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77julia77 [94]
2 years ago
6

Find the distance between points A = (2, 0) and

Mathematics
1 answer:
allochka39001 [22]2 years ago
3 0

Answer:

  9.2

Step-by-step explanation:

You want the distance between A(2, 0) and B(0, 9).

<h3>Distance</h3>

The distance formula is based on the Pythagorean theorem. It tells you the distance between (x1, y1) and (x2, y2) is ...

  d = √((x2 -x1)² +(y2 -y1)²)

For the given points, this becomes ...

  d = √((0 -2)² +(9 -0)²) = √(4+81) = √85

  d ≈ 9.2

The distance between A and B is about 9.2 units.

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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
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Answer:

Answer: 42.5

Step-by-step explanation:

It says 1 inch equals 5 feet. So, every inch is on the map is an extra 5 feet in real space. So if you think about it, all this is is a simple multiplication problem.

Here is the math:

8.5 * 5 = 42.5

Think about it, for every inch there is on the map there is an extra 5 feet in real space. There is 8 inches, so we need 5 extra feet for each of those 8 inches. So what we get for 1 inch is 5 feet, for 2 inches 10 feet, 3 inches 15 feet, etc etc until we reach 8 inches. For the 0.5 inches alone that would equal 2.5 feet in real life since 1 inch is 5 feet.

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Answer:

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Step-by-step explanation:

Given that:

Total point scored = 26

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Number of free throws = x + x + 4 = 2x + 4

Hence,

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