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1 year ago

Help pls ! This is trigonometric function

Mathematics

1 answer:

storchak [24]1 year ago

8 0

Answer:

Amplitude: 4

Period: π

midline: y = 1

Step-by-step explanation:

r(x) = -4 sin(2x) + 1

r(x) = a sin(bx + c) + d where |a| is the amplitude and |b| for the period

a = -4 |a| = 4 : Amplitude = 4

b = 2 |b| = 2 period of sin(x) = 2π

period of sin(bx + c) = 2π/|b| = 2π/2 = π

range of sin(2x) ... -1 ≤ sin(2x) ≤ 1

range of -4 sin(2x) + 1: -4+1 ≤ -4 sin(2x) + 1 ≤ 4+1

-3 ≤ -4 sin(2x) + 1 ≤ 5

midline: y = (-3 + 5) / 2 = 1 y = 1

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The distance between two points on a number line can be found by taking the ____A_____ of the ____B_____ of the coordinates. Fil

xeze [42]

Answer:

The distance between two points on a number line can be found by taking the absolute value of the difference of the coordinates.

Step-by-step explanation:

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6 0

2 years ago

Find the derivative of

kirill [66]

Answer:

$\displaystyle y'(1, \frac{3}{2}) = -3$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Coordinates (x, y)
Functions
Function Notation
Terms/Coefficients
Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$

Calculus

Derivatives

Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

$\displaystyle y = \frac{3}{2x^2}$

$\displaystyle \text{Point} \ (1, \frac{3}{2})$

Step 2: Differentiate

[Function] Rewrite [Exponential Rule - Rewrite]: $\displaystyle y = \frac{3}{2}x^{-2}$
Basic Power Rule: $\displaystyle y' = -2 \cdot \frac{3}{2}x^{-2 - 1}$
Simplify: $\displaystyle y' = -3x^{-3}$
Rewrite [Exponential Rule - Rewrite]: $\displaystyle y' = \frac{-3}{x^3}$

Step 3: Solve

Substitute in coordinate [Derivative]: $\displaystyle y'(1, \frac{3}{2}) = \frac{-3}{1^3}$
Evaluate exponents: $\displaystyle y'(1, \frac{3}{2}) = \frac{-3}{1}$
Divide: $\displaystyle y'(1, \frac{3}{2}) = -3$