11)

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 ra

lukranit [14]

Answer:

$\frac{dA}{dt} = 28800 \ m^2/year$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Geometry

Area of a Rectangle: A = lw

Algebra I

Exponential Property: $w^n \cdot w^m = w^{n + m}$

Calculus

Derivatives

Differentiating with respect to time

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Explanation:

Step 1: Define

Area is A = lw

2w = l

w = 300 m

$\frac{dw}{dt} = 24 \ m/year$

Step 2: Rewrite Equation

Substitute in l: A = (2w)w
Multiply: A = 2w²

Step 3: Differentiate

Differentiate the new area formula with respect to time.

Differentiate [Basic Power Rule]: $\frac{dA}{dt} = 2 \cdot 2w^{2-1}\frac{dw}{dt}$
Simplify: $\frac{dA}{dt} = 4w\frac{dw}{dt}$

Step 4: Find Rate

Use defined variables

Substitute: $\frac{dA}{dt} = 4(300 \ m)(24 \ m/year)$
Multiply: $\frac{dA}{dt} = (1200 \ m)(24 \ m/year)$
Multiply: $\frac{dA}{dt} = 28800 \ m^2/year$

3 0

3 years ago

Read 2 more answers

A 1060-kg car moving west at 16 m/s collides with and locks onto a 1830-kg stationary car. determine the velocity of the cars ju

iren [92.7K]

M1U1 + M2V2 = (M1+M2)V, where M1 is the mass of the moving car, M2 is the mass of the stationary car, U1 is the initial velocity, and V is the common velocity after collision.
therefore;
(1060× 16) + (1830 ×0) = (1060 +1830) V
16960 = 2890 V
V = 5.869 m/s
The velocity of the cars after collision will be 5.689 m/s

5 0

3 years ago

Which characteristics describe a point charge?

wolverine [178]

Answer:

C

Explanation:

becauase i just tooke the test

6 0

3 years ago

How much energy is contained in the mass of a 60-kilogram person?

Feliz [49]

The energy in the body depends on the work and the type of food the person had in a 60 kg person / 40 kg person.
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Hope that helped!

5 0

3 years ago

A) Millions of years of rain and wind

barxatty [35]

Answer:

B. Millions of years of high pressure and temperature.

Millions of years of high pressure and temperature the ancient forests turn into fossil fuels.

Explanation:

Fossil fuels were formed from the dead remains of living organisms millions of years ago. They were formed under high pressure and high temperature.

Coal : about 300 million years ago the earth had this forest in low lying wetland areas. Due to natural processes like flooding, these forest god buried under the soil. As more soil deposited over them, they were compressed. Under high pressure and high temperature, dead plants got slowly converted into coal.
Petroleum : Petroleum was formed from organisms living in the sea. As these organisms died, their bodies settled at the bottom of the sea and got covered with layers of soil and clay. Over millions of years, absence of air, high pressure and high temperature transformed the dead organisms into Petroleum.

Coal, Petroleum and natural gas are fossil fuels.

6 0

2 years ago