13/24 as a decimal rounded to the nearest tenth

Simplify -3(x + 5) + 5(x – 2) + 8

PtichkaEL [24]

Answer:

Hey there,

Just do this to solve your problem:

2x-17

Hope, this helps :)

7 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 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

To take the neighbor's children to the

madam [21]

Answer:

h>27

Step-by-step explanation:

process of elimination on numbers I'm assuming this is not requiring decimals

3 0

2 years ago

Read 2 more answers

The weight of bags of coffee beans at the grocery store follows a Normal distribution with a mean of μ = 7 ounces and a standard

aleksley [76]

Answer:

C.

Step-by-step explanation:

The random variable W is Normal, with a mean of 28 ounces and a standard deviation of four ounces.

mean of total = 7+7+7+7 = 28

Variance of total = 4+4+4+4 = 16

SD of total = sqrt(16) = 4

4 0

2 years ago

The normal monthly precipitation (in inches) for August is listed for 20 different U.S. cities. Find the mean of the data. 3.5 1

Burka [1]

Answer:

The correct answer is 2.94 in.

Step-by-step explanation:

The monthly precipitation for August in 20 different U.S. cities are observed in inches.

The data is given by: 3.5, 1.6, 2.4, 3.7, 4.1, 3.9, 1.0, 3.6, 4.2, 3.4, 3.7, 2.2, 1.5, 4.2, 3.4, 2.7, 0.4, 3.7, 2.0 and 3.6.

We intend to find the mean of the given data.

Therefore mean of the precipitation is ∑data ÷ 20 = $\frac{58.8}{20}$ = 2.94 inches.

Thus the mean of the data is 2.94 inches.

5 0

3 years ago