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dianasr424
27.12.2020 •
Physics
An inner city revitalization zone is a rectangle that is twice as long as it is wide. The width of the region is growing at a rate of 24 m per year at a time when the region is 300 m wide. How fast is the area changing at that point in time
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Ответ:
28,800 m²/yr
Explanation:
This rectangle has dimensions such that:
width = wlength = 2wWe are given
and want to find
when w = 300 m.
The area of a rectangle is denoted by Area = length * width.
Let's multiply the width and length (with respect to w) together to have an area equation in terms of w:
Differentiate this equation with respect to time t.
Let's plug known values into the equation:
Simplify this equation.
The area is changing at a rate of 28,800 m²/yr at this point in time.
Ответ:
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Geometry
Area of a Rectangle: A = lwAlgebra I
Exponential Property:Calculus
Derivatives
Differentiating with respect to time
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Explanation:
Step 1: Define
Area is A = lw
2w = l
w = 300 m
Step 2: Rewrite Equation
Substitute in l: A = (2w)wMultiply: A = 2w²Step 3: Differentiate
Differentiate the new area formula with respect to time.
Differentiate [Basic Power Rule]:Step 4: Find Rate
Use defined variables
Substitute:Ответ:
24
Explanation: