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ZanzabumX [31]
3 years ago
5

Find the area of this parallelogram, top= 14 left= 11 right = 10

Mathematics
1 answer:
Kamila [148]3 years ago
4 0

Answer:

140 cm^2

Step-by-step explanation:

Formula for area of a Parallelogram: base*height

14 cm * 10cm = 140 cm^{2}

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Which points are on the graph of g(x) = (1/5)^x
11111nata11111 [884]

Answer:

A) The point( -1 , 5)  is satisfies the  given graph  g(x) = (\frac{1}{5} )^{x}

B) The point( 3 , 1/125)  is satisfies the  given graph  g(x) = (\frac{1}{5} )^{x}

Step-by-step explanation:

<u><em>Explanation:-</em></u>

Given graph  

               y =      g(x) = (\frac{1}{5} )^{x}

Put the point ( -1 , 5)

Put y =5 and x =-1

            5 = (\frac{1}{5} )^{-1} = 5

The point( -1 , 5)  is satisfies the  given graph

ii)

Given graph  

               y =      g(x) = (\frac{1}{5} )^{x}

             \frac{1}{125}  = (\frac{1}{5} )^{3} = \frac{1}{125}

The point( 3 , 1/125)  is satisfies the  given graph  g(x) = (\frac{1}{5} )^{x}

                 

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Find the value of x in the figure below 13x+8 2x+7
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Step-by-step explanation:

step 1. (13x + 8) + (2x + 7) = 180 (definition of same side interior angles)

step 2. 15x + 15 = 180 (like terms)

step 3. 15x = 165 (subtract 15 from each side)

step 4. x = 11. (divide both sides by 15)

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Hello again! This is another Calculus question to be explained.
podryga [215]

Answer:

See explanation.

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>Algebra I</u>

Functions

  • Function Notation
  • Exponential Property [Rewrite]:                                                                   \displaystyle b^{-m} = \frac{1}{b^m}
  • Exponential Property [Root Rewrite]:                                                           \displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Derivative Property [Multiplied Constant]:                                                           \displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)

Derivative Property [Addition/Subtraction]:                                                         \displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]

Basic Power Rule:

  1. f(x) = cxⁿ
  2. 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:

We are given the following and are trying to find the second derivative at <em>x</em> = 2:

\displaystyle f(2) = 2

\displaystyle \frac{dy}{dx} = 6\sqrt{x^2 + 3y^2}

We can differentiate the 1st derivative to obtain the 2nd derivative. Let's start by rewriting the 1st derivative:

\displaystyle \frac{dy}{dx} = 6(x^2 + 3y^2)^\big{\frac{1}{2}}

When we differentiate this, we must follow the Chain Rule:                             \displaystyle \frac{d^2y}{dx^2} = \frac{d}{dx} \Big[ 6(x^2 + 3y^2)^\big{\frac{1}{2}} \Big] \cdot \frac{d}{dx} \Big[ (x^2 + 3y^2) \Big]

Use the Basic Power Rule:

\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} (2x + 6yy')

We know that y' is the notation for the 1st derivative. Substitute in the 1st derivative equation:

\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 6y(6\sqrt{x^2 + 3y^2}) \big]

Simplifying it, we have:

\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 36y\sqrt{x^2 + 3y^2} \big]

We can rewrite the 2nd derivative using exponential rules:

\displaystyle \frac{d^2y}{dx^2} = \frac{3\big[ 2x + 36y\sqrt{x^2 + 3y^2} \big]}{\sqrt{x^2 + 3y^2}}

To evaluate the 2nd derivative at <em>x</em> = 2, simply substitute in <em>x</em> = 2 and the value f(2) = 2 into it:

\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = \frac{3\big[ 2(2) + 36(2)\sqrt{2^2 + 3(2)^2} \big]}{\sqrt{2^2 + 3(2)^2}}

When we evaluate this using order of operations, we should obtain our answer:

\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = 219

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

Unit: Differentiation

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