The <em>trigonometric</em> function that represents the curve seen in the picture is f(x) = 4.5 · sin (π · x / 2 - π) - 6.5.
<h3>How to derive a sinusoidal expression</h3>
In this problem we need to find a <em>sinusoidal</em> expression that models the curve seen in the picture. The most typical <em>sinusoidal</em> model is described below:
f(x) = a · sin (b · x + c) + d (1)
Where:
- a - Amplitude
- b - Angular frequency
- c - Angular phase
- d - Vertical midpoint
Now we proceed to find the value of each variable:
Amplitude
a = - 2 - (-6.5)
a = 4.5
Angular frequency
b = 2π / T, where T is the period.
0.25 · T = 4 - 3
T = 4
b = 2π / 4
b = π / 2
Midpoint
d = - 6.5
Angular phase
- 2 = 4.5 · sin (π · 4/2 + c) - 6.5
4.5 = 4.5 · sin (π · 4/2 + c)
1 = sin (2π + c)
π = 2π + c
c = - π
The <em>trigonometric</em> function that represents the curve seen in the picture is f(x) = 4.5 · sin (π · x / 2 - π) - 6.5.
To learn more on trigonometric functions: brainly.com/question/15706158
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-2y + 5z = -3
y = -5x - 4z - 5
x = 4z + 4
-2(-5(4z + 4) - 4z - 5) + 5z = -3
-2(-20z - 20 - 4z - 5) + 5z = -3
-2(-20z - 4z - 20 - 5) + 5z = -3
-2(-24z - 25) = -3
48z + 50 = -3
<u> - 50 - 50</u>
<u>48z</u> = <u>-53</u>
48 48
z = -1⁵/₄₈
x = 4(-1⁵/₄₈) + 4
x = -4⁵/₁₂ + 4
x = ⁵/₁₂
y = -5(⁵/₁₂) - 4(-1⁵/₄₈) - 5
y = -2¹/₂ + 4⁵/₁₂ - 5
y = 1¹¹/₁₂ - 5
y = -3¹/₂
(x, y, z) = (⁵/₁₂, -3¹/₂, -1⁵/₄₈)
Answer:
Just combine the x
Step-by-step explanation:
Answer:
Step-by-step explanation:
x^2-8x+x-8
x(x-8)+1(x-8)
(x+1)(x-8)
The negative number is x=-1
