Given the following question:

$4\frac{5}{8} +r=9$

Rewrite the expression to find the value of r:

$9-4\frac{5}{8}$

Subtract by finding the common denominator:
$9-4\frac{5}{8}$
$9=\frac{9}{1}$
$4\frac{5}{8} =8\times4=32+5=37=\frac{37}{8}$
$\frac{9}{1} -\frac{37}{8}$
$\frac{9}{1} \times8=\frac{72}{8}$
$\frac{37}{8} \times1=\frac{37}{8}$
$\frac{72}{8} -\frac{37}{8}$
$72-37=35$
$=\frac{35}{8}$
$\frac{35}{8} =35\div8=4\frac{3}{8}$
$r=4\frac{3}{8}$
$4\frac{5}{8} +4\frac{3}{8} =9$

Hope this helps.

4 0

2 years ago

Let p(x) = 7x + 5 and r(x) = x - 1. Find and evaluate (r x p) (5)

quester [9]

Answer: 39

Step-by-step explanation:

Given

P(x)=7x+5

r(x)=x-1

r(p(x))=7x+5-1=7x+4

so, r(p(5))

$\Rightarrow r(p(5))=7\times 5+4=35+4=39$

8 0

3 years ago

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