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velikii [3]
2 years ago
6

A garden is shaped like a rectangle whose perimeter is 150 ft. The length is 2 times as long as the width. Find the length and t

he width.
Mathematics
1 answer:
vlabodo [156]2 years ago
6 0

Answer:

Step-by-step explanation:

L=2W

P=2(L+W), using L=2W this becomes

P=2(2W+W)

P=2(3W)

P=6W, given P=150

6W=150

W=25, and since L=2W

L=50 so

L=50ft and W=25ft

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Answer:

\displaystyle y' = 2x + 3\sqrt{x} + 1

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<u> </u>

<u>Algebra I</u>

  • Terms/Coefficients
  • Anything to the 0th power is 1
  • Exponential Rule [Rewrite]:                                                                              \displaystyle b^{-m} = \frac{1}{b^m}
  • Exponential Rule [Root Rewrite]:                                                                     \displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}<u> </u>

<u>Calculus</u>

Derivatives

Derivative Notation

Basic Power Rule:

  • f(x) = cxⁿ
  • f’(x) = c·nxⁿ⁻¹

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

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

<em />\displaystyle y = (x + \sqrt{x})^2<em />

<em />

<u>Step 2: Differentiate</u>

  1. Chain Rule:                                                                                                        \displaystyle y' = 2(x + \sqrt{x})^{2 - 1} \cdot \frac{d}{dx}[x + \sqrt{x}]
  2. Rewrite [Exponential Rule - Root Rewrite]:                                                     \displaystyle y' = 2(x + x^{\frac{1}{2}})^{2 - 1} \cdot \frac{d}{dx}[x + x^{\frac{1}{2}}]
  3. Simplify:                                                                                                             \displaystyle y' = 2(x + x^{\frac{1}{2}}) \cdot \frac{d}{dx}[x + x^{\frac{1}{2}}]
  4. Basic Power Rule:                                                                                             \displaystyle y' = 2(x + x^{\frac{1}{2}}) \cdot (1 \cdot x^{1 - 1} + \frac{1}{2}x^{\frac{1}{2} - 1})
  5. Simplify:                                                                                                             \displaystyle y' = 2(x + x^{\frac{1}{2}}) \cdot (1 + \frac{1}{2}x^{-\frac{1}{2}})
  6. Rewrite [Exponential Rule - Rewrite]:                                                              \displaystyle y' = 2(x + x^{\frac{1}{2}}) \cdot (1 + \frac{1}{2x^{\frac{1}{2}}})
  7. Multiply:                                                                                                             \displaystyle y' = 2[(x + x^{\frac{1}{2}}) + \frac{x + x^{\frac{1}{2}}}{2x^{\frac{1}{2}}}]
  8. [Brackets] Add:                                                                                                 \displaystyle y' = 2(\frac{2x + 3x^{\frac{1}{2}} + 1}{2})
  9. Multiply:                                                                                                             \displaystyle y' = 2x + 3x^{\frac{1}{2}} + 1
  10. Rewrite [Exponential Rule - Root Rewrite]:                                                     \displaystyle y' = 2x + 3\sqrt{x} + 1

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

Unit: Derivatives

Book: College Calculus 10e

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Divide -3x3 - 4x2 + 4x +3 by x-2
kobusy [5.1K]

Answer:

-3x² - 10x - 16 r. \dfrac{-29}{x-2}

Step-by-step explanation:

You can easily do this through synthetic division:

First step is to get all the numeric coefficients of the expression and write them down. Don't forget to bring their signs along with them.

-3x³ - 4x² + 4x +3

    | -3     -4     +4    +3

    |______________

Next we find the root that is associated with the divisor:

x  - 2 = 0

x = 2

We use this and put it outside:

 2   | -3     -4     +4    +3

      |______________

Okay now we bring down the first coefficient:

  2  | -3     -4     +4    +3

      |______________

        -3

Then we multiply it by the root and put the product under the next coefficient:

2  x - 3 = -6

2  | -3     -4     +4    +3

    |<u>         -6                  </u>

      -3

Then we add them:

2  | -3     -4     +4    +3

    |<u>         -6                  </u>

      -3    -10

Do the same steps until the end:

2  | -3     -4     +4       +3

    |<u>         -6      -20     -32              </u>

      -3     -10     -16     -29

Now that you have that, remember that since the divisor is in the 1st degree, quotient will have a degree will be one degree below as well.

-3x² - 10x - 26

Your last coefficient is going to be your remainder:

-3x² - 10x - 16 r. \dfrac{-29}{x-2}

3 0
3 years ago
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