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3 years ago

Which equation is equivalent to: 11r+4=55

Mathematics

1 answer:

Lina20 [59]3 years ago

5 0

Answer:

Equation B

Step-by-step explanation:

If you subtract 4 from the original equation, you get equation B.

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Convert 2FA.C8 base 16. express in Octal form, Quinary or pental form and Binary form

Sunny_sXe [5.5K]

Using base conversion method, 2FA.C8 base 16 can be expressed as:

1372.628 in octal
11022.3423120034 in pental
1011111010.11001 in binary

<h3>What is 2FA.C8 base 16 expressed in Octal form?</h3>

To express 2FA.C8 in octal form, it is first converted to a decimal form as follows:

where:

F = 15

A = 10

C = 12

2FA.C8 = 2 × 16^2 + F × 16^1 + A × 16^0 + C × 16^-1 + 8 × 16^-2

2FA.C8 = 762.7812510 in decimal.

Then, convert 762.7812510 to octal as follows:

First the integral part is converted to octal by repeated division by 8.
The fractional part is converted to octal by repeated multiplication by 8 until we get to zero (here, we calculate up to ten digits)
add the integral and fractional part together

762 / 8 = 95 remainder 2

95 / 8 = 11 remainder 7

11 / 8 = 1 remainder 3

1 / 8 = 0 remainder 1

762 = 1372

Then;

0.78125 × 8 = 6 + 0.25

0.25 × 8 = 2 + 0

0.78125 = 0.62

Therefore, 762.78125 in decimal = 1372.628 in octal

<h3>What is 2FA.C8 base 16 expressed in pental form?</h3>

To convert 2FA.C8 base 16 to pental form, we use its value in decimal for conversion.

2FA.C8 base 16 = 762.7812510 base 10

Then, convert 762.7812510 to pental as follows:

First the integral part is converted to pental by repeated division by 5
The fractional part is converted to pental by repeated multiplication by 5 until we get to zero (here, we calculate up to ten digits)
add the integral and fractional part together

762 / 5 = 152 remainder 2

152 / 5 = 30 remainder 2

30 / 5 = 6 remainder 0

6 / 5 = 1 remainder 1

1 / 5 = 0 remainder 1

762 in decimal = 11022 in pental

Then 0.78125 to pental:

0.78125 × 5 = 3 + 0.90625

0.90625 × 5 = 4 + 0.53125

0.53125 × 5 = 2 + 0.65625

0.65625 × 5 = 3 + 0.28125

0.28125 × 5 = 1 + 0.40625

0.40625 × 5 = 2 + 0.03125

0.03125 × 5 = 0 + 0.15625

0.15625 × 5 = 0 + 0.78125

0.78125 × 5 = 3 + 0.90625

0.90625 × 5 = 4 + 0.53125

Thus, 0.78125 in decimal = 0.3423120034 in pental

Therefore, 762.78125 in decimal = 11022.3423120034 in pental.

<h3>What is 2FA.C8 base 16 expressed in Binary form?</h3>

To convert 2FA.C8 base 16 to binary form, we use its value in decimal for conversion.

2FA.C8 base 16 = 762.7812510 base 10

Then, convert 762.7812510 to binary as follows:

First the integral part is converted to binary by repeated division by 2
The fractional part is converted to binary by repeated multiplication by 2 until we get to zero (here, we calculate up to ten digits)
add the integral and fractional part together

762 / 2 = 381 remainder 0

381 / 2 = 190 remainder 1

190 / 2 = 95 remainder 0

95 / 2 = 47 remainder 1

47 / 2 = 23 remainder 1

23 / 2 = 11 remainder 1

11 / 2 = 5 remainder 1

5 / 2 = 2 remainder 1

2 / 2 = 1 remainder 0

1 / 2 = 0 remainder 1

762 base 10 = 1011111010 base two

Then 0.78125 to binary:

0.78125 × 2 = 1 + 0.5625

0.5625 × 2 = 1 + 0.125

0.125 × 2 = 0 + 0.25

0.25 × 2 = 0 + 0.5

0.5 × 2 = 1 + 0

0.78125 base 10 = 0.11001 base two

Therefore, 762.78125 base 10 = 1011111010.11001 base two.

Learn more about base conversion at: brainly.com/question/17946394

4 0

2 years ago

PLEASE HELP QUICKLY 25 POINTS

Natalija [7]

Answer:

○ $\displaystyle \pi$

Step-by-step explanation:

$\displaystyle \boxed{y = 3sin\:(2x + \frac{\pi}{2})} \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{4}} \hookrightarrow \frac{-\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 3$

$\displaystyle \boxed{y = 3cos\:2x} \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 3$

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of <em>sine</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 $\displaystyle y = 3sin\:2x,$ in which you need to replase "cosine" with "sine", 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 horisontal shift formula 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>sine</em> graph [photograph on the right] is shifted $\displaystyle \frac{\pi}{4}\:unit$ to the right, which means that in order to match the <em>cosine</em> graph [photograph on the left], we need to shift the graph BACKWARD $\displaystyle \frac{\pi}{4}\:unit,$ which means the C-term will be negative, and by perfourming your calculations, you will arrive at $\displaystyle \boxed{-\frac{\pi}{4}} = \frac{-\frac{\pi}{2}}{2}.$ So, the sine graph of the cosine graph, accourding to the horisontal shift, is $\displaystyle y = 3sin\:(2x + \frac{\pi}{2}).$ Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit $\displaystyle [-1\frac{3}{4}\pi, 0],$ from there to $\displaystyle [-\frac{3}{4}\pi, 0],$ they are obviously $\displaystyle \pi\:units$ apart, telling you that the period of the graph is $\displaystyle \pi.$ Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the <em>midline</em>. The midline 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>three units</em> beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.