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LenaWriter [7]
3 years ago
6

For which points is the Y- coordinate less than - 1.5?

Mathematics
1 answer:
nexus9112 [7]3 years ago
8 0

Given:

The location of 4 points on a coordinate plane.

To find:

The points whose y-coordinate is less than -1.5.

Solution:

From the given graph it is clear that, the coordinates of the given points are A(2,1), B(-4,-4), C(-1,1) and D(1.5,-2).

For the point A(2,1), the y-coordinate is 1>-1.5.

For the point B(-4,-4), the y-coordinate is -4.

For the point C(-1,1), the y-coordinate is 1>-1.5.

For the point D(1.5,-2), the y-coordinate is -2.

The y-coordinates of the points B and D are less than -1.5.

Therefore, the correct options are B and D.

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If f(x) = 9x10 tan−1x, find f '(x).
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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

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Write and evaluate the expression. Then, complete the statements. Ten less than the quotient of thirty and a number Evaluate whe
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Answer:

expression:  (30/t) - 10

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Step-by-step explanation:

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Answer:

V≈318.09ft³

Step-by-step explanation:

V=πr2h/3

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