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3 years ago

Simplify?6(2 - 7v) - 4(-6v + 7)

Mathematics

1 answer:

iragen [17]3 years ago

4 0

Answer:

-18v - 16

Step-by-step explanation:

6(2 - 7v) - 4(-6v + 7)

= 6×2 - 6×7v - 4×(-6v) -4×7

= 12 - 42v + 24v - 28

= -18v - 16

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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:

$\displaystyle \frac{dA}{dt} = 102 \ m^2/day$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Geometry

Area of a Rectangle: A = lw

l is length
w is width

Calculus

Derivatives

Derivative Notation

Implicit Differentiation

Differentiation with respect to time

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

Step-by-step explanation:

Step 1: Define

$\displaystyle l = 10 \ meters$

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

$\displaystyle w = 23 \ meters$

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

Step 2: Differentiate

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

Step 3: Solve

[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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4 years ago

Write 0.3 as a fraction in simplest form.

s344n2d4d5 [400]

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4 years ago

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PtichkaEL [24]

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4 years ago

Read 2 more answers

Work out the difference between 5/9and4/9

tatiyna

Answer:

1/9

Step-by-step explanation:

Subtract them

5/9-4/9=1/9 Answer

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3 years ago

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Mashutka [201]

Answer:

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3 years ago

Simplify?6(2 - 7v) - 4(-6v + 7)​

Simplify?6(2 - 7v) - 4(-6v + 7)