Explain how recycling practices can lead to environmental sustainability.
Recycling practices can lead to environmental sustainability in several ways:
1. Reducing the amount of waste in landfills: By recycling materials such as paper, plastics, glass, and metals, there is less waste going to landfills. This helps to reduce the amount of greenhouse gas emissions and other harmful environmental pollutants that are generated by landfills.
2. Conserving natural resources: Recycling conserves natural resources by reducing the need to extract new materials from the earth. For example, recycling aluminum cans can conserve up to 95% of the energy needed to produce new cans.
3. Reducing energy consumption: Recycling materials rather than producing new materials from scratch uses less energy. This is because recycling often requires less processing and transportation than producing new materials.
4. Preserving wildlife and habitats: By reducing the amount of waste going to landfills, recycling helps to preserve habitats and wildlife. It also reduces the amount of pollution in the air and water, which can have a positive impact on wildlife health.
Overall, recycling practices help to create a more sustainable environment by reducing waste, conserving natural resources, and reducing energy consumption and pollution levels.
The water level varies from 10 inches at low tide to 40 inches at high tide. Low tide occurs at 9:15 a.m. and high tide occurs at 3:30 p.m. What is a cosine function that models the variation in inches above and below the water level as a function of time in hours since 9:15 a.m.?
EXPLAIN SHOW WORK
We can use a cosine function to model the variation in inches above and below the water level as a function of time since 9:15 a.m. The basic form of a cosine function is:
y = A cos(Bx + C) + D
where:
- A is the amplitude of the function (half the distance between the highest and lowest points),
- B is the frequency of the function (the number of full cycles in 2π units of the input variable),
- C is the phase shift of the function (the horizontal displacement of the wave),
- D is the vertical shift of the function (the midpoint or mean value).
In this case, we know that the water level varies from 10 inches (lowest point or D) to 40 inches (highest point or D + A) and completes one cycle (from low tide to high tide and back to low tide) in 6 hours (from 9:15 a.m. to 3:15 p.m.).
So we can set up the cosine function as follows:
y = 15 cos(π/3 x + π/2) + 25
where:
- A = 15 (half the distance between 40 and 10)
- B = π/3 (one cycle in 6 hours or 2π/6 = π/3 radians per hour)
- C = π/2 (the function reaches its maximum value halfway between the low tide and high tide times)
- D = 25 (the midpoint or mean value between 10 and 40)
To see why the phase shift is π/2, we can think of it this way: at 9:15 a.m., the water level is at its lowest point (10 inches), so we want the cosine function to start at the low point on the horizontal axis. The standard cosine function starts at its maximum point (at x = 0), so we need to shift it by π/2 radians to the right to start at the low point. This means that the maximum point of the function will be halfway between the low tide (9:15 a.m.) and high tide (3:30 p.m.) times, which is at 12:22:30 p.m. (halfway between 9:15 a.m. and 3:30 p.m.).
So the cosine function that models the variation in inches above and below the water level as a function of time in hours since 9:15 a.m. is:
y = 15 cos(π/3 x + π/2) + 25
where x is the time in hours since 9:15 a.m. For example, at 10:30 a.m. (1.25 hours since 9:15 a.m.), the water level would be:
y = 15 cos(π/3 x + π/2) + 25
y = 15 cos(π/3 (1.25) + π/2) + 25
y ≈ 27.5 inches (above the 10-inch low tide level)
Recycling practices play a crucial role in promoting environmental sustainability in several ways:
1. Conservation of resources: Recycling reduces the need for extracting and processing raw materials, such as trees, minerals, and oil. By reusing materials, recycling helps conserve natural resources, which are often limited or non-renewable. This preservation of resources helps maintain ecological balance and supports long-term sustainability.
2. Energy conservation: The process of manufacturing products from recycled materials usually requires less energy compared to producing them from scratch. For example, recycling aluminum cans requires only about 5% of the energy needed to produce new metal. By conserving energy in this way, recycling reduces greenhouse gas emissions from power plants and reduces dependence on fossil fuels, thus helping to combat climate change.
3. Waste reduction: Recycling diverts waste from landfills. Landfills are not only unsightly but also emit harmful greenhouse gases, particularly methane, which contributes to global warming. Moreover, landfills can contaminate soil and water, leading to ecological damage. By reducing the amount of waste sent to landfills, recycling mitigates these negative impacts on the environment.
4. Decreased pollution and emissions: Recycling reduces pollution associated with extracting, refining, and processing raw materials. These industrial processes cause air and water pollution, which negatively affect ecosystems, human health, and biodiversity. Recycling reduces the demand for such processes, thereby decreasing pollution and emissions of harmful substances.
5. Creation of green jobs: Recycling and the sustainable waste management sector create jobs that contribute to economic growth while minimizing environmental impact. From collection and sorting to processing and manufacturing new products, recycling operations require human labor. These job opportunities contribute to local economies and promote sustainable practices, fostering long-term environmental and economic balance.
By implementing and supporting recycling practices, individuals, communities, and industries can collectively contribute to environmental sustainability by conserving resources, conserving energy, reducing waste, decreasing pollution and emissions, and creating green jobs.