If f’(x) = 3 x^ 2 + 2x and f(2) = 3, then f(1) =

Answers

Answer 1

We can solve this problem using integration and the fundamental theorem of calculus. First, let's integrate f’(x):

∫f’(x) dx = ∫(3x^2 + 2x) dx
f(x) = x^3 + x^2 + C

To find the value of C, we can use the given condition f(2) = 3:

f(2) = 2^3 + 2^2 + C = 8 + 4 + C = 12 + C = 3
C = -9

Now we have the complete expression for f(x):

f(x) = x^3 + x^2 - 9

Finally, we can find f(1) by substituting x=1:

f(1) = 1^3 + 1^2 - 9 = 1 + 1 - 9 = -7

Therefore, f(1) = -7.

Related Questions

TWO PARTS:
1. of the MSW generated in 2017, 61 million tonnes was recycled and 24 million tonnes was composted. what percentage of the total MSW generated was either recycled or composed?

2. a further 31 million tonnes of MSW was combusted for energy recovery. what percentage of MSW actually went to landfill in 2017?

Answers

1. The MSW generated in 2017, 61 million tons was recycled and 24 million tons was composted and approximately 22.41% of the MSW generated in 2017 went to landfill.

2.The 31 million tons of MSW was combusted for energy recovery and approximately 22.41% of the MSW generated in 2017 went to landfill.

To solve these questions, we need to calculate the total amount of Municipal Solid Waste (MSW) generated in 2017 and then determine the percentages of recycling, composting, energy recovery, and landfill disposal.

1. To calculate the percentage of MSW that was either recycled or composted:

Total MSW generated = 61 million tonnes (recycled) + 24 million tonnes (composted)

Total MSW generated = 85 million tonnes

Percentage of MSW recycled or composted:

((61 million tonnes + 24 million tonnes) / 85 million tonnes) * 100 = 85.88%

Therefore, approximately 85.88% of the total MSW generated was either recycled or composted.

2. To calculate the percentage of MSW that went to landfill in 2017:

Total MSW disposed = 85 million tonnes (recycled and composted) + 31 million tonnes (combusted for energy recovery)

Total MSW disposed = 116 million tonnes

Percentage of MSW sent to landfill:

((116 million tonnes - (61 million tonnes + 24 million tonnes + 31 million tonnes)) / 116 million tonnes) * 100 = 22.41%

Therefore, approximately 22.41% of the MSW generated in 2017 went to landfill.

It's worth noting that the calculations assume that all the recycled, composted, and combusted waste is diverted from landfill disposal.

However, in practice, there might be cases where a small portion of the recycled or composted waste still ends up in landfills. The percentages provided give a general understanding of the waste management practices but might not account for all nuances in waste disposal.

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Activity 2: Gathering information
2.1. Identify 3 current human rights violations to living in a safe and healthy way
in South Africa.
(3x1=3)

Answers

Three current human rights violations to living safely and healthily in South Africa are:

Gender-Based Violence (GBV): South Africa faces a pervasive problem of gender-based violence, including domestic violence, sexual assault, and femicide. Women and girls are particularly vulnerable to these violations, which have severe physical, psychological, and social consequences. GBV undermines the right to live free from violence and poses a significant barrier to a safe and healthy life for many in South Africa.

Access to Healthcare: Despite constitutional guarantees of the right to healthcare, South Africa faces challenges in ensuring equal and adequate access to healthcare services. Limited resources, unequal distribution of healthcare facilities, and socioeconomic disparities contribute to barriers to accessing quality healthcare, particularly for marginalized communities. The lack of accessible healthcare undermines the right to health and hinders individuals' ability to live a safe and healthy life.

Lack of Adequate Housing: Many South Africans face inadequate housing conditions, including informal settlements, shacks, and overcrowded living spaces. Lack of access to adequate housing violates the right to live in a safe and healthy environment. Inadequate housing exacerbates health risks, such as diseases, poor sanitation, and limited access to clean water and basic amenities. This contributes to the cycle of poverty and compromises individuals' well-being.

These violations highlight the need for concerted efforts by the South African government, civil society organizations, and international partners to address gender-based violence, improve healthcare accessibility, and ensure adequate housing for all citizens. Upholding these human rights is crucial for creating a society where individuals can live in safety and enjoy their health.

Assume the United States economy is in short-run macroeconomic equilibrium at an output level greater than potential output.

Answers

(a) An increase in government spending by $100 billion will shift the AD curve to the right.

(b) Household savings will decrease by $400 billion in the short run.

(d) An increase in the interest rate in the short run leads to a decrease in the prices of previously issued bonds

(e) An increase in the inflation rate in the United States relative to the inflation rate in the European Union will lead to a decrease in the demand for dollars in the foreign exchange market.

(f) If the Federal Reserve attempts to keep the value of the dollar constant in the foreign exchange market, it should sell dollars and buy euros.

How to calculate the value

The maximum change in real output can be calculated using the formula:

∆Y = ∆Spending × (1 / (1 - MPC))

where MPC is the marginal propensity to consume.

∆Y = $100 billion × (1 / (1 - 0.8)) = $500 billion

The maximum change in household savings can be calculated as follows:

∆S = -MPC × ∆Y

∆S = -0.8 × $500 billion = -$400 billion

If the Federal Reserve attempts to keep the value of the dollar constant in the foreign exchange market, it should sell dollars and buy euros. This is because the dollar has depreciated in the foreign exchange market, and selling dollars will increase the demand for dollars and raise its value.

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