The Altitude of a Triangle Is Increasing at a Rate $1 \mathrm {~cm} / \mathrm { min }$

question 113

Short Answer

The altitude of a triangle is increasing at a rate of $1 \mathrm {~cm} / \mathrm { min }$ while the area of the triangle is increasing at a rate of $2 \mathrm {~cm} ^ { 2 } / \mathrm { min }$ . At what rate is the base of the triangle changing when the altitude is $10 \mathrm {~cm}$ and the area is $100 \mathrm {~cm} ^ { 2 }$ .

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Definitions:

Antitrust Authorities

Government or regulatory entities responsible for enforcing laws designed to promote competition and prevent monopolistic practices within markets.

Natural Monopolies

Market structures where a single firm can supply a good or service to an entire market at a lower cost than two or more firms, typically due to high fixed costs.

Creative Accounting

The manipulation of financial records and reports to present a more favorable view of a company's business activities.

Economic Substitution

The act of replacing one product with another due to changes in price, preferences, or other factors, reflecting the flexibility of consumption choices.