Assume real numbers R for now. Consider relation on R, x y iff x .pdf
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Assume real numbers R for now. Consider relation on R, x y iff x y Z. (a) Is it an equivalence relation? (b) Compute [1/2] (c) Classify all elements of R/ . That is state: “Every element of R/ is of the form ...” – include all the details, so that you don’t count any element twice. (d) Bonus question: (you don’t need to answer): Is there a geometric way to think about R/ ? Solution a) x-x=0 is in Z for all real numbers x SO R is reflexive IF, x-y is in Z then y-x is also in Z So, R is symmetrix IF, x-y and y-z are in Z then x-y+y-z=x-z is also in Z Hence, R is transitive Hence, R is an equivalence relation b) [1/2]={n+1/2: n is in Z} c) Elements of R/~ are of the form: a+R, where, a is a real number in (0,1] We need only consider real numbers outside this interval because all other real numbers will differ by an integer from one of the numbers in this interval..
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![Assume real numbers R for now. Consider relation on R, x y iff x y Z.
(a) Is it an equivalence relation?
(b) Compute [1/2]
(c) Classify all elements of R/ . That is state: “Every element of R/ is of the form ...” – include
all the details, so that you don’t count any element twice.
(d) Bonus question: (you don’t need to answer): Is there a geometric way to think about R/ ?
Solution
a)
x-x=0 is in Z for all real numbers x
SO R is reflexive
IF, x-y is in Z then y-x is also in Z
So, R is symmetrix
IF, x-y and y-z are in Z
then x-y+y-z=x-z is also in Z
Hence, R is transitive
Hence, R is an equivalence relation
b)
[1/2]={n+1/2: n is in Z}
c)
Elements of R/~ are of the form:
a+R, where, a is a real number in (0,1]
We need only consider real numbers outside this interval because all other real numbers will
differ by an integer from one of the numbers in this interval.](https://image.slidesharecdn.com/assumerealnumbersrfornow-230704070831-b4739712/85/Assume-real-numbers-R-for-now-Consider-relation-on-R-x-y-iff-x-pdf-1-320.jpg)
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Maths chapter wise Important questions
Chapter wise important questions in Mathematics for Karnataka 2 year PU Science students. This is taken from the PU board website and compiled together.
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3.Complex Number,For most human tasks, real numbers (or even rational numbers) offer an adequate description of data. Fractions such as 2/3 and 1/8 are meaningless to a person counting stones, but essential to a person comparing the sizes of different collections of stones. Negative numbers such as -3 and-5 are meaningless when measuring the mass of an object, but essential when keeping track of monetary debits and credits.
All numbers are imaginary (even "zero“ was contentious once). Introducing the square root(s) of minus one is convenient because
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it saves using matrix representations for objects that square to-1 (such objects representing an important part of the structure of linear equations which appear in quantum mechanics ,heat,diffusion,optics,etc) .The hottest contenders for numbers without purpose are probably the p-adic numbers (an extension of the rationales),and perhaps the expiry dates on army ration packs.
4.Complex Number is defined as an ordered pair of real number X & Y and is denoted by (X,Y)
It is also written as 𝒛=𝒙,𝒚=𝒙+𝒊𝒚,where 𝑖^2=−1
𝑥 is called Real Part of z and written as Re(z)
Y is called imaginary part of z and written as Im(z).
-If R(z) = 0 then 𝑧=𝑖𝑦, is called Purely Imaginary Number.
-If I(z) = 0 then 𝑧=𝑥, is called Purely Real Number.
-Here 𝑖can be written as (0, 1) = 0 ±1𝑖
Note:-−𝒂= 𝑎−1=𝑖𝑎
-If 𝑧=𝑥+𝑖𝑦is complex number then its conjugate or complex conjugate is defined as 𝒛=𝒙−𝒊𝒚.
5.DIFFERENT FORMS OF COMPLEX NUMBER
Cartesian or Rectangular Form :-𝑧=𝑥+𝑖𝑦
Polar Form :-𝑧=𝑟(cos𝜃+𝑖sin𝜃) 𝑜𝑟 𝑧=𝑟∠𝜃
Exponential Form :-𝑧=𝑟𝑒^𝑖𝜃
MODULUS & ARGUMENT OF COMPLEX NUMBER
Modulus of complex number (|z|) OR mod(z) OR 𝑟=√(𝑋^2+𝑌^2 )
Argument OR Amplitude of complex number (𝜃) OR arg (𝑧) OR amp(z)=tan^(−1)(𝑥/𝑦)
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Mathematician Argand represent a complex number in a diagram known as Argand diagram. A complex number x+iy can be represented by a point P whose co–ordinate are (x,y).The axis of x is called the real axis and the axis of y the imaginary axis. The distance OP is the modulus and the angle, OP makes with the x-axis, is the argument of x+iy.
7.Addition of Complex Numbers
Let a+ib and c+id be two numbers, then
(a+ib)+(c+id)=(a+c)+i(b+d)
Procedure: In addition of complex numbers we add real parts with real parts and imaginary parts with imaginary parts.
8.Subtraction of Complex Numbers
Let a+ib and c+id be two numbers, then
(a+ib)-(c+id)=(a-c)+i(b-d)
Procedure: In subtraction of complex numbers we subtract real parts w
Unary and binary set operations
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IIT JAM MATH 2021 Question Paper | Sourav Sir's Classes
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MATH 200-004 Multivariate Calculus Winter 2014Chapter 12.docx
MATH 200-004: Multivariate Calculus Winter 2014
Chapter 12: Vector-Valued Functions
Extra Credit Scribe: Charles Burnette
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal publications.
They may be distributed outside this class only with my permission.
These notes cover some topics in addition to what you are expected to know about vector-valued functions.
You will not be tested on material from sections 12.3 – 12.6. An extra credit quiz on the content of these
notes is available at the end. Problems marked with a ? are ‘‘for your entertainment’’ and are not essential.
12.1 Introduction to Vector-Valued Functions
In general, a function is a rule that assigns to each element in the domain an element in the range. A
vector-valued function , or vector function , is simply a function whose domain is a set of real numbers
and whose range is a set of vectors. We are most interested in vector functions r whose values are three-
dimensional vectors. This means that for every t in the domain of r there is a unique vector denoted by r(t).
If f(t), g(t), and h(t) are the components of the vector r(t), then f, g, and h are real-valued functions called
the component functions of r and we can write
r(t) = 〈f(t), g(t), h(t)〉 = f(t)i + g(t)j + h(t)k.
We use the letter t to denote the independent variable, because it represents time in most applications of
vector functions.
Example 12.1 If
r(t) =
⟨
t3, ln(3− t),
√
t
⟩
,
then the component functions are
f(t) = t3 g(t) = ln(3− t) h(t) =
√
t.
By our usual convention, the domain of r consists of all values of t for which the expression r(t) is defined.
The expressions t3, ln(3− t), and
√
t are all defined when 3− t > 0 and t ≥ 0. Therefore, the domain of r is
the interval [0, 3).
We now wish to develop a notion of what it means for a vector function r in 2-space or 3-space to
approach a limiting vector L as t approaches a number a. That is, we want to define
12-1
12-2 Chapter 12: Vector-Valued Functions
Figure 12.1: Visualization of Limits for Vector Functions
lim
t→a
r(t) = L. (12.1)
One way to motivate a reasonable definition of (12.1) is to position r(t) and L with their initial points at the
origin and interpret this limit to mean that the terminal point of r(t) approaches the terminal point of L as t
approaches a or, equivalently, that the vector r(t) approaches the vector L in both length and direction as t
approaches a (Figure 12.1). Algebraically, this is equivalent to stating that
lim
t→a
||r(t)− L|| = 0 (12.2)
(Figure 12.1). Thus, we make the following definition.
Definition 12.2 Let r(t) be a vector function that is defined for all t in some open interval containing the
number a, except that r(t) need not be defined at a. We will write
lim
t→a
r(t) = L
if and only if
lim
t→a
||r(t)− L|| = 0.
Theorem 12.3 If r has a limit at a, then this limit is unique.
Proof: Suppose that r has limits L1 and L2 at a. Let � > 0 be given, but fixe ...
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The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
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Similar to Assume real numbers R for now. Consider relation on R, x y iff x .pdf
Complex Analysis
Complex analysis and its application
2.Contents,Complex number
Different forms of complex number
Types of complex number
Argand Diagram
Addition, subtraction, Multiplication & Division
Conjugate of Complex number
Complex variable
Function of complex variable
Continuity
Differentiability
Analytic Function
Harmonic Function
Application of complex Function
3.Complex Number,For most human tasks, real numbers (or even rational numbers) offer an adequate description of data. Fractions such as 2/3 and 1/8 are meaningless to a person counting stones, but essential to a person comparing the sizes of different collections of stones. Negative numbers such as -3 and-5 are meaningless when measuring the mass of an object, but essential when keeping track of monetary debits and credits.
All numbers are imaginary (even "zero“ was contentious once). Introducing the square root(s) of minus one is convenient because
all n-degree polynomials with real coefficients then haven roots, making algebra "complete";
it saves using matrix representations for objects that square to-1 (such objects representing an important part of the structure of linear equations which appear in quantum mechanics ,heat,diffusion,optics,etc) .The hottest contenders for numbers without purpose are probably the p-adic numbers (an extension of the rationales),and perhaps the expiry dates on army ration packs.
4.Complex Number is defined as an ordered pair of real number X & Y and is denoted by (X,Y)
It is also written as 𝒛=𝒙,𝒚=𝒙+𝒊𝒚,where 𝑖^2=−1
𝑥 is called Real Part of z and written as Re(z)
Y is called imaginary part of z and written as Im(z).
-If R(z) = 0 then 𝑧=𝑖𝑦, is called Purely Imaginary Number.
-If I(z) = 0 then 𝑧=𝑥, is called Purely Real Number.
-Here 𝑖can be written as (0, 1) = 0 ±1𝑖
Note:-−𝒂= 𝑎−1=𝑖𝑎
-If 𝑧=𝑥+𝑖𝑦is complex number then its conjugate or complex conjugate is defined as 𝒛=𝒙−𝒊𝒚.
5.DIFFERENT FORMS OF COMPLEX NUMBER
Cartesian or Rectangular Form :-𝑧=𝑥+𝑖𝑦
Polar Form :-𝑧=𝑟(cos𝜃+𝑖sin𝜃) 𝑜𝑟 𝑧=𝑟∠𝜃
Exponential Form :-𝑧=𝑟𝑒^𝑖𝜃
MODULUS & ARGUMENT OF COMPLEX NUMBER
Modulus of complex number (|z|) OR mod(z) OR 𝑟=√(𝑋^2+𝑌^2 )
Argument OR Amplitude of complex number (𝜃) OR arg (𝑧) OR amp(z)=tan^(−1)(𝑥/𝑦)
6.Argand Diagram
Mathematician Argand represent a complex number in a diagram known as Argand diagram. A complex number x+iy can be represented by a point P whose co–ordinate are (x,y).The axis of x is called the real axis and the axis of y the imaginary axis. The distance OP is the modulus and the angle, OP makes with the x-axis, is the argument of x+iy.
7.Addition of Complex Numbers
Let a+ib and c+id be two numbers, then
(a+ib)+(c+id)=(a+c)+i(b+d)
Procedure: In addition of complex numbers we add real parts with real parts and imaginary parts with imaginary parts.
8.Subtraction of Complex Numbers
Let a+ib and c+id be two numbers, then
(a+ib)-(c+id)=(a-c)+i(b-d)
Procedure: In subtraction of complex numbers we subtract real parts w
Unary and binary set operations
A unary operation is an operation with only one operand while a binary operation is a calculation that combines two elements of operands.
IIT JAM MATH 2021 Question Paper | Sourav Sir's Classes
IIT JAM Math Previous Year Question Paper
IIT JAM Math 2021 Question Paper
IIT JAM Preparation Strategy
For any query about exams feel free to contact us
Call - 9836793076
MATH 200-004 Multivariate Calculus Winter 2014Chapter 12.docx
MATH 200-004: Multivariate Calculus Winter 2014
Chapter 12: Vector-Valued Functions
Extra Credit Scribe: Charles Burnette
Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal publications.
They may be distributed outside this class only with my permission.
These notes cover some topics in addition to what you are expected to know about vector-valued functions.
You will not be tested on material from sections 12.3 – 12.6. An extra credit quiz on the content of these
notes is available at the end. Problems marked with a ? are ‘‘for your entertainment’’ and are not essential.
12.1 Introduction to Vector-Valued Functions
In general, a function is a rule that assigns to each element in the domain an element in the range. A
vector-valued function , or vector function , is simply a function whose domain is a set of real numbers
and whose range is a set of vectors. We are most interested in vector functions r whose values are three-
dimensional vectors. This means that for every t in the domain of r there is a unique vector denoted by r(t).
If f(t), g(t), and h(t) are the components of the vector r(t), then f, g, and h are real-valued functions called
the component functions of r and we can write
r(t) = 〈f(t), g(t), h(t)〉 = f(t)i + g(t)j + h(t)k.
We use the letter t to denote the independent variable, because it represents time in most applications of
vector functions.
Example 12.1 If
r(t) =
⟨
t3, ln(3− t),
√
t
⟩
,
then the component functions are
f(t) = t3 g(t) = ln(3− t) h(t) =
√
t.
By our usual convention, the domain of r consists of all values of t for which the expression r(t) is defined.
The expressions t3, ln(3− t), and
√
t are all defined when 3− t > 0 and t ≥ 0. Therefore, the domain of r is
the interval [0, 3).
We now wish to develop a notion of what it means for a vector function r in 2-space or 3-space to
approach a limiting vector L as t approaches a number a. That is, we want to define
12-1
12-2 Chapter 12: Vector-Valued Functions
Figure 12.1: Visualization of Limits for Vector Functions
lim
t→a
r(t) = L. (12.1)
One way to motivate a reasonable definition of (12.1) is to position r(t) and L with their initial points at the
origin and interpret this limit to mean that the terminal point of r(t) approaches the terminal point of L as t
approaches a or, equivalently, that the vector r(t) approaches the vector L in both length and direction as t
approaches a (Figure 12.1). Algebraically, this is equivalent to stating that
lim
t→a
||r(t)− L|| = 0 (12.2)
(Figure 12.1). Thus, we make the following definition.
Definition 12.2 Let r(t) be a vector function that is defined for all t in some open interval containing the
number a, except that r(t) need not be defined at a. We will write
lim
t→a
r(t) = L
if and only if
lim
t→a
||r(t)− L|| = 0.
Theorem 12.3 If r has a limit at a, then this limit is unique.
Proof: Suppose that r has limits L1 and L2 at a. Let � > 0 be given, but fixe ...
Riemann hypothesis proof_highlights_presentation
Why the Riemann Xi function has only real zeros - using 2 integration approaches to Riemann's original equation to create a series of incomplete gamma functions and a power series and investigating the behaviour of the curves and the zeros when varying components. Conclusion - only real zeros (Riemann Hypothesis is true).
μ-RANGE, λ-RANGE OF OPERATORS ON A HILBERT SPACE
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
Chapter 2: Relations
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IIT JAM MATH 2021 Question Paper | Sourav Sir's Classes
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treatment levels? Explain how the author used replication in both space and time. 3. The author
presents data on bird densities within sites in both Table 1 and Figure 3. Which presentation do
you find more interpretable and why? What information is common to both, what is unique to
either one or the other? Could you limit the redundancy of these two presentations by combining
them into one table or figure? If so, which would you choose and how would you lay it out? 4.
The golf course had the highest bird species richness, density, and biomass (when Rock Doves
were excluded from the analysis), and the second highest diversity (Figure 4). Summarize the
author’s explanation for this result. 5. Based on the study results, briefly argue the pros and cons
of golf courses as they relate to bird diversity and abundance.
Solution
1: The author predicts three groups of birds which he called as urban exploiters, urban avoiders
and suburban adaptable. The urban exploiters are expected to get adapted to the changes and to
reach their highest densities at the developed sites. The urban avoiders are expected to respond in
a sensitive way to the anthropogenic changes in their habitat and are expected to have their
maximum densities at the natural sites only. The suburban adaptables are expected to exploit
some additional available resources leading to their moderate development..
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An attack in which an authentic-looking e-mail or website entices a user to enter his or her
username, password, or other sensitive information is called ________. (Select the most specific
answer.)
A- a spyware attack
B-identity theft
C- phishing
D- social engineering
A- a spyware attack
B-identity theft
C- phishing
D- social engineering
Solution
C - phishing ,
is the method that attackers use to get login credentials and other sensitive information by
sending emails that resemble original login authentication procedure..
Consider a relation T with six attributes ABCDEF where AB is a compo.pdf
Consider a relation T with six attributes ABCDEF where AB is a composite primary key for T.
Assume T has the following functional dependencies:
AB -> CDEF
A -> CEF
F -> E
In what normal form is relation T? Explain why?
Is it possible to decompose T into a number of relations in order to achieve a higher normal
form? Explain how.
Solution
T(A,B,C,D,E,F)
AB -> CDEF
A -> CEF
F -> E
The relation T is in First Normal Form assuming all attribute values are atomic. But it is not in
second normal form because attribute E is functionally dependent on the attribute F.But F is not
part of key attributes so relation is not in second normal form. attribute.A relation is in second
normal form if all non key attributes are fully functionally deprndent on attribute keys.
Yes , it is possisble to decompose the relation into number of relations in order to achieve the
higher normalization. Following are the tables into which we can decompose the relation T
Table1(A,C,E,F)
Table2 (A,B,D)
Table3 (F,E)
underlined attributes are primary keys.
A vague appointment Four people make an appointment to meet each ot.pdf
A vague appointment: Four people make an appointment to meet each other at the café in town.
However, this particular town has four cafés. What is the probability that none of them meet?
Solution
There are 4^4 = 256 ways to go to the 4 cafes.
Meanwhile, there are 4! = 24 ways to permute them, so that no 2 people are on the same cafe.
Thus,
P(none meets) = 24/256 = 0.09375 [answer].
An enzyme aggase requires 16 units of activity for wild type functio.pdf
An enzyme aggase requires >16 units of activity for wild type function. Two alleles of aggase
have been identified. Wild type allele A_1 produces 12 units of enzyme and mutant allele A_2
produces 5 units of enzyme. Which allele is dominant and which is haploinsufficient? Explain
your reasoning.
Solution
Haploinsufficiency is a potential mechanism in which a diploid species can express a single
functional copy of that gene and the other one copy of gene function will be lost due to mutation
finally trigger loss-of-function mutation so that it is not possible to generate a complete wild-type
phenotype with one functional copy of allele. Therefore, in the above case, enzyme aggase need
>16 units of enzyme, in which only A1 generates 12 units & the remaining A2 produced 5 units
together 17 units to produce a complete wild-type phenotype. Here, haplosuffciency can occur
with a single functional copy of gene, A1 & A2 alleles \"individually\" both are does not produce
enough product to meet >16 units of enzyme to display the wild type\'s so that both are
considered as haplosufficient
Dominance can be observed only in allele A1 because it can mask the allelic recessive locus due
to heterozygosity & Mendelian inheritance in which A1 is responsible for the phenotype
Other reason:
1. Dominant gain of function in which protein expressed from the mutant gene is constitutively
active due to base substitutions finally protein expression is further downregulated because of
increase in expression of enzyme proteins.
2. Loss of Function/ Haploinsufficiency: It is also due to loss of heterozygosity thereby by loss
of gene function with haploinsufficiency. Finally, resultant organism possesses only one
functional gene copy with truncated protein..
17. Of these, which represents a heterozygote a. aa b. Ab c. .pdf
17. Of these, which represents a heterozygote?
a. aa
b. Ab
c. AA
d. both a. and c.
18. Active transport across a cell membrane is
a. moving a molecule from lower to higher concentcation
b. moving a molecule from higher to lower concentration
c. moving a from outside the cell to inside the cell
d. by which cells tet rid of waste products
19. All of the following are true about the cell membrane except _____.
a. They are mainly composed of lipids and
b. All polar molecules pass freely, directly through the membrane
c. They are selectively permeable.
d. They have a lipid bilayer
20. Which cellular process produces the most ATP?
a. Photosynthesis
b. aerobic respiration
c. meiosis
d. anaerobic respiration
21. A plant can regulate the amount of water in its cells by
a. moving to a more aqueous environment
b. increasing the amount of solute in the cytoplasm
c. reducing its rate of respiration
d. drinking a tall glass of refreshing rain water
22. Eye color is represented by the alleles AaBBCc. This is an example of ______.
a-complete dominant inheritance
b. heterozygote advantage
c-sex-linked inheritance
d-polygenic inheritance
23. During amniocentesis the baby\'s cells are obtained from the ____.
a. fluid around the embryo
b. placenta
c. uterine wall
d. developing embryo
Solution
17. Heterozygous is represented by
b. Ab
18. Active transport across cell membrane is
a. moving molecule from lower to higher concentration.
19. All are true about cell membrane except
a. They are mainly composed of lipids.
20. Which cellular process produces most ATP?
b. Aerobic respiration
21. A plant can regulate the amount of water in its cells by
b. increasing the amount of solute in the cytoplasm.
22. Eye colour represented by the alleles AaBBCc is an example of
d. Polygenic inheritance
23. During amniocentesis the baby\'s cells are obtained from the
a. fluid around the the embryo.
1. Match the decription listed with the corresponding structureA. .pdf
1. Match the decription listed with the corresponding structure
A. corpus callosum
B. hypothalamus
C. mammillary bodies
D. pineal body (gland)
1. controls hormone secretion from the pituitary gland
2. fiber tract that connects the left cerebral hemisphere to the right cerebral hemisphere
3. involved in suckling reflex and chewing
4. primary relay center for sensory information coming into the brain
5. secretes the hormone melatonin from its precursor molecule serotonin
Solution
Ans). A. corpus callosum - 2. fiber tract that connects the left cerebral hemisphere to the right
cerebral hemisphere
B. hypothalamus - 1. controls hormone secretion from the pituitary gland
C. mammillary bodies - 4. primary relay center for sensory information coming into the brain
D. pineal body (gland) - 5. secretes the hormone melatonin from its precursor molecule serotonin.
1.) What are some factors that should be taken into account when est.pdf
1.) What are some factors that should be taken into account when establishing criteria for
recruitment and selection of employees in a global corporation?
2.) What are the most important factors that should be taken into account when establishing
criteria for recruitment and selection of employees for international assignments and why?
Solution
1. the people who are representing in global corportaion should have good skills and positive at
the work and even after the work also. they should be in a position to mould them selves
according to the need and requirement. they should have awareness about different culture,
tradition and respect the people who follows it. they need to konw differences between the
company norms and rules in host country and parent country also. some times the legal aspects
and other aspects related to work will be different. the person who wants to work for different
global companies should know the variations and differences also.
the major part is cultural barriers, the new comers should adapt or ready to adapt new culture and
practice it. they should know the traditions and values followed by the people and respect them.
even they need to consider the race, gender, and community aspects also.
2. the first factor is the strength in the group, how many people requires to complete the
assignment.
second factor is how the group should form, who are the different kinds and specilists represents
in the group. do they ready to work in teams as well as individuals with out having any ego or
personal problems, should assess. the seniority and skill expertise of the people should be match,
otherwise it creates new problems. the traditions and cultures which they follows and are they
open to adapt and follow the new culture should be consider.
there are two kinds of problems in this type of group, one is related to work. it can be resolved
and every one can note and complete their given tasks. they can perform their roles correctly and
achieve the targets. the second problem is relates to out of work. it may relates to personal egos,
differentiations in the payments among the members, respect the others and their cultures and so
on. these kind of problems are vary difficult to solve and the team representatives should not
create these sort of problems..
Write a program that asks the user for the name of a file. The progr.pdf
Write a class named testscores. The class constructor should accept an array of rest scores as its
argument., The class should have a member function that returns the average of the test scores. If
any test score in the array is negative or greater than 100, the class should throw an exception.
Demonstrate the class in a program.
Solution
#include
#include
using namespace std;
class TestScores{
private:
float total = 0; //intiialising total marks
int length; //declaring variable for the size of scores array
bool invalid = false;
public:
TestScores(vector scores){
length = scores.size(); //length of vector of scores
for(int i = 0; i100){
cout<<\"Error! Invalid test score!\"; //error for invalid input
total = 0;
invalid = true;
}
else{
total+=scores[i];
}
}
}
float average(){
if(invalid==true){
return 0;
}
return this->total/this->length;
}
};
int main(){
vector scores;
scores.push_back(20);
scores.push_back(25);
scores.push_back(30);
scores.push_back(35);
scores.push_back(40);
scores.push_back(455);
scores.push_back(50);
TestScores testScores = TestScores(scores);
cout<<\"Average: \"<.
Write a program that obtains the execution time of selection sort, bu.pdf
Write a java program called Question39 that does the following: Gets input for temperature
Utilizing a branching statement: If temperature is 76-100, call method outputHot passing the
temperature input as an argument. If temperature is 0-39, call method outputCold passing the
temperature input as an argument. If temperature is 40 to 75, call method outputJustRight
passing the temperature input as an argument. If temperature is outside these ranges, output
“Temperature outside range” to the screen. Be precise, import modules, include comments,
prologue, etc. as needed.
Solution
Question39.java
import java.util.Scanner;
public class Question39 {
public static void main(String[] args) {
Scanner scan = new Scanner(System.in);
System.out.println(\"Enter temperature: \");
int temp = scan.nextInt();
if(temp >=76 && temp <=100){
outputHot(temp);
}
else if(temp >=0 && temp <=39){
outputCold(temp);
}
else if(temp >=40 && temp <=75){
outputJustRight(temp);
}
else{
System.out.println(\"Temperature outside range\");
}
}
public static void outputHot(int temp){
System.out.println(\"Temperature \"+temp+\" Hot \");
}
public static void outputCold(int temp){
System.out.println(\"Temperature \"+temp+\" Cold \");
}
public static void outputJustRight(int temp){
System.out.println(\"Temperature \"+temp+\" Just Right \");
}
}
Output:
Enter temperature:
45
Temperature 45 Just Right.
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Why is an engine with port injection vs. carburetion more likely to have fuel dilute the
lubricating oil? Why did some aircraft engines in World War II have water injection? What is
the physical phenomenon? What is the difference between multipoint port injection systems and
a common rail system?
Solution
11.
Combustion in SI Engine Mixture preparation: - Carburation (no longer used in North
American markets) - Port injection - fuel is sprayed into the air stream just before the inlet valve.
Direct injection - fuel is injected into the cylinder (DISI).
Ignition: spark plug Flame kernel initiation and propagation model 101
Most car engines use port injection or a carburetor. Diesel engines use direct fuel injection -- the
diesel fuel is injected directly into the cylinder. The injector on a diesel engine is its most
complex component. The injector has to be able to withstand the temperature and pressure inside
the cylinder and still deliver the fuel in a fine mist. Some diesel engines contain a glow plug that
heats the combustion chambers and raises the air temperature when the engine is cold so that the
engine can start.
12.
cause, Water injection (engine) In internal combustion engines, water injection, also known as
anti-detonant injection (ADI), can spray waterinto the incoming air or fuel-air mixture, or
directly into the cylinder, in order to cool certain parts of the induction system where \"hot
points\" could produce premature ignition.
War Emergency Power (WEP) is an American term for a throttle setting on some World War II
military aircraft engines. For use in emergency situations, it produced more than 100% of the
engine\'s normal rated power for a limited amount of time, often about five minutes.
Maximum normal power would be limited by a mechanical stop, for instance a wire across the
throttle lever slot, but a more forceful push would break the wire, allowing extra power.
13.
Assuming you are aware of the basic functioning of an engine, CRDi and MPFi are both
electronically operated fuel supply systems for diesel and petrol engines respectively.
CRDi - common rail diesel ignition
MPFI - multi-point fuel injection
CRDi consists of a common rail which holds fuel at a very high pressure (~1400 bar) and injects
diesel directly into the cylinder during the transition from compression stroke to power stroke.
Due to the high pressure injection, the fuel burns efficiently and hence power and fuel efficiency
figures are improved.
MPFI on the other hand is simply multi point fuel injection. Here, the carburetor is replaced with
a MAP sensor and injection points in the intake manifold. the MAP sensor relays to the ECU as
to the amount of air entering the manifold and accordingly the quantity of fuel to be injected into
the cylinder heads is ascertained (to maintain the best possible air-fuel mixture as per the
requirements).
the main purpose of an injection system is to supply properly metered fuel to the combustion
chamber via intake valve.
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Which of the Karnaugh maps below represents the expression, X = AC + BC + B? The greatest
single-digit value in the octal number system equals 1 8 9 7 Which of the following is a
correct form of Boolean addition? A synchronous inputs are best described as having full
control over the FF, regardless of the input or clock states being to the clock, but not to the
inputs being tied to the inputs, but independent of the clock having little or no control over the
FF, except during the active clock input Which statement below best describes the function of a
decoder? Decoders are used to prevent improper operation of digital systems. A decoder will
convert a binary number into a specific output representing a particular character or digit.
Decoders are special ICs that are used to make it possible for one brand of computer to talk to
another. A decoder will convert a decimal number into the proper binary equivalent.
Solution
37)
None of the fig represents AC+BC+B
38)
The greatest single digit value in octal is 7.
39)
0+1=1 is correct
41) decoder expression is option B.
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Introduction to AI for Nonprofits with Tapp Network
Introduction to AI for Nonprofits with Tapp Network
Instructions for Submissions thorugh G- Classroom.pptx
Instructions for Submissions thorugh G- Classroom.pptx
Assume real numbers R for now. Consider relation on R, x y iff x .pdf
- 1. Assume real numbers R for now. Consider relation on R, x y iff x y Z. (a) Is it an equivalence relation? (b) Compute [1/2] (c) Classify all elements of R/ . That is state: “Every element of R/ is of the form ...” – include all the details, so that you don’t count any element twice. (d) Bonus question: (you don’t need to answer): Is there a geometric way to think about R/ ? Solution a) x-x=0 is in Z for all real numbers x SO R is reflexive IF, x-y is in Z then y-x is also in Z So, R is symmetrix IF, x-y and y-z are in Z then x-y+y-z=x-z is also in Z Hence, R is transitive Hence, R is an equivalence relation b) [1/2]={n+1/2: n is in Z} c) Elements of R/~ are of the form: a+R, where, a is a real number in (0,1] We need only consider real numbers outside this interval because all other real numbers will differ by an integer from one of the numbers in this interval.