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3 years ago

There are 48 female performers in a dance recital. The ratio of men to women is 5:6. How many men are in the dance recital?

Mathematics

1 answer:

Rainbow [258]3 years ago

5 0

Since you said men to women, there are 5 men in the dance recital and 6 women in the dance recital.

1. Look how the problem states. Ex: Ratio of men to women.

2. Look at the ratio. 5:48.

3. We know that there are 48 female performers at the dance recital.

So, there are 5 men at the dance recital.

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The problem is attached, thanks.

NeX [460]

Answer:

$\displaystyle \frac{dy}{dx} \bigg| \limit_{(1, 4)} = 2$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Coordinates (x, y)
Exponential Rule [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$
Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Implicit Differentiation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

$\displaystyle \sqrt{x} - \sqrt{y} = -1$

Point (1, 4)

Step 2: Differentiate

[Function] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle x^{\frac{1}{2}} - y^{\frac{1}{2}} = -1$
[Implicit Differentiation] Basic Power Rule: $\displaystyle \frac{1}{2}x^{\frac{1}{2} - 1} - \frac{1}{2}y^{\frac{1}{2} - 1}\frac{dy}{dx} = 0$
[Implicit Differentiation] Simplify Exponents: $\displaystyle \frac{1}{2}x^{\frac{-1}{2}} - \frac{1}{2}y^{\frac{-1}{2}}\frac{dy}{dx} = 0$
[Implicit Differentiation] Rewrite [Exponential Rule - Rewrite]: $\displaystyle \frac{1}{2x^{\frac{1}{2}}} - \frac{1}{2y^{\frac{1}{2}}}\frac{dy}{dx} = 0$
[Implicit Differentiation] Isolate y terms: $\displaystyle -\frac{1}{2y^{\frac{1}{2}}}\frac{dy}{dx} = -\frac{1}{2x^{\frac{1}{2}}}$
[Implicit Differentiation] Isolate $\displaystyle \frac{dy}{dx}$ : $\displaystyle \frac{dy}{dx} = \frac{2y^{\frac{1}{2}}}{2x^{\frac{1}{2}}}$
[Implicit Differentiation] Simplify: $\displaystyle \frac{dy}{dx} = \frac{y^{\frac{1}{2}}}{x^{\frac{1}{2}}}$

Step 3: Evaluate

Substitute in point [Derivative]: $\displaystyle \frac{dy}{dx} = \frac{(4)^{\frac{1}{2}}}{(1)^{\frac{1}{2}}}$
Exponents: $\displaystyle \frac{dy}{dx} = \frac{2}{1}$
Division: $\displaystyle \frac{dy}{dx} = 2$

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Implicit Differentiation

Book: College Calculus 10e

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