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2 years ago

What is the value of x in the equation 3/4 x + 24 = x − 12 ?

Mathematics

1 answer:

marin [14]2 years ago

4 0

Answer:

x = 144

Step-by-step explanation:

3/4x + 24 = x - 12

3/4x - x = -12 - 24

3/4x - 4/4x = -36

-1/4x = -36

x = -36/-1/4

x = 144

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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

8 0

3 years ago

Please help!!!!!!!!!!!!!!!!!!!!!

3241004551 [841]

Answer:

C and D

Step-by-step explanation:

The arc length is calculated as

arc = circumference of circle × fraction of circle

= 2πr × $\frac{60}{360}$

= 2π × 10 × $\frac{1}{6}$ = $\frac{20\pi }{6}$ = $\frac{10\pi }{3}$ cm → C

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The area (A) of a sector is calculated as

A = area of circle × fraction of circle

= πr² × $\frac{60}{360}$

= π × 10² × $\frac{1}{6}$ = $\frac{100\pi }{6}$ = $\frac{50\pi }{3}$ cm² → D

6 0

2 years ago

What is the area of this figure? Enter your answer in the box. m² A parallelogram with a right triangle created inside it with a

igomit [66]

Answer:

the answer is 81 m if i am right hope this help

6 0

3 years ago

Read 2 more answers

Write three different complex fractions that simplify to 1/4

madam [21]

There's my answer
25/100
27/108
31/124
these three equal 1/4 or 1:4
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2 years ago

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nekit [7.7K]

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3 years ago