Area and Cosine Laws

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Questions and Answers

Which action by the Bank of Canada best demonstrates its pursuit of price stability?

Adjusting the overnight interest rate to manage inflation. (correct)
Collaborating with international financial institutions to develop common policy frameworks.
Intervening in foreign exchange markets to stabilize the Canadian dollar.
Providing loans to small businesses during economic downturns.

What is the main goal of the Canada Small Business Financing Program?

To make it easier for small businesses to get loans from financial institutions (correct)
To provide grants to innovative startups in the technology sector
To offer tax incentives for corporations investing in research and development
To fund large-scale infrastructure projects across Canada

How does the Bank of Canada foster financial system stability?

By providing financial advice to individual consumers and businesses.
By directly regulating the lending practices of Canadian banks.
By acting as a lender of last resort to financial institutions facing liquidity issues. (correct)
By guaranteeing all deposits held in Canadian financial institutions.

Which statement accurately describes the role of Crown corporations in Canada's economic landscape?

Crown corporations focus on sectors of the economy that may not be adequately served by private enterprise. (B) Signup and view all the answers

In what way does EDC (Export Development Canada) support Canadian businesses?

By providing insurance and financial services to reduce the risks of exporting. (B) Signup and view all the answers

Which function aligns with the Bank of Canada's responsibility for maintaining the value of money?

Controlling inflation through monetary policy adjustments. (C) Signup and view all the answers

How does the Canada Small Business Financing Program help new businesses?

By facilitating access to loans for assets like equipment and leasehold improvements. (D) Signup and view all the answers

What role does the Bank of Canada play in the payments system?

It operates the country's main clearing and settlement system. (D) Signup and view all the answers

Which of the following is a typical activity of a Crown corporation like Canada Post?

Providing essential services to Canadians across the country. (A) Signup and view all the answers

How does Export Development Canada (EDC) support Canadian exports?

By offering risk mitigation services to Canadian exporters. (C) Signup and view all the answers

Why is maintaining financial system stability a key objective of the Bank of Canada?

To prevent financial crises and protect the economy. (A) Signup and view all the answers

How does the Canada Small Business Financing Program mitigate risk for lenders?

By offering a government guarantee on a portion of the loan (D) Signup and view all the answers

What is the function of Lynx, which is operated by the Bank of Canada?

A high-value payment system for large transactions (D) Signup and view all the answers

What is a characteristic feature of Crown corporations in the Canadian economy?

They often have a mandate to provide public services that are not commercially viable. (B) Signup and view all the answers

How does the Export Development Canada (EDC) assist Canadian companies in expanding their international sales?

By providing insurance, financing, and guarantee services to mitigate risks associated with exporting (B) Signup and view all the answers

Which of the following best describes the Bank of Canada's approach to economic forecasting?

Using a range of models and indicators to inform policy decisions. (D) Signup and view all the answers

Why might a small business choose to seek financing through the Canada Small Business Financing Program rather than a conventional loan?

The CSBFP may approve loans to businesses that might not qualify for conventional financing. (A) Signup and view all the answers

How does Lynx contribute to the overall efficiency of Canada's financial system?

By providing same-day settlement for large-value payments. (C) Signup and view all the answers

What is a key difference between Crown corporations and private sector companies?

Crown corporations are ultimately accountable to the government and the public. (A) Signup and view all the answers

How does EDC's provision of political risk insurance support Canadian companies?

By protecting against losses due to political instability or conflict in foreign markets. (D) Signup and view all the answers

Flashcards

Canada First Objective

Focuses on Canadian issues and promotes Canadian content for international distribution.

Canada First (Clarity)

Ensures accountability to Canadian laws and acts as an advocate for stronger contributions.

As-Is

Allows easier access to the market with statutory support and encourages content creation, benefiting audiences and storytellers.

More Strings

Requires more domestic investment, which could potentially reduce funding for a U.S. distributor to invest in Canadian content.

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Study Notes

In an obtuse triangle, an altitude from a vertex can lie outside the triangle.
For example, in obtuse triangle ABC, the altitude from B meets side AC at point D, which is outside the triangle.
In triangle BDA, sin(π - A) = BD/AB, where BD is the altitude and AB is a side of the triangle.
Since sin(π - A) = sin(A), the length of the altitude BD is given by BD = ABsin(A).
The area of triangle ABC is (1/2) * AC * BD = (1/2) * AC * AB * sin(A).

Area of a Triangle

The area of a triangle is half the product of two sides and the sine of the included angle.
Area(triangle ABC) = (1/2)absin(C) = (1/2)bcsin(A) = (1/2)ca*sin(B).
This formula is applicable to both obtuse and acute triangles.

Law of Cosines

In any triangle ABC:
a² = b² + c² - 2bc*cos(A)
b² = c² + a² - 2ca*cos(B)
c² = a² + b² - 2ab*cos(C)

Proof of Law of Cosines

Area(triangle ABC) = (1/2)absin(C) = (1/2)bcsin(A) = (1/2)ca*sin(B)
Multiplying by 2abc: a²b²sin(C) = b²c²sin(A) = c²a²sin(B)
Dividing by a²b²c² : sin(A)/a = sin(B)/b = sin(C)/c

Example Application of Law of Cosines

Given triangle ABC where a = 5, b = 6, and angle C = 60°.
To find side c, the Law of Cosines is used: c² = a² + b² - 2ab*cos(C).
Substituting the given values: c² = 5² + 6² - 2(5)(6)cos(60°) = 25 + 36 - 30 = 31.
c = √31.

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