X + 7у = 23 3х + 14у = 48

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 sinusoidal 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 periodic function based on the information from statement. Sinusoidal 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 inverse trigonometric 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 sinusoidal 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

What is the quotient of 1/8 divided by 4/9

kifflom [539]

You would want to use the Keep, Change , Flip

method. So you keep the 1/8, change division into multiplication, the flip the 4 into 1/4.

Step-by-step explanation:

(1/8) / 4

(1/8) * (1/4)

answer: 1/32 or 0.03125

3 0

3 years ago

When constructing an inscribed square how many lines will be drawn

Oksanka [162]

From the research I just did, it seems that 6 lines will be drawn when constructing an inscribed square.

Hope this helped :)

4 0

3 years ago

X^2+3x-28 which is a biomial of this trinomial

Nostrana [21]

Our polynomial is $x^{2} +3x-28$
We can tell from -28 that the binomials are one positive and one negative.
We can use a factoring chart. What adds to make +3x and multiplies to make -28. $blank + blank=+3x
blank*blank=-28$
To get a negative 28, we can multiply -4 and positive seven, which add together after being multiplied by x to get +3x. Therefore, you are left with (x+7) and (x-4).
$(x+7)(x-4)$

8 0

3 years ago

Read 2 more answers

Find the length of side x in simplest radical form with a rational denominator.

kondaur [170]

Answer:

4√2

Step-by-step explanation:

This is a special right triangle with angle measures 90° 45° 45° and the side lengths for the ones that sees 45° = a and the one that sees 90° = a√2 (hypotenuse)

7 0

3 years ago

X + 7у = 23 3х + 14у = 48​

X + 7у = 23 3х + 14у = 48