5500div5050div50 = 1101
Result
Cost of 50 sofa sets
f(50) = Rs. 110
4.3.4.A function T(d) = d/60 represents the time T in hours to travel a distance d kilometres. How long will it take to travel 180 km?
Given
Function
T(d) = d60,quad d=180
Working
T(180) = 18060
Result
Time to travel 180 km
T(180) = 3 hours
4.3.5.A company charges Rs. 100 for an encoding work. In addition, the company charges Rs. 5 per page of printed output. The model of function f(x) = 100 + 5x, where x represents the number of pages printed out. How much will company charge for 55 page encoding and printing work?
Given
Function
f(x) = 100+5x,quad x=55
Working
f(55) = 100+5(55)
= 100+275
Result
Charge for 55 pages
f(55) = Rs. 375
4.3.6.A chemical reaction is stable at 37°C. The process must be stopped if the temperature deviates by more than 2.5°C. The condition is modeled as: |T - 37°| > 2.5°, T be the temperature. For what temperature values must the process be stopped?
Given
Condition
|T-37circ| > 2.5circ
Case 1
T-37circ > 2.5circ implies T > 39.5circ
Case 2
T-37circ < -2.5circ implies T < 34.5circ
Result
Result
T < 34.5circ or T > 39.5circ
4.3.7.A factory produces metal rods that must be 2.5 metres long, with a tolerance of ± 0.04 metres. An absolute value inequality models this: |x - 2.5| \le 0.04. What is the range of acceptable lengths?
Given
Condition
|x-2.5| le 0.04
-0.04 le x-2.5 le 0.04
Add 2.5 to all parts
-0.04+2.5 le x le 0.04+2.5
Result
Range of acceptable lengths
2.46 le x le 2.54 (metres)
4.3.8.A machine part must be aligned so that its centre is exactly at 0. If it shifts more than 0.1 mm, the part is rejected. The model is given by |x| > 0.1. What positions of the centre cause rejection?
Given
Condition
|x| > 0.1
Case 1
x > 0.1
Case 2
x < -0.1
Result
Positions causing rejection
x < -0.1 mm or x > 0.1 mm