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Answers toStudent Questions

Physics

What is the relationship between frequency and period?

Oscillations are repeating motions that occur at regular time intervals. The time for one complete cycle of the motion before it repeats is called the period. For example, the period of the Earth orbiting the Sun is approximately 365 days, and the period of the Earth’s rotation around its axis is one day. If a person is playing jump rope, the period of the rope’s turns could be approximately two seconds, or for a spinning ceiling fan, it might take just half a second for a complete cycle. The SI symbol for period is $\textit{T}$. The examples here show that period is a time measurement per cycle. The concept of a period can also be written as an equation: $\hspace{3em}$ $\ce{period}=\dfrac{\ce{time}}{\ce{cycle}}$ Frequency is a value that tells us the number of cycles of a repeating motion that occur in a given amount of time. The symbol for frequency is $f$. If we say that a person has a heart rate of 55 beats per minute, we are stating the frequency of their heartbeat. Vinyl records used for playing music typically rotate at 33 rpm or revolutions per minute, which is also a measure of frequency. We can say that the frequency of Earth’s rotation is one rotation per day. Notice that all of the examples above involve a number of cycles per unit time. The definition of frequency can also be written as an equation: $\hspace{3em}$ $\ce{frequency}=\dfrac{\ce{cycles}}{\ce{time}}$ The relationship between frequency and period is that they are inverses of one another. This relationship can be expressed through the equations: $\hspace{3em}$ $f=\dfrac{1}{T} \hspace{3em}$and $ \hspace{3em}T=\dfrac{1}{f}$ We can show how this equation connects the definitions of period and frequency from the first two paragraphs. $\hspace{3em}$ $\ce{period}=\dfrac{\ce{time}}{\ce{cycle}}$ $\hspace{3em}$ $\ce{frequency}=\dfrac{1}{\ce{period}}=\dfrac{1}{\frac{\ce{time}}{\ce{cycle}}}=\dfrac{\ce{cycle}}{\ce{time}}$ Note that in IB Standard Level Physics and IB Higher Level Physics, period is normally given in the units of seconds (s), and frequency has an SI unit of hertz (Hz). Through the relationship between frequency and period, we can explore the relationship between these two units. $\hspace{3em}$ $f=\dfrac{1}{T} \hspace{3em}$therefore$\hspace{3em}\ce{Hz}=\dfrac{1}{\ce{s}} =\ce{s}^{-1}$ As an example, consider an object that oscillates with a frequency of 5 Hz. If we want to find the period, we can apply the equation $\hspace{3em}$ $T=\dfrac{1}{f}=\dfrac{1}{5\ \ce{Hz}}=$ 0.2 s Therefore, it takes 0.2 s for the object to complete one oscillation. Waves are generated by an oscillating source. The source causes a disturbance in the medium, resulting in the particles in that medium undergoing oscillations. The frequency of a wave is equal to the frequency of these individual oscillations of its particles. The period of the wave can be found from the same inverse relationship as before, $\hspace{3em}$ $T=\dfrac{1}{f}$

Biology

What is the correct general equation for cellular respiration?

The general equation for aerobic cellular respiration, the process by which cells convert glucose and oxygen into ATP, is: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + ATP This equation shows that one molecule of glucose (C₆H₁₂O₆) reacts with six molecules of oxygen (O₂) to produce six molecules of carbon dioxide (CO₂), six molecules of water (H₂O), and energy in the form of ATP (adenosine triphosphate). ATP is the primary energy currency of the cell; it stores and transfers energy for nearly all cellular processes. When ATP is broken down into ADP (adenosine diphosphate) and inorganic phosphate (Pi), energy is released to power activities such as muscle contraction, active transport across membranes, protein synthesis, and cell division. Cellular respiration occurs in several stages: glycolysis (in the cytoplasm), the link reaction and Krebs cycle (in the mitochondrial matrix), and the electron transport chain (across the inner mitochondrial membrane). Oxygen is essential in the final stage, acting as the terminal electron acceptor in the electron transport chain, which enables the production of most of the ATP during respiration. In total, aerobic respiration can yield up to 36 to 38 ATP molecules per glucose molecule, making it far more efficient than anaerobic pathways, which produce only 2 ATP per glucose molecule. This efficiency makes aerobic respiration vital for energy-demanding organisms like animals, plants, and many fungi.

Business Management

What is Steeple Analysis, and how can it be used?

A STEEPLE is a Business Management planning tool used to examine factors in the external business environment that affect its operations. STEEPLE includes seven categories of factors that impact business operations and decision-making. STEEPLE stands for: - **S**ocial - **T**echnological - **E**nvironmental - **E**thical - **P**olitical - **L**egal - **E**conomic Managers use this tool to examine the external environment and its impacts on the business. The external environment can create opportunities or threats, and it is, therefore, important for managers to understand changes in the external environment to determine how they can be used to a business's advantage or how to minimise threats. Businesses cannot control changes in the external environment, but managers must monitor them to create strategies and plan ahead so they can react appropriately. Social factors in a STEEPLE analysis relate to people, their values, lifestyles, and how these influence economic activity. They include demographics, cultural norms, religious beliefs, and attitudes towards ethics and discrimination. Examples include delayed parenthood, an ageing population, migration trends, and rising retirement ages, which affect workforce availability, recruitment, spending patterns, and consumer behaviour. Technological factors in a STEEPLE relate to the impact of innovation, automation and technological advancement on the business environment. The technological environment in business refers to the constant changes in machinery, equipment, and digital tools that influence operations, efficiency, and growth. Advances such as personal computers, smartphones, automation, 3D printing, and social media have created opportunities (e-commerce, digital marketing, new jobs like app developers) and challenges (job losses, barriers to entry, and risks like hacking or system failures). Technology shapes competitiveness by driving innovation and introducing potential risks and disruptions. Environmental factors in a STEEPLE analysis focus on the ecological impact of business activity and the growing demand for sustainable practices. Businesses face pressure from stakeholders to adopt green technologies, renewable energy, and eco-friendly designs as concerns about resource depletion and climate change rise. These factors directly affect operations, with stricter government policies and adverse weather events (such as floods, droughts, or storms) creating organisational risks and opportunities. In a STEEPLE analysis, Ethical factors focus on the moral principles and values that guide business behaviour. They go beyond just following laws and look at whether a company is acting in a way that is fair, responsible, and socially acceptable in the eyes of stakeholders. Business ethics is about doing what is proper and accountable as part of corporate social responsibility (CSR). Examples include engaging in fair trade with suppliers, treating employees fairly, using honest marketing practices, respecting intellectual property rights, maintaining transparent accounting procedures, and adopting sustainable operations that protect the environment. In a STEEPLE analysis, Political factors refer to how government actions, policies, and political stability affect businesses and their decision-making. These factors shape the overall business environment, creating both opportunities and challenges. Political decisions shape confidence, competitiveness, and market conditions in various ways. For instance, the level of political stability in a country strongly affects both business and consumer confidence—prolonged instability or conflict can deter foreign direct investment. Legal factors in a STEEPLE analysis refer to the laws and regulations influencing how businesses operate and consumers behave. Legislation can affect business formation, quality standards, consumer protection, employment rights, intellectual property, environmental compliance, and restrictions on harmful products like alcohol and tobacco. For example, lawsuits against fast-food companies over misleading nutrition information show how legal standards can directly affect corporate practices, reputation, and profitability. Economic factors in a STEEPLE analysis relate to the conditions determining an economy's overall performance, often measured by GDP and explained through the business cycle. The cycle includes phases of boom (rising activity, jobs, and prices), peak (unsustainable highs), recession (decline in output and confidence), slump or trough (lowest point with high unemployment), and recovery (renewed growth and employment). Consumer and business confidence, production costs, exchange rates, interest rates, and inflation influence fluctuations in activity. These factors affect competitiveness, spending, and investment, shaping the external environment businesses operate in. By systematically analysing these seven factors, managers can better anticipate changes, adapt strategies, and position their business to maximise opportunities while minimising potential risks in an ever-changing external environment.

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