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2 years ago

10

you ride your bike around the neighborhood block eight times a day after school. The distance around the neighborhood block is 3

980 feet. How many miles do you ride on your bike during a normal school week?

1 answer:

LiRa [457]2 years ago

3 0

8(3980)(5) = 159200
1 mile = 5280 ft
30.15 miles per week

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Antoine and Adriane are each at the top of a Ferris wheelAfter one revolution each will again be at the topWhich sinusoid (sine

Valentin [98]

Answer(s):

$\displaystyle y = 100sin\:(\frac{\pi}{50}x + \frac{\pi}{2}) + 100 \\ y = 100cos\:\frac{\pi}{50}x + 100$

Step-by-step explanation:

$\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 100 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-25} \hookrightarrow \frac{-\frac{\pi}{2}}{\frac{\pi}{50}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{100} \hookrightarrow \frac{2}{\frac{\pi}{50}}\pi \\ Amplitude \hookrightarrow 100$

<em>OR</em>

$\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 100 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{100} \hookrightarrow \frac{2}{\frac{\pi}{50}}\pi \\ Amplitude \hookrightarrow 100$

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 by all means, go for it, but be careful and follow what is explained here. Now, as you can see, the photograph on the right displays the trigonometric graph of $\displaystyle y = 100sin\:\frac{\pi}{50}x + 100,$ 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>co</em><em>sine</em> graph [photograph on the left], accourding to the <u>horisontal shift formula above</u>. 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 $\displaystyle 25\:units$ 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 $\displaystyle 25\:units,$ which means the C-term will be negative, and by perfourming your calculations, you will arrive at $\displaystyle \boxed{-25} = \frac{-\frac{\pi}{2}}{\frac{\pi}{50}}.$ So, the sine graph of the cosine graph, accourding to the horisontal shift, is $\displaystyle y = 100sin\:(\frac{\pi}{50}x + \frac{\pi}{2}) + 100.$ 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 hits $\displaystyle [220, 100],$ from there to $\displaystyle [120, 100],$ they are obviously $\displaystyle 100\:units$ apart, telling you that the period of the graph is $\displaystyle 100.$ 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 $\displaystyle y = 100,$ in which each crest is extended <em>one hundred units</em> beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

**I knew exactly what you were talking about the moment you posted this, so here was what you were looking for. It really does not matter which sinusoid and person you select because you will get the same information either way.

I am delighted to assist you at any time.

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1 year ago

Please both the question please

Alexus [3.1K]

Answer: (i) 2/6=0.33 and (ii) 4/6=0.66
Explanation: if you were to add everything up there would be 17 boys and 17 girl and then you would end up with 6 people who write with their left hand and 28 people who right with their right hand. I hope this helps

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2 years ago

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RSM QUESTION NEED HELP!!!!!! A pharmacist has a 13 % alcohol solution and another 18 % alcohol solution. How much of each must h

Luden [163]

Answer:

40 grams of 13% alcohol solution and 10 grams of 18% alcohol solution.

Step-by-step explanation:

13%(x) + 18%(50-x) = 14%*50g Multiply them all

0.13x + (9-0.18x) = 7

0.13x-0.18x + 9 = 7 Simplify the equation and subtract 0.13x from 0.18x

9-0.05x = 7 Add 0.05x to each side

9 = 7+0.05x Subtract 7 from both sides

0.05x = 2 Multiply each side by 100

5x = 200 Divide both sides by 5

x = 40

50 - 40 = 10

40 grams and 10 grams

Your welcome

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2 years ago

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In a sale, there is 25% off all prices. A chair costs £100 before the sale. How much was it in the sale?

Black_prince [1.1K]

It would be 75 after the sale. Hope it helps! :)

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2 years ago

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Rework problem 35 from the Chapter 2 review exercises in your text, involving auditioning for a play. For this problem, assume 9

sweet-ann [11.9K]

Answer: 1) 6300 ways

2) 2520 ways

3) 0.067

Step-by-step explanation:

For this problem, assume 9 males audition, one of them being Winston, 5 females audition, one of them being Julia, and 6 children audition. The casting director has 3 male roles available, 1 female role available, and 2 child roles available.

How many different ways can these roles be filled from these auditioners?

Available: 9M and 5F and 6C

Cast: 3M and 1F and 2C

As it is not ordered: C₉,₃ * C₅,₁ * C₆,₂

C₉,₃ = 9!/3!.6! = 84

C₅,₁ = 5!/1!.4! = 5

C₆,₂ = 6!/2!.4! = 15

C₉,₃ * C₅,₁ * C₆,₂ = 84.5.15 = 6300

How many different ways can these roles be filled if exactly one of Winston and Julia gets a part?

2 options Winston gets or Julia gets it:

1) Winston gets it but Julia no:

8 male for 2 spots

4 females for 1 spot

6 children for 2 spots

C₈,₂ * C₄,₁ * C₆,₂

C₈,₂ = = 8!/2!.6! = 28

C₄,₁ = 4!/1!.3! = 4

C₆,₂ = 6!/2!.4! = 15

C₈,₂ * C₄,₁ * C₆,₂ = 28.4.15 = 1680

2) Julia gets it but Winston does not

8 male for 3 spots

1 female for 1 spot

6 children for 2 spots

C₈,₃ * C₆,₂

C₈,₃ = 8!/3!.5! = 56

C₆,₂ = 6!/2!.4! = 15

C₉,₃ * C₆,₂ = 56.15 = 840

1) or 2) = 1) + 2) = 1680 + 840 = 2520

What is the probability (if the roles are filled at random) of both Winston and Julia getting a part?

8 male for 2 spots

1 female for 1 spot

6 children for 2 spots

C₈,₂ * C₆,₂

C₈,₂ = = 8!/2!.6! = 28

C₆,₂ = 6!/2!.4! = 15

C₈,₂ * C₆,₂ = 28.15 = 420

p = 420/6300 = 0.067

6 0

3 years ago