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3 years ago

Which one is correct ?

Mathematics

2 answers:

Assoli18 [71]3 years ago

4 0

Answer:

The hypotenuse is equal to twice the length of the shorter leg.

Step-by-step explanation:

The hypotenuse is equal to twice the length of the shorter leg, which as a rule will be the side across from the 30 degree angle

scoray [572]3 years ago

3 0

D and F are true statements

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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):

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

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

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

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

5 0

3 years ago

If you form a triangle from two given angle measures and the length of the included side, will you always get one triangle or wi

Ann [662]

Answer:

It is not always possible to construct a triangle from a given side length and two angles. If the two given angles add to more than 180°, the sides of the triangle will diverge and never meet.

Step-by-step explanation:

7 0

3 years ago

Upper and lower quartile? What do they mean?

Contact [7]

The upper quartile is the numbers after the median and the lower is the numbers before the median. you find the median of each quartile

4 0

3 years ago

I need help please I'll give you 25 points

ikadub [295]

Answer:

t = 11/21

Step-by-step explanation:

Hope this helps!!

3 0

3 years ago

How do youSimplify 24/64

vlada-n [284]

Answer:3/8.

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 24 and 64 is 8

Divide both the numerator and denominator by the GCD

24 ÷ 8

64 ÷ 8

Reduced fraction:

Therefore, 24/64 simplified to lowest terms is 3/8.

7 0

2 years ago