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ser-zykov [4K]
3 years ago
14

6. A pitcher has 16 cups of water in it. During the day, Aditi drank 5⁄2 cups, Kavitha drank 15⁄4 cups, and Rahul drank 33⁄8 cup

s. What are these amounts as mixed fractions? A. Aditi 21⁄2 cups, Kavitha 33⁄4 cups, and Rahul 41⁄8 cups B. Aditi 21⁄4 cups, Kavitha 31⁄4 cups, and Rahul 37⁄8 cups C. Aditi 13⁄2 cups, Kavitha 27⁄4 cups, and Rahul 39⁄8 cups D. Aditi 31⁄2 cups, Kavitha 41⁄4 cups, and Rahul 35⁄8 cups
Mathematics
1 answer:
Crank3 years ago
4 0

Answer:

A. Aditi 2 1/2 cups, Kavitha 3 3/4 cups, and Rahul 4 1/8 cups

Step-by-step explanation:

2*2=4 5-4=1      2 1/2

3*4=12  15-12=3       3 3/4

4*8-32  33-32=1     4 1/8

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Implicit differentiation Please help
Anvisha [2.4K]

Answer:

y''(-1) =8

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

<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)}

Step-by-step explanation:

<u>Step 1: Define</u>

-xy - 2y = -4

Rate of change of the tangent line at point (-1, 4)

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

<em>Find 1st Derivative</em>

  1. Implicit Differentiation [Product Rule/Basic Power Rule]:                            -y - xy' - 2y' = 0
  2. [Algebra] Isolate <em>y'</em> terms:                                                                               -xy' - 2y' = y
  3. [Algebra] Factor <em>y'</em>:                                                                                       y'(-x - 2) = y
  4. [Algebra] Isolate <em>y'</em>:                                                                                         y' = \frac{y}{-x-2}
  5. [Algebra] Rewrite:                                                                                           y' = \frac{-y}{x+2}

<u>Step 3: Find </u><em><u>y</u></em>

  1. Define equation:                    -xy - 2y = -4
  2. Factor <em>y</em>:                                 y(-x - 2) = -4
  3. Isolate <em>y</em>:                                 y = \frac{-4}{-x-2}
  4. Simplify:                                 y = \frac{4}{x+2}

<u>Step 4: Rewrite 1st Derivative</u>

  1. [Algebra] Substitute in <em>y</em>:                                                                               y' = \frac{-\frac{4}{x+2} }{x+2}
  2. [Algebra] Simplify:                                                                                         y' = \frac{-4}{(x+2)^2}

<u>Step 5: Differentiate Pt. 2</u>

<em>Find 2nd Derivative</em>

  1. Differentiate [Quotient Rule/Basic Power Rule]:                                          y'' = \frac{0(x+2)^2 - 8 \cdot 2(x + 2) \cdot 1}{[(x + 2)^2]^2}
  2. [Derivative] Simplify:                                                                                      y'' = \frac{8}{(x+2)^3}

<u>Step 6: Find Slope at Given Point</u>

  1. [Algebra] Substitute in <em>x</em>:                                                                               y''(-1) = \frac{8}{(-1+2)^3}
  2. [Algebra] Evaluate:                                                                                       y''(-1) =8
6 0
3 years ago
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