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3 years ago

9

HELP WITH WORD PROBLEM - The quality control engineer of top notch tool company finds flaws in 8 of 60 wrenches examined. Predic

t the number of flawed wrenches in a batch of 2400

1 answer:

USPshnik [31]3 years ago

6 0

Answer:

The expected ratio: 8/60 = x/2400

=> The number of flawed wrenches in a batch of 2400:

x = 2400*8/60 = 320

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If -y-2x^3=Y^2 then find D^2y/dx^2 at the point (-1,-2) in simplest form

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Answer:

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General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

<u>Algebra I</u>

Factoring

<u>Calculus</u>

Implicit Differentiation

The derivative of a constant is equal to 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Product Rule: $\frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Chain Rule: $\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Quotient Rule: $\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

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-y - 2x³ = y²

Rate of change of tangent line at point (-1, -2)

<u>Step 2: Differentiate Pt. 1</u>

<em>Find 1st Derivative</em>

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[Algebra] Factor <em>y'</em>: $-6x^2=y'(2y+1)$
[Algebra] Isolate <em>y'</em>: $\frac{-6x^2}{(2y+1)}=y'$
[Algebra] Rewrite: $y' = \frac{-6x^2}{(2y+1)}$

<u>Step 3: Differentiate Pt. 2</u>

<em>Find 2nd Derivative</em>

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[Derivative] Simplify: $y'' = \frac{-24xy-12x+12x^2y'}{(2y+1)^2}$
[Derivative] Back-Substitute <em>y'</em>: $y'' = \frac{-24xy-12x+12x^2(\frac{-6x^2}{2y+1} )}{(2y+1)^2}$
[Derivative] Simplify: $y'' = \frac{-24xy-12x-\frac{72x^4}{2y+1} }{(2y+1)^2}$

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