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2 years ago

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A farmer has a feed trough in the shape of rectangular prism with a height of 40 cm and a base that is 30 cm wide by 200 cm long

. During the course of one week, the trough needed to be filled 2 times. How many cubic centimeters of feed were needed during the week?

1 answer:

inysia [295]2 years ago

5 0

Answer:

Step-by-step explanation:

You're welcome :)

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The length of a rectangle is increasing at a rate of 4 meters per day and the width is increasing at a rate of 1 meter per day.

puteri [66]

Answer:

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General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right<u> </u>

<u>Geometry</u>

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<u>Calculus</u>

Derivatives

Derivative Notation

Implicit Differentiation

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Derivative Rule [Product Rule]: $\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Step-by-step explanation:

<u>Step 1: Define</u>

<u /> $\displaystyle l = 10 \ meters$ <u />

<u /> $\displaystyle \frac{dl}{dt} = 4 \ m/day$ <u />

<u /> $\displaystyle w = 23 \ meters$ <u />

<u /> $\displaystyle \frac{dw}{dt} = 1 \ m/day$ <u />

<u />

<u>Step 2: Differentiate</u>

[Area of Rectangle] Product Rule: $\displaystyle \frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}$

<u>Step 3: Solve</u>

[Rate] Substitute in variables [Derivative]: $\displaystyle \frac{dA}{dt} = (10 \ m)(1 \ m/day) + (23 \ m)(4 \ m/day)$
[Rate] Multiply: $\displaystyle \frac{dA}{dt} = 10 \ m^2/day + 92 \ m^2/day$
[Rate] Add: $\displaystyle \frac{dA}{dt} = 102 \ m^2/day$

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Implicit Differentiation

Book: College Calculus 10e

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