Water Treatment
M.M. Ghangrekar
Department of Civil Engineering
Indian Institute of Technology
Kharagpur
Water Demand
Various types of water demands for a city
Domestic water demands
Commercial & industrial demand
Fire demand
Demand for public uses
Say a police man is interested in clocking the speed of a
vehicle by using measurements of its relative distance.
At different times ti we measure distance bi .
Assuming the vehicle is traveling at constant speed we know a
linear formula for this, but the
Warm-Up Exercises
Find the x-intercept and y-intercept
1. 3x 5y = 15
ANSWER
5; 3
2. y = 2x + 7
ANSWER
7 ;7
2
Warm-Up Exercises
3. A ball is thrown so its height h, in feet, is given by the
equation h = 16t2 + 10t, where t is the time in
seconds. What is
Warm-Up Exercises
Evaluate the expression without using a calculator.
1. 52
ANSWER
2. 8
1
25
2
3
ANSWER
4
Warm-Up Exercises
Evaluate the expression without using a calculator.
3. 3 4
3
2
ANSWER
24
4. State the domain and range of the function
y = (x 2)2 +
The
The Chemistry
Chemistry of
of Acids
Acids and
and
Bases
Bases
Chapter 16
Acid and Bases
Acid and Bases
Acid and Bases
Acids
Have a sour taste. Vinegar is a solution of acetic acid. Citrus
fruits contain citric acid.
React with certain metals to produc
Warm-Up Exercises
1. Solve x2 2x 24 = 0.
ANSWER
2. Solve
ANSWER
4, 6
8 < 3x 5 < 7.
1 < x < 4
Warm-Up Exercises
3. A point on a graph moves so that the function
y = 2x2 3x 20 describes how the vertical
position y is related to the horizontal position x.
Wh
Warm-Up Exercises
3
1. Simplify
ANSWER
4
5
12 + 3 5
11
Solve the equation.
2. 3x2 + 8 = 23
ANSWER
5 , 5
Warm-Up Exercises
Solve the equation.
3. 2(x + 7)2 = 16
ANSWER
7+2
2,7 2 2
4. Three times the square of a number is 15. What is the
number?
ANSWER
5 ,
Warm-Up Exercises
1. Write an equation in slope-intercept form for the line
through (2, 5) and (6, 3).
ANSWER
y = 2x + 9
2. Write an equation in point-slope form for the line
through (2, 4.53) and (5, 5.22).
ANSWER
y 4.53 = 0.23(x 2) or y 5.22 = 0.23(x 5)
Warm-Up Exercises
Evaluate the expression without using a calculator.
1.
1
3
3
ANSWER
2. 2
5
27
0
ANSWER
1
Warm-Up Exercises
Evaluate the expression without using a calculator.
3. 4 2
3
2
+1
ANSWER
10
4. A savings account pays 3% interest compounded
month
Warm-Up Exercises
Find the exact value.
1. 49
ANSWER
7
2. 144
ANSWER
12
Warm-Up Exercises
3. Use a calculator to approximate the value of 82
16
to the nearest tenth.
ANSWER
2.3
4. The area of half of a square mural is 60 21 square
feet. What is the length
Warm-Up Exercises
1. Find the inverse of the function y = 3x 5.
ANSWER
y=
5
1
x+
3
3
2. An account that pays 3% annual interest compounded
continuously has a balance of $10,000 on June 1, 2008.
If no money is added, what is the balance on June 1,
2010?
AN
ommu
/_,_
18.06 Exam II Lecturer: Townsend 6th November, 2015
Your PRINTED name is:
Please CIRCLE your section:
Grading 21:
1917-128 Miriam Farber
38-166 Sam Raskin 2:
E17-128 Miriam Farber
38-166 Sam Raskin 3:
E17433 Nate Harman
E174 39 Tanya Khovanova
4
Section 7.2 Linear Programming: The Graphical Method
Many problems in business, science, and economics involve finding the optimal value of a function (for
instance, the maximum value of the profit function or the minimum value of the cost function), subj
1. Which one is the largest component of DNA among the following:
a. Nucleoside
c. Nucleotide
b. Purine base
d. Pentose sugar
2. One complete turn of a DNA double-helix measures
a. 2.0 nm
b. 3.6 nm
c. 0.34 nm
3.
d. 10 nm
In DNA double helix, the two DNA c
Assignment-I
1. Let
be the triangular pulse and
be the unit impulse train shown in Fig. 3.
is expressed as
Determine and sketch
a) T=3
b) T=2
c) T=1.5
for the following values of T
Fig. 3
2. Compute the output y ( t ) for a continuous-time LTI system whos
Department of Mathematics, Indian Institute of Technology, Kharagpur
Assignment 2, Probability and Stochastic Processes (MA 20106).
Due : Feb-03, 2016
1.
Check if the following functions define cdf's :
(a) F(x) = 0, if x < 0, = x, if 0 x 1/2, and
= 1, if
EC29008: Analog Electronic Circuits Laboratory
E & ECE Department, I.I.T., Kharagpur
Guidelines of preparing laboratory report :
It should be Short and precise containing the following information:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
Experiment title
Exper
Department of Mathematics, Indian Institute of Technology, Kharagpur
Assignment 1, Probability and Stochastic Processes (MA 20106).
Due : Jan-19, 2016
1. A coin is tossed until for the rst time the same result appear twice in succession. To an
outcome req
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by Ca
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by Ca
Solve the system of linear equations by finding rank of the augmented
matrix and coefficient matrix.
cfw_Or, Examine for consistency and if consistent then solve it.
2 x 1 + x 2 x3 +3 x 4 =8
3 x1 +2 x 2 x 3=6
x 1+ x 2 +x 3x 4=2
;
;
4
x 2+3 x 3 +2 x 4 + 8=
18.06 Exam I Lecturer: Townsend 5th October, 2015
Your PRINTED name is:
Please CIRCLE your section:
1317128
38-166
E17428
38-166
E17~133
BIT-139
1317133
38-166
38-166
Miriam Father
Sam Raskin
Miriam Father
Sum Raskin
N ate Harman
Tanya Khovsmova
Tanya K
18.06: Linear algebra
Spring 2016
Lecturer: C. Barwick
Office :
Office hours :
Email :
2-476
Tue. and Thur., 11 am noon
clarkbar@gmail.com
Course website : https:/stellar.mit.edu/S/course/18/sp16/18.06/
Textbook
We will be using:
Strang. Introduction to l
Warm-Up Exercises
1. Write 15x2 + 6x = 14x2 12 in standard form.
ANSWER
x2 + 6x +12 = 0
2. Evaluate b2 4ac when a = 3, b = 6, and c = 5.
ANSWER
24
Warm-Up Exercises
3. A student is solving an equation by completing the
square. Write the step in the soluti