Solve for the given length:

Dan earns £9.80 per hour how much will I earn for eight hours work

Andrews [41]

Answer:

£78.4

Step-by-step explanation:

Since he earns £9.80 per hour, we multiply this by how many hours there are. So £9.80 times 8 is £78.4. I hope this helps!

6 0

2 years ago

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goldfiish [28.3K]

It's B and C
hope this helps

4 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

Lori ran 5 1/2 km on Monday, 6 1/4 km on Tuesday, 4 1/2 km on Wednesday, and 2 3/4 km on Thursday. What is the average number of

pishuonlain [190]

The average is 4 3/4 km.

you would have to add the distance she ran for each day and then divide by the number of days she ran to find the average.

5 1/2 + 6 1/4 + 4 1/2 + 2 3/4 =19

19 (the total distance ran) divided by 4 (the number of days) = 4 3/4

8 0

2 years ago

Jim Jane Ann and Bill measure an object's length density mass and volume respectively with students measurement might be in lite

AnnyKZ [126]

It would most likely be Bill's

5 0

3 years ago

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