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Alona [7]
3 years ago
10

What are the zeros of the following function?

Mathematics
1 answer:
jarptica [38.1K]3 years ago
4 0

Answer:

Hence , (a,0) is a zeros of a function

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Marie pays $2.50 for 5 pencils. Use the drop-down menus to explain how to determine and
Luden [163]

Answer:

<h2>The constant of proportionality is 0.50</h2>

Step-by-step explanation:

The constant of proportionality is the unit ratio between variables.

According to the problem, Marie pays $2.50 for 5 pencils. So, the unit ratio os this would be the constant of proportionaliy. To find it, we just need to divide.

C=\frac{\$ 2.50}{5 \ pencils}=0.50

Therefore, the constant of proportionality is 0.50, which means Marie paid $0.50 per pencil.

3 0
4 years ago
When played, the middle C key on a piano has a frequency of 262 cycles per second.
IgorC [24]

Answer:

\displaystyle y = \frac{1}{2}sin\:524\pi{x}

Step-by-step explanation:

\displaystyle \boxed{y = \frac{1}{2}cos\:(524\pi{x} - \frac{\pi}{2})} \\ \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{1}{1048}} \hookrightarrow \frac{\frac{\pi}{2}}{524\pi} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{1}{262}} \hookrightarrow \frac{2}{524\pi}\pi \\ Amplitude \hookrightarrow \frac{1}{2}

<em>OR</em>

\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{1}{262}} \hookrightarrow \frac{2}{524\pi}\pi \\ Amplitude \hookrightarrow \frac{1}{2}

You will need the above information to help you interpret the graph. First off, keep in mind that although the exercise told you to write the sine equation based on the speculations it gave you, if you plan on writing your equation as a function of <em>cosine</em>, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of \displaystyle y = \frac{1}{2}cos\:524\pi{x},in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the <em>sine</em> graph [photograph on the left], accourding to the <u>horisontal shift formula</u> above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY <em>REALLY</em> ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the <em>cosine</em> graph [photograph on the right] is shifted \displaystyle \frac{1}{1048}\:unitto the left, which means that in order to match the <em>sine</em> graph [photograph on the left], we need to shift the graph FORWARD \displaystyle \frac{1}{1048}\:unit,which means the C-term will be positive, and by perfourming your calculations, you will arrive at \displaystyle \boxed{\frac{1}{1048}} = \frac{\frac{\pi}{2}}{524\pi}.So, the cosine graph of the sine graph, accourding to the horisontal shift, is \displaystyle y = \frac{1}{2}cos\:(524\pi{x} - \frac{\pi}{2}).Now, with all that being said, in this case, sinse you ONLY have the exercise to wourk with, take a look at the above information next to \displaystyle Wavelength\:[Period].It displays the formula on how to define each wavelength of the graph. You just need to remember that the B-term has \displaystyle \piin it as well, meaning both of them strike each other out, leaving you with just a fraction. Now, the amplitude is obvious to figure out because it is the A-term, so this is self-explanatory. The <em>midline</em> is the centre of your graph, also known as the vertical shift, which in this case the centre is at \displaystyle y = 0,in which each crest is extended <em>one-half unit</em> beyond the midline, hence, your amplitude. So, no matter what the vertical shift is, that will ALWAYS be the equation of the midline, and if viewed from a graph, no matter how far it shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

4 0
3 years ago
Convert the decimal 3.88888 to a fraction
Darya [45]
As a fraction it would be 388888/100000.
6 0
3 years ago
Read 2 more answers
Find The constant of proportionality in the following equation: y=2/3 x
julia-pushkina [17]
The constant of proportionality is 2/3x. This is because the equation states that the equation/line will travel constantly without speeding or slowing down.
7 0
4 years ago
Read 2 more answers
Lucia is helping her grandmother make a quilt. They have 4 yards of fabric, which is equal to 144 inches. They need an additiona
lana66690 [7]

Answer:

They need an additional 54 inches of fabric

Step-by-step explanation:

This can be solved by using the unitary method.

Unitary method is that we find the measure of 1 unit and then mulitply it with the required number to get the actual measurement.

4 yards of fabric  is equal to 144 inches

1 yard of fabric  is equal to 144 inches/4= 36 inches

They need an additional 1 1/2 yards of fabric

So multiplying 1 1/2*36= 3/2*36= 3*36/2= 108/2= 54 inches

They need an additional 54 inches of fabric

5 0
3 years ago
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