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4 years ago

casey is six time as old as Ralph, In two years, she will be four time as old as Ralph. How old is each of them now?

1 answer:

7 0

Statement 1: Casey is 6 times as old as Ralph gives

C = 6R

where C and R represent Casey and Ralph’s current ages respectively.
Statement 2: In 2 years, Casey will be four times as old as Ralph gives

C + 2 = 4 (R + 2)

Expanding the brackets gives

C + 2 = 4R + 8

Substituting in C from the first equation gives

6R + 2 = 4R + 8

Which can be rearranged as

2R = 6

Implying R = 3 and C = 6R = 18

Therefore, Ralph is 3; Casey is 18

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3 years ago

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3 years ago

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puteri [66]

Answer:

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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

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Step 3: Solve

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[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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