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nlexa [21]
3 years ago
5

Someone help me with this! Brainliest + 20 plints

Mathematics
1 answer:
Reika [66]3 years ago
3 0

You must use multiple different angle theorems in order to answer these questions.

In the first question, you use a Z angle theorem, where since the angles lie on a parallel line, angles a and b will equal to 180.

Angle a will equal 40 due to the alternate angles, and b will equal 140 since 180 - 40 = 140.

In the second question, you use corresponding angles. b will equal 72 since they are alternate angles and follow the Z angle theorem, and angle a = angle c. To get these, take 180 - angle b to get angle c, which is 180 - 72 = 108. Angle c = 108 and angle a = 108 since they are opposite angles.

In the third question, since everything takes place in a parallelogram, opposite angles will equal each other, thus angle b will equal 79. To get angle a, you do 180 - angle b or 79, 180 - 79 = 101. Angle a will equal 101.

*assume each number has a degree on them*

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Arrange in descending order 1/2, 3/4, 2/3​
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When an article is sold for $132.00, a profit of 10% is made. The cost of the<br> article is?
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3 0
2 years ago
If f(x) = 9x10 tan−1x, find f '(x).
djverab [1.8K]

Answer:

\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + \frac{9x^{10}}{x^2 + 1}

General Formulas and Concepts:

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

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

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

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

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle f(x) = 9x^{10} \tan^{-1}(x)

<u>Step 2: Differentiate</u>

  1. [Function] Derivative Rule [Product Rule]:                                                   \displaystyle f'(x) = \frac{d}{dx}[9x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]
  2. Rewrite [Derivative Property - Multiplied Constant]:                                  \displaystyle f'(x) = 9 \frac{d}{dx}[x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]
  3. Basic Power Rule:                                                                                         \displaystyle f'(x) = 90x^9 \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]
  4. Arctrig Derivative:                                                                                         \displaystyle f'(x) = 90x^9 \tan^{-1}(x) + \frac{9x^{10}}{x^2 + 1}

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

Unit: Differentiation

7 0
3 years ago
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