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pogonyaev
3 years ago
9

What is the smallest four digit odd number you can make

Mathematics
1 answer:
Effectus [21]3 years ago
8 0
The smallest 4 digit odd number. Well think about it. What are the smallest odd number? It is 1 and 0. So the smallest 4 digit odd number is 1,000
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The problem is attached, thanks.
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Answer:

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

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

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

<u>Algebra I</u>

  • 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}

<u>Calculus</u>

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:

<u>Step 1: Define</u>

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

Point (1, 4)

<u>Step 2: Differentiate</u>

  1. [Function] Rewrite [Exponential Rule - Root Rewrite]:                               \displaystyle x^{\frac{1}{2}} - y^{\frac{1}{2}} = -1
  2. [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
  3. [Implicit Differentiation] Simplify Exponents:                                               \displaystyle \frac{1}{2}x^{\frac{-1}{2}} - \frac{1}{2}y^{\frac{-1}{2}}\frac{dy}{dx} = 0
  4. [Implicit Differentiation] Rewrite [Exponential Rule - Rewrite]:                   \displaystyle \frac{1}{2x^{\frac{1}{2}}} - \frac{1}{2y^{\frac{1}{2}}}\frac{dy}{dx} = 0
  5. [Implicit Differentiation] Isolate <em>y</em> terms:                                                       \displaystyle -\frac{1}{2y^{\frac{1}{2}}}\frac{dy}{dx} = -\frac{1}{2x^{\frac{1}{2}}}
  6. [Implicit Differentiation] Isolate \displaystyle \frac{dy}{dx}:                                                               \displaystyle \frac{dy}{dx} = \frac{2y^{\frac{1}{2}}}{2x^{\frac{1}{2}}}
  7. [Implicit Differentiation] Simplify:                                                                 \displaystyle \frac{dy}{dx} = \frac{y^{\frac{1}{2}}}{x^{\frac{1}{2}}}

<u>Step 3: Evaluate</u>

  1. Substitute in point [Derivative]:                                                                     \displaystyle \frac{dy}{dx} = \frac{(4)^{\frac{1}{2}}}{(1)^{\frac{1}{2}}}
  2. Exponents:                                                                                                     \displaystyle \frac{dy}{dx} = \frac{2}{1}
  3. 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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Find the missing sides of the triangle. Leave your answers in simplest radical form.
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The correct answer to this equation is C
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Suppose you guess that there are 300 gum balls in a jar, but there are actually 400. What was the percent error?
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I believe the answer is 25%.

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For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to
kiruha [24]

Answer:

D) 11/3

Step-by-step explanation:

Let x represent monthly salary.

We have been given that for each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity.        

Salary earned in 11 months would be 11x.

Money donated in 11 months would be \frac{11x}{10}.

Further we are told that in December, the worker earned N times his usual monthly salary and donated one-fifth of his earnings to charity.

Salary for December would be Nx.

Money donated in December would be \frac{Nx}{5}.  

The worker's charitable contributions totaled one-eighth of his earnings for the entire year that is \frac{1}{8}\cdot (11x+Nx).

\frac{11x}{10}+\frac{Nx}{5}=\frac{1}{8}\cdot (11x+Nx)

Dividing whole equation by x, we will get:

\frac{11x}{10x}+\frac{Nx}{5x}=\frac{1}{8x}\cdot x(11+N)                

\frac{11}{10}+\frac{N}{5}=\frac{1}{8}\cdot (11+N)

\frac{11}{10}+\frac{N}{5}=\frac{11}{8}+\frac{N}{8}

Combine like terms:

\frac{N}{5}-\frac{N}{8}=\frac{11}{8}-\frac{11}{10}

\frac{N}{5}*40-\frac{N}{8}*40=\frac{11}{8}*40-\frac{11}{10}*40

8N-5N=11*5-11*4

3N=55-44

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\frac{3N}{3}=\frac{11}{3}\\\\N=\frac{11}{3}

Therefore, the value of N is 11/3 and option D is the correct choice.

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3 years ago
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