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-Dominant- [34]
3 years ago
6

42/50 in simplest form

Mathematics
2 answers:
Nady [450]3 years ago
7 0
She is correct that's how you do it to get the answer your looking for
gulaghasi [49]3 years ago
4 0
To find the simpliest form of a fraction, all you need to do is divide the numerator and denominator by their greatest common factor, in which in this case, is 2. And so all you need to do is divide the numerator(42) and the denominator(50) by 2, to get 21/25. This means that the simpliest form of 42/50 is 21/25.
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What is the value of x in the equation 2(x-3)+9=3(x+1)+x?
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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

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
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