What is a trigonometric identity How and why do we use trigonometri.pdf

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What is a trigonometric identity? How and why do we use trigonometric identities in mathematics? How can you verify an identity? Give some examples. Solution Trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables where both sides of the equality are defined Sometimes it is possible to write some complex trignmetric functions in really simple form fr example instead f writing Sinx/Cosx we can write that as Tanx so as we can see here it is easy to identify Tanx rather than first finding Sinx and then finding Cosx and then divide them to get our answer Here is an example below: we need to prove that left side is equal to right side cot x/csc x=cos x So let us simplify left side, (cos x/sin x)/(1/sin x) applying keep change flip (cos x/sin x)*sin x now we can cancel out sin x so we are left with cos x which is equal to right side of the equation hence proved..

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in C++ , Design a linked list class named IntegerList to hold a series of integers. The class must have public member functions for appending , inserting, deleting and displaying nodes. The append function must append a node to the end of the list. The insert function must insert node in ascending order. The delete function must delete the node with the given value. The display function should display the list from head to tail. The IntegerList class should also have a destructor that destroys the list and release memory. The list node must be declared as a structure using keyword struct. This structure is a private member of IntegerList. You should also store the head of the list as a private member. Write a test program to test the implementation your IntegerList class works properly. Solution Here is the code for the above scenario: #include using namespace std; struct ListNode { float value; ListNode *next; }; ListNode *head; class LinkedList { public: int insertNode(float num); int appendNode(float num); void deleteNode(float num); void destroyList(); void displayList(); LinkedList(void) {head = NULL;} ~LinkedList(void) {destroyList();} }; int LinkedList::appendNode(float num) { ListNode *newNode, *nodePtr = head; newNode = new ListNode; if(newNode == NULL) { cout << \"Error allocating memory for new list member!\ \"; return 1; } newNode->value = num; newNode->next = NULL; if(head == NULL) { cout << \"List was empty - \" << newNode->value; cout << \" is part of list\'s first node.\ \"; head = newNode; } else { while(nodePtr->next != NULL) nodePtr = nodePtr->next; nodePtr->next = newNode; } return 0; } int LinkedList::insertNode(float num) { struct ListNode *newNode, *nodePtr = head, *prevNodePtr = NULL; newNode = new ListNode; if(newNode == NULL) { cout << \"Error allocating memory for new list member!\ \"; return 1; } newNode->value = num; newNode->next = NULL; if(head==NULL) { cout << \"List was empty - \" << newNode->value; cout << \" is part of list\'s first node.\ \"; head = newNode; } else { while((nodePtr != NULL) && (nodePtr->value < num)) { prevNodePtr = nodePtr; nodePtr = nodePtr->next; } if(prevNodePtr==NULL) newNode->next = head; else newNode->next = nodePtr; prevNodePtr->next = newNode; } return 0; } void LinkedList::deleteNode(float num) { struct ListNode *nodePtr = head, *prevNodePtr = NULL; if(head==NULL) { cout << \"The list was empty!\ \"; return; } if(head->value == num) { head = nodePtr->next; delete [] nodePtr; } else { while((nodePtr!= NULL)&&(nodePtr->value != num)) { prevNodePtr = nodePtr; nodePtr = nodePtr->next; } if(nodePtr==NULL) cout << \"The value \" << num << \" is not in this list!\ \"; else { prevNodePtr->next = nodePtr->next; delete [] nodePtr; } } } void LinkedList::destroyList() { struct ListNode *nodePtr = head, *nextNode = nodePtr; if(head==NULL) { cout << \"The list is empty!\ \"; return; } while (nodePtr != NULL) { nextNode = nodePtr->next; delete [] nodePtr; nodePtr = nextNode; } } void LinkedList.

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In addition to the fossil record, what other kinds of evidence reinforce the evolutionary of life? You may want to use your textbook as a reference. Solution In addition to fossil record, application of Molecular Systematics is very much helpful for easy identification of fossilized organism. Molecular systematics involves comparisons of nucleic acids or other molecules to presume the degree of relatedness which can disclose phylogenetic relationships which usually cannot be determined by non-molecular methods like comparative anatomy. For example, molecular systematics helps us to uncover evolutionary relationships between groups and allow us to reconstruct phylogenic trees among groups of present-day organisms for which the fossil record is poor or lacking entirely. For example, the DNA that encodes for ribosomal RNA (rRNA) changes comparatively slowly. Therefore, comparisons of DNA sequences in these genes are valuable for investigating relationships between taxa that diverged hundreds of millions of years ago. Other molecular methods useful for determining phylogeny from fossil record include Nucleic acid sequencing, Genomic fingerprinting (RFLP) and Amino acid sequencing..

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How much 0.521 M NaOH will be needed to raise the pH of 0.161 L of 4.51 M ascorbic acid (H2C6H6O6) to a pH of 11.60? Solution pH of acidic buffer = pka2 + log(salt/acid) No of mol of ascorbic acid = 0.161*4.51 = 0.726 mol No of mol of salt = x mol pka2 = 11.6, pH = 11.6 11.6 = 11.6 + log(x/(0.726-x)) x = 0.363 NO of mol of NaOH required = 2x = 2*0.363 = 0.726 mol volume of NaOH must take = 0.726/0.521 = 1.4 L answer: 1.4 L.

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I am writing a program that places bolcks on a grid the the sape of different letters. It can also move the blocks and checks if they overlap. I have most of the test cases figured out except for four. Can someone help me out? Thanks in advance. output: input: output: input: output: I CAN ONLY MODIFY ONE FILE SHAPE.CPP #ifndef SHAPE_CPP #define SHAPE_CPP #include #include #include \"Shape.h\" using namespace std; // Constructor for O O::O(int posx, int posy) { x = new int[1]; y = new int[1]; x[0] = posx; y[0] = posy; } char O::name() const { return \'O\'; } int O::size() const { return 1; } // Constructor for I I::I(int posx, int posy) { x = new int[2]; y = new int[2]; x[0] = x[1] = posx; y[0] = posy; y[1] = posy+1; } char I::name() const { return \'I\'; } int I::size() const { return 2; } // Constructor for L L::L(int posx, int posy) { x = new int[3]; y = new int[3]; x[0] = x[2] = posx; y[0] = y[1] = posy; x[1] = posx+1; y[2] = posy+1; } char L::name() const { return \'L\'; } int L::size() const { return 3; } // Constructor for S S::S(int posx, int posy) { x = new int[4]; y = new int[4]; x[0] = posx; x[1] = posx+1; x[2] = posx+1; x[3] = posx+2; y[0] = y[1] = posy; y[2] = y[3] = posy+1; } char S::name() const { return \'S\'; } int S::size() const { return 4; } /* Constructor for X the constructor initialises the cell co-ordinates X is spread across 5 cells * * * * * The Numbering of cells is done from bottom-top and left to right (x[0], y[0]) is the position of bottom most cell (x[1], y[1]) is the position of left most cell of the 2nd row from bottom (x[2], y[2]) is the position of the middle cell in the 2nd row from bottom .... */ X::X(int posx, int posy) { x = new int[5]; y = new int[5]; x[0] = x[2] = x[4] =posx; x[1] = posx-1; x[3] = posx+1; y[0] = posy; y[1] = y[2] = y[3] = posy+1; y[4] = posy+2; } /* This function returns the name of type of object i.e it is a X, or L, or U ... */ char X::name() const { return \'X\'; } int X::size() const { return 5; } // Constructor for U U::U(int posx, int posy) { x = new int[7]; y = new int[7]; x[0] = x[3] = x[5] = posx; x[1] = posx+1; x[2] = x[4] = x[6] = posx+2; y[0] = y[1] = y[2] = posy; y[3] = y[4] = posy+1; y[5] = y[6] = posy+2; } char U::name() const { return \'U\'; } int U::size() const { return 7; } void Shape::print() const { //get the size of the object i.e no of cells across which this is spread int sz = size(); // get the type of object i.e O, L, X... char n = name(); cout< > st; int sz1 = t.size(); int sz2 = size(); for(int i = 0 ; i < sz1 ; i++) { st.insert(make_pair(t.x[i], t.y[i])); } for(int i = 0 ; i < sz2 ; i++) { if(st.find(make_pair(x[i], y[i]))!= st.end()) return true; } return false; } /* This function creates a new object of type ch */ Shape * Shape::makeShape(char ch, int posx, int posy) { if(ch == \'O\') return new O(posx, posy); else if(ch == \'I\') return new I(posx, posy); else if(ch == \'L\') return new L(posx, posy); else if(ch == \'S\') return new S(posx, posy); else if.

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How do teams bring value to an organization? How are high performing teams built? When a team is working well together and the project is proceeding as planned what can happen to derail even the high performing teams? Solution Teams are of important value to any organization as they determine not only the success of an organization but also the level with which the organization grow. 1. Teams bring about exchange of ideas which benefit the organization in terms of innovation as well as different ways of approaching difficulties. 2. Teams use the skill sets that come varied personalities to form a comprehensive part of the work force. 3. Teams help an organization to develop good communication and commitment values a factor that strengthens an organization both internally and externally. 4. Teams help organizations realize goals set through combination of effort. High performing teams are build through choosing of a visionary, enthusiastic and committed team leader. The leader then sets to choose a group of equally visionary, skilled and hard working individuals who are united and willing to work towards a common goal a process that entails forging of trust between the leader and the team. The team is then put through various projects in which it is expected to complete with utmost success a process which defines and makes the team better with team to a level of high performance. 1. Calamities such as sickness or death or a team member may derail the high performance. 2. Lack of motivation especially by the team leader may derail the high performance. 3. Laziness may be also stand as a factor especially when the teams assume that the set objectives have been achieved 4. Conflict amongst the team members or the team leader and members may derail the teams\' performance..

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how can we use empricism to figure out if a fact is true? Solution Empiricism is nothing but Knowledge by observation. Nothing is accepted without touching it, Experiencing it or sensing the things directly. So, empiricism helps a person to accept that fact by working on it or experimenting on it. Empiricism demands logic to believe any particular fact to accept. By using these many ways one can believe the fact is true from Empiricism..

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For each step of DNA replication, predict the outcome if: concentration of nitrogenous bases is low primase is inhibited DNA polymerase were inhibited DNA ligase were inhibited Helicase were inhibited AND Identify cellular process(es) that require DNA replication THANKS Solution concentration of nitrogenous bases is low- DNA molecule is made up of nitrogenous bases adenine, guanine, cytosine, and thymine. These nitrogenous bases form the template and the sequence of DNA in replication. They specify the order of these bases in the complementary template strand being formed. primase is inhibited- Enzyme primase is of key importance in DNA replication because it is the only enzyme that can initiate DNA synthesis strand without an initial PNA or CNA primer. Hence primase is essential as it catalysis the synthesis of a primer complementary to ssDNA template aiding in the initiation of DNA replication to take place. DNA polymerase were inhibited- DNA polymerase is an essential enzyme involved in the repair of any damage to DNA molecule and it also plays a vital role in DNA replication; it connects the Okazaki fragments (complementary fragements to the lagging template strand ) by deleting RNA primers and replacing it with DNA. DNA ligase were inhibited- Ligase enzyme is useful in DNA repair (single-strand or double- strand breaks of DNA) and in replication by joining the double DNA strands through phosphodiester bond formation (3\'OH end and 5\'P end). DNA double helicular structure is thus formed through ligation of both strands on replication. Helicase were inhibited- Helicases help in the seperation of nucleic acid strands required during the cellular processes like DNA replication, transcription, repair. This seperation is done by Helicase enzyme by moving through a nucleic acid phosphodiester backbone that exists in DNA, RNA, or DNA-RNA hybrid. cellular process that require DNA replication- In mitosis DNA replication is essential (S stage of interphase) which gets distributed to the resulting daughter cells at the end of cytokinesis. This ensures two similar daughter cells having common genetic material..

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Explain THREE unique characteristics of fungi. Solution Three unique characteristics of fungi are- 1)Fungi are filamentous and not truly multicellular. They are composed of unique thread-like filamentous structures called hyphae. In higher fungi, these hyphae anastomose to form a network called mycelium.The cell wall of fungi is composed of chitin or cellulose. Fungi can build mutual relationships with other organisms in order to get nutritional benefits from such association. For example: The symbiotic relationship between funfi and algae is called lichen. 2) They need preformed food, optimum temperature, pH and moisture to grow properly. In order to avoid dessication, they also require some amount of water to grow. They are resistant to osmotic pressure and hence, can grow in relatively high salt and sugar concentrations. 3)Fungi are heterotrophic and they lack plastids.They collect nutrients from the environment, from dead or living organisms. Fungi are capable of metabolising complex carbohydrates (like lignin)..

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Explain the basic relationship between humans and microorganisms Solution Answer= The basic relationship between humans & microorganisms are as follows The surfaces of human body inside & outside ,for example skin ,mouth & intestines are covered in millions of individual microbes The microbes that do not harm in fact they helps to protect us becoming infected with harmful microbes they are known as normal body flora There are 3 types of symbiotic relationships between humans & bacteria 1] Commensalism = Is a relationship that is beneficial to the bacteria ,but does not help or harmthe host most are reside on epithelial surfaces that come in contact with the external environment commonly found on skin ,respiratory tract & gastrointestinal tract They aquire nutrients & place to live & grow from their host some are pathogenic & cause disease may provide benefit to host 2] Mutuliastic relationship-= Both bacteria & host are beneficial for example there are several kinds of bacteria that live on skin & inside the mouth ,nose,throat & intestines of humans These bacteria received a place to live & feed while keeping other harmful microbes from taking up residence bacteria in digestive system assist in nutrient metabolism ,vitamin production & waste processing 3] Parasitic relatioship= is one in which the bacteria benefit while the host is harmed pathogenic parasites ,which cause disease,do so by resisting the hosts defences & growing at the expense of host These bacteria produces poisonous substances called endotoxins & exotoxins are responsible for the symptoms to occure with an illness Disease causing bacteria are responsible for a number of diseases including meningitis ,pneumonia .tuberculosis& several types of food borne diseases.

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discuss the rationale for the global harmonization of financial reporting and disclosure requirements Solution The focus and rationale of global harmonization of financial reporting and disclosure requirements is for achieving a level of compatibility for the statements. There is less complication for the companies and individuals to present the financial statements and its interpretations. The differences between financial reporting standards are erased with international harmonization of financial reporting. When there is achievement of international harmonization in finial reporting then it benefits countries and improves the access effectively for the financial market. The confidence and investor\'s K owned he is increased. According to Wiley (2000) even though the rationale behind harmonization is smooth preparation and presentation of financial statements; there may be differences based on the factors like taxation and political aspects. It focuses on creation of similar set of procedures with the help of boundary establishment and how they can differ globally. It also benefits accounting standards on national and international levels. The disclosure requirements include the information related to nature and the extent of risks which arises from financial instruments. The importance of financial instutments for the purpose of finial position and performance of entity. It includes financial assets, held to maturity investments, loans and receivables, sale assets etc..

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Describe the need to multitask in BBC (behavior-based control) systems? Solution Behavior-based control employs a set of distributed, in-teracting modules, called behaviors that collectively achieve the desired system-level behavior. To an ex-ternal observer, behaviors are patterns of the robot’s activity emerging from interactions between the robot and its environment. To a programmer, behaviors are control modules that cluster sets of constraints in order to achieve and maintain a goal. Each behavior receives inputs from sensors and/or other behaviors in the system, and provides outputs to the robot’s actuators or to other behaviors. Thus, a behavior-based controller is a structured network of interacting behaviors, with no centralized world representation or focus of control. In-stead, individual behaviors and networks of behaviors maintain any state information and models. The basic principles of behavior-based control can be summarized briefly as follows: • Behaviors are implemented as control laws (some-times similar to those used in control theory), either in software or hardware, as a processing element or as a procedure. • Each behavior can take inputs from the robot’s sen-sors (e.g., proximity sensors, range detectors, contact sensors, camera) and/or from other modules in the system, and send outputs to the robot’s effectors (e.g., wheels, grippers, arm, speech) and/or to other modules. • Many different behaviors may independently re- ceive input from the same sensors and output action commands to the same actuators. • Behaviors are encoded to be relatively simple, and are added to the system incrementally. • Behaviors (or subsets thereof) are executed con- currently, not sequentially, in order to exploit parallelism and speed of computation, as well as the interaction dynamics among behaviors and between behaviors and the environment. The ability to improve performance over time and to reason about the world, in the context of a chang-ing and dynamic environment, is an important area of research in situated robotics. Unlike in classical ma-chine learning, where the goal is typically to optimize performance over a long period of time, in situated learning the aim is to adapt relatively quickly, toward attaining efficiency in the light of uncertainty. Models from biology are often considered, given its proper- ties of learning directly from environmental feedback. Variations and adaptations of machine learning, and in particular reinforcement learning, have been effectively applied to behavior-based robots, which have demon- strated learning to walk [38. , navigate and create topological maps, di-vide tasks, behave socially , and even identify opponents and score goals in robot soc- cer. Methods from artificial life, evolutionary computation/genetic algorithms, fuzzy logic, vision and learning, multi-agent systems, and many other research areas continue to be actively explored and applied to behavior-based robots as their role in ani.

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ble below to calculate the Gross Domestic Product uning the ral Gross Domestic Product? Fully explain your anower. (4 mak) or rea overnment expenditures on goods and service Wages, salaries and supplementary labour income 2,000 reciation nvestment 400 sumption expenditure et exports direct taxes 150 Solution Gross domestic product be expenditure method= consumption expenditure+ government expenditure+ investment+ net export =2200+500+400+(-50) =3050 This is the nominal GDP as well as real GDP because base year price and current year price is not given. Hence real GDP and nominal GDP will be same..

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1.The limbic system: A. matures before the prefrontal cortex B. is another name for the prefrontal cortex C. is responsible for emotional regulation and impulse control D. matures before the amygdala Solution The limbic system is responsible for emotional regulationand impules control. Limbic system is that portion of the brain which deals with the emotions, arousal, learning aw well as formation of memories. It has a complicated structure that lies on the both side of the thalamus just beneath the cerebrum. It includes amygdala, hippocampus, thalamus, hypothalamus, basal ganglia and cingulate gyrus. Amygdala also known as the emotional centre of the brain. Hippocampus helps in the formation of new memories from our past experinces. While thalamus and hypothalamus are governs the changes occuring to the emotional activities. Basal ganglia involved in motor control and habbit learning. And cingulate gyrus manage smell and sight and regulate our behaviour..

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Why is leadership a critical factor in implementing change and quality improvement initiatives? Why is leadership a critical factor in implementing change and quality improvement initiatives? Solution Leadership is required for inspiring and motivating followers to work towards common objectives. The leader employs enthusiasm and charisma to motivate the employees to think out of the box.Leader lays emphasis on the values, morals, ideas and needs of the organization and the followers. Leadership is critical for transformation and change in the firm in a turbulent and challenging environment. By concentrating on innovation and creation rather than just daily planning and execution, the leader ensures that the changes are implemented with minimum resistance. Below is how the leaders can implement change and quality improvement initiatives while overcoming resistance- 1. Communicating the objective of the change and how it would positively affect the productivity of the employees and the organization 2. Developing training and mentoring programs to train the employees to adopt to the new process or system 3. Removing fears from the minds of employees through openhouse discussions etc. 4. Explaining the employees how the change would help in the development of the individuals..

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Why are there bubbles in beer and champagne? Solution Bubbles of gas, typically carbon dioxide are produced from beer and champagne , rising to the surface. Because . yeasts ferment sugars and form carbon dioxide gas during fermentation. In the bottle, where the pressure is high, the carbon dioxide disappears. However, when you open the bottle and lower the pressure, the carbon dioxide escapes in the form of bubbles. In Champagne and other sparkling wines, the bubbles pop, while in beer, the bubbles remain and form the beer\'shead..

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Which ethnic groups were a part of the former Yugoslavia? Croats, Serbs, Bosnian Muslims, Macedonians Janjaweed Israelis, Palestinians, Arabs Hutu & Tutsis Croats, Serbs, Bosnian Muslims, Macedonians Janjaweed Israelis, Palestinians, Arabs Hutu & Tutsis Solution The ethnic group can be defined as a social category based on common culture or nationality. In other words, it can be said that an ethnic group is a category of people who recognize with each other based on similarities for example as a common ancestry, language, society, culture or nation. First Yugoslavia contains people of the Kingdom of Serbs, Croats and Slovenes (1918–29). Hence it can be said that the ethnic groups which were a part of the former Yugoslavia were Croats, Serbs, Bosnian Muslims, Macedonians. Hence option first is the correct answer. Option first; Croats, Serbs, Bosnian Muslims, Macedonians.

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What would the components of the development be in an early learning(1st – 3rd) website environment be? Solution For a website,major components include Front end,images,contents navigation,page structure. For early learning website.As it for the children,content along with effective graphic design is most preferable. Graphic design: Many of the elements described, such as the logo, the navigation menus, the layout, images, etc., fall under the general category of graphic design. But graphic design is more than these. It is the look and feel the website will have as a result of proper use and integration of all these elements. Content management is considered. The website is not recommended to be a static as it should be more creative and changes is necessary. Content management system: This is the ability to update your website without having to directly edit the html. Simple systems create areas on a web page that can be easily changed on a regular basis. Include multiedia and databases. Multi-media. It is for than just text and images. Photo-tours, video-clips, sound-clips all can add to the experience if they are well matched to the type of site and profile of the target audience..

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