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Alchen [17]
3 years ago
12

For the sequence below, identify the type of sequence and its important features:

Mathematics
2 answers:
In-s [12.5K]3 years ago
4 0

Answer:

neither

Step-by-step explanation:

the sequence doesn't go up by a specific amount each time nor does it gets multiplied by a single number each time. there is no pattern

Verdich [7]3 years ago
4 0
Neither because it is going up at random
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What is the fuction for the graph?
Andrews [41]

The <em>piecewise defined</em> function is formed by the following three functions: y = 40, for 0 ≤ x < 15, y = 0.0425 · x² - 3.8 · x + 87.438, for 15 ≤ x < 65 and y = 0.4 · x - 6, for x ≥ 65.

<h3>What is the piecewise defined function behind the graph?</h3>

In this problem we have a <em>piecewise defined</em> function formed by three functions: (i) <em>Linear</em> equation, (ii) <em>Quadratic</em> equation, (iii) <em>Linear</em> equation. The <em>first</em> function is y = 40, for 0 ≤ x < 15.

The <em>second</em> function can be found based on the knowledge of three points:

y = a · x² + b · x + c

(x₁, y₁) = (15, 40)

40 = 225 · a + 15 · b + c

(x₂, y₂) = (45, 2.5)

2.5 = 2025 · a + 45 · b + c

(x₃, y₃) = (65, 20)

20 = 4225 · a + 65 · b + c

And the <em>quadratic</em> equation is y = 0.0425 · x² - 3.8 · x + 87.438, for 15 ≤ x < 65.

And the <em>latter linear</em> equation is:

y = m · x + b

m = (30 - 20)/(90 - 65)

m = 0.4

And the x-intercept is:

b = y - m · x

b = 20 - 0.4 · 65

b = - 6

The <em>linear</em> equation is y = 0.4 · x - 6, for x ≥ 65.

The <em>piecewise defined</em> function is formed by the following three functions: y = 40, for 0 ≤ x < 15, y = 0.0425 · x² - 3.8 · x + 87.438, for 15 ≤ x < 65 and y = 0.4 · x - 6, for x ≥ 65.

To learn more on piecewise defined functions: brainly.com/question/12561612

#SPJ1

7 0
2 years ago
Please help thank you very much
Tom [10]

Answer:

4x^{2} -6x

Step-by-step explanation:

3 0
3 years ago
the function intersects its midline at (-pi,-8) and has a maximum point at (pi/4,-1.5) write an equation
Tcecarenko [31]

The equation that represents the <em>sinusoidal</em> function is x(t) = -8 + 6.5 \cdot \sin \left[\left(\frac{2}{3} \pm \frac{4\cdot i}{3}\right)\cdot t + \left(\frac{2\pi}{3} \pm \frac{7\pi \cdot i}{3}  \right)\right], i\in \mathbb{Z}.

<h3>Procedure - Determination of an appropriate function based on given information</h3>

In this question we must find an appropriate model for a <em>periodic</em> function based on the information from statement. <em>Sinusoidal</em> functions are the most typical functions which intersects a midline (x_{mid}) and has both a maximum (x_{max}) and a minimum (x_{min}).

Sinusoidal functions have in most cases the following form:

x(t) = x_{mid} + \left(\frac{x_{max}-x_{min}}{2} \right)\cdot \sin (\omega \cdot t + \phi) (1)

Where:

  • \omega - Angular frequency
  • \phi - Angular phase, in radians.

If we know that x_{min} = -14.5, x_{mid} = -8, x_{max} = -1.5, (t, x) = (-\pi, -8) and (t, x) = \left(\frac{\pi}{4}, -1.5 \right), then the sinusoidal function is:

-8 +6.5\cdot \sin (-\pi\cdot \omega + \phi) = -8 (2)

-8+6.5\cdot \sin\left(\frac{\pi}{4}\cdot \omega + \phi \right) = -1.5 (3)

The resulting system is:

\sin (-\pi\cdot \omega + \phi) = 0 (2b)

\sin \left(\frac{\pi}{4}\cdot \omega + \phi \right) = 1 (3b)

By applying <em>inverse trigonometric </em>functions we have that:

-\pi\cdot \omega + \phi = 0 \pm \pi\cdot i, i \in \mathbb{Z} (2c)

\frac{\pi}{4}\cdot \omega + \phi = \frac{\pi}{2} + 2\pi\cdot i, i \in \mathbb{Z} (3c)

And we proceed to solve this system:

\pm \pi\cdot i + \pi\cdot \omega = \frac{\pi}{2} \pm 2\pi\cdot i -\frac{\pi}{4}\cdot \omega

\frac{3\pi}{4}\cdot \omega = \frac{\pi}{2}\pm \pi\cdot i

\omega = \frac{2}{3} \pm \frac{4\cdot i}{3}, i\in \mathbb{Z} \blacksquare

By (2c):

-\pi\cdot \left(\frac{2}{3} \pm \frac{4\cdot i}{3}\right) + \phi =\pm \pi\cdot i

-\frac{2\pi}{3} \mp \frac{4\pi\cdot i}{3} + \phi = \pm \pi\cdot i

\phi = \frac{2\pi}{3} \pm \frac{7\pi\cdot i}{3}, i\in \mathbb{Z} \blacksquare

The equation that represents the <em>sinusoidal</em> function is x(t) = -8 + 6.5 \cdot \sin \left[\left(\frac{2}{3} \pm \frac{4\cdot i}{3}\right)\cdot t + \left(\frac{2\pi}{3} \pm \frac{7\pi \cdot i}{3}  \right)\right], i\in \mathbb{Z}. \blacksquare

To learn more on functions, we kindly invite to check this verified question: brainly.com/question/5245372

5 0
2 years ago
In the circle below, F is the center and lies on line segment AD and BC.
Sidana [21]

Answer:

I guess option (C)

Step-by-step explanation:

Hope it helps!!!!

3 0
2 years ago
Determine the value of y if x is -10:<br> y= l x -9 l +2
cricket20 [7]

Answer:

y = 21

Step-by-step explanation:

y = | x - 9 | + 2 ( substitute x = - 10 )

  = | - 10 - 9 | + 2

  = | - 19 | + 2

  = 19 + 2

  = 21

8 0
2 years ago
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