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Rufina [12.5K]
3 years ago
8

Which pair of slopes represent perpendicular lines?

Mathematics
1 answer:
Artist 52 [7]3 years ago
3 0
The correct answer is C.

Perpendicular lines have opposite reciprocal slopes. This mean you will flip the original number upside down, and change its sign (negative to positive and vice versa). So, the opposite of -1/4 will be 4.


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Sin (3x) dx = ?<br> find the integral
AVprozaik [17]

Answer:

\displaystyle \displaystyle \int {sin(3x)} \, dx = \frac{-cos(3x)}{3} + C

General Formulas and Concepts:

<u>Calculus</u>

Antiderivatives - Integrals

Integration Constant C

Integration Property [Multiplied Constant]: \displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx

Trig Integration: \displaystyle \int{sin(x)} \, dx = -cos(x) + C

U-Substitution

Step-by-step explanation:

<u>Step 1: Define</u>

\displaystyle \int {sin(3x)} \, dx

<u>Step 2: Identify Substitution Variables</u>

u = 3x

du = 3dx

<u>Step 3: Integrate</u>

  1. [Integral] Rewrite:                                                                                           \displaystyle \frac{1}{3}\int {3sin(3x)} \, dx
  2. [Integral] U-Substitution:                                                                                \displaystyle \frac{1}{3}\int {sin(u)} \, du
  3. [Integral] Trig Integration:                                                                              \displaystyle \frac{1}{3}[-cos(u)] + C
  4. [Expression] Multiply:                                                                                     \displaystyle \frac{-cos(u)}{3} + C
  5. [Expression] Back-Substitute:                                                                        \displaystyle \frac{-cos(3x)}{3} + C
8 0
3 years ago
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