How do I solve this???

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

8 0

3 years ago

Make like units, and then add. * 1 1/2+2/5

aksik [14]

Answer:

1 5/10+4/10= 1 9/10

Step-by-step explanation:

the answer is 1 and 9/10ths

3 0

3 years ago

Hii i’ll give brainliest please help thanks :)

Juliette [100K]

Answer:

Step-by-step explanation:

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest.

Hope this help

6 0

3 years ago

Write the equation for the vertical line that contains point E(-7,7)

Levart [38]

Vertical line are represented by x = a number....that number being the x value in ur set of points

so ur equation is : x = -7

5 0

4 years ago

Solve for g: 4g/14 - 3/7 - g/14 = 3/14

Luden [163]

Answer:
g = 3

Explanation:
To solve for g, we will need to isolate the g on one side of the equation.
This can be done as follows:
 $\frac{4g}{14} - \frac{3}{7} - \frac{g}{14} = \frac{3}{14}$ 

1- multiply all terms by 14 to get rid of the fraction:
4g - 6 - g = 3

2- Combine like terms:
4g - g = 3 + 6
3g = 9

3- Isolate the g:
 $\frac{3g}{3} = \frac{9}{3}$

g = 3

Hope this helps :)

8 0

3 years ago

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