Antoine and Adriane are each at the top of a Ferris wheelAfter one revolution each will again be at the topWhich sinusoid (sine or cosine) should you graph to model the ride of your chosen rider? Why? Assume that each Ferris wheel starts at time= 0 seconds
Answers
Answer(s):
[tex]\displaystyle y = 100sin\:(\frac{\pi}{50}x + \frac{\pi}{2}) + 100 \\ y = 100cos\:\frac{\pi}{50}x + 100[/tex]
Step-by-step explanation:
[tex]\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[/tex]
OR
[tex]\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[/tex]
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 sine, 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 [tex]\displaystyle y = 100sin\:\frac{\pi}{50}x + 100,[/tex] 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 cosine 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 REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle 25\:units[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle 25\:units,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-25} = \frac{-\frac{\pi}{2}}{\frac{\pi}{50}}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 100sin\:(\frac{\pi}{50}x + \frac{\pi}{2}) + 100.[/tex]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 [tex]\displaystyle [220, 100],[/tex]from there to [tex]\displaystyle [120, 100],[/tex]they are obviously [tex]\displaystyle 100\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle 100.[/tex]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 midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 100,[/tex]in which each crest is extended one hundred units 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.
The graph of cosine function is to model the ride of your chosen rider.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Let us assume that,
Function is,
f(x) = sin(x)
The curve of the sine function crosses the y-axis at the origin, heads up to y = 1 at x = π/2 and down to y = -1 at x = 3π/2.
Domain: (-∞, ∞)
Range: [-1, 1]
For f(x) = cos(x)
The curve of the cosine function crosses the y-axis at (0, 1) which is its maximum, heads down to y = -1 at x = π then heads up again.
Domain: (-∞, ∞)
Range: [-1, 1]
Given information:
Antoine and Adriane begin their journey at the top of the Ferris wheel.
After one revolution, they will again be at the top of the wheel.
If the wheel starts when time t = 0 seconds, and they begin their journey at the top of the wheel (the maximum point), the most appropriate graph to model their ride is the graph of the cosine function since it is at its highest point when x = 0.
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ2
Related Questions
Which expression is equivalent to 5 (w 4) when w = 9? 5 (9) 9 (5) 5 (9) 4 5 (9) 20.
Answers
Expression consists of numbers, variables, and mathematical operations. The expression f(w)=5(w+4) is equal to f(9)=5(9)+20.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The expression is given to you is,
[tex]f(w)= 5(w+4)[/tex]
Now, if we solve the expression it can be written as,
[tex]f(w)=5w+20[/tex]
substituting the value of w, we will get,
[tex]f(9)=5(9)+20[/tex]
Hence, the expression f(w)=5(w+4) is equal to f(9)=5(9)+20.
Learn more about Expression:
https://brainly.com/question/13947055
Answer:
c
Step-by-step explanation:
I got it right.
I need help its due today
Answers
Answer:
60
Step-by-step explanation:
D
PLEASE PLEASE PLEASE ANSWER!!!!!!!!
Answers
Answer:
Step-by-step explanation:
x + 44x = 180
45x = 180
x = 4
180-x = 176
answer is 4
can someone help me with the fraction
Answers
Answer:
6) 1 over 12
7) 10 over 12
8)9 over 12
6.
[tex]\tt \dfrac{1}{6}\times \dfrac{2}{2}=\dfrac{2}{12}[/tex]
7.
[tex]\tt \dfrac{5}{6}\times \dfrac{2}{2}=\dfrac{10}{12}[/tex]
8.
[tex]\tt \dfrac{3}{4}\times \dfrac{3}{3}=\dfrac{9}{12}[/tex]
please show steps will give brainliest
Answers
Answer:
3x²-3x+2
Step-by-step explanation:
To find A-B:
Substitute A and B with given values:
x²-(-2x²+3x-2)
Epand the bracket since there is a -1 in front of the bracket (the 1 is invisible)
x²+2x²-3x+2
Simplify:
3x²-3x+2
((2 (x - 1))/3) - ((3 (x - 2))/4) = 1
Answers
Answer:
[tex] \frac{2x - 2}{3} - \frac{3x - 6}{4} = 1 \\ \frac{8x - 8 - 9x + 18}{12} = 1 \\ - x + 10 = 12 \\ - x = 12 - 10 \\ x = - 2[/tex]
Select the correct answer. A laboratory assistant reacts ammonia and nitric acid to get a test batch of ammonium nitrate. The theoretical yield was 872. 7 grams of product, but the process yielded only 529. 4 grams of the product. What was the percent yield? A. 16. 48% B. 39. 33% C. 60. 66% D. 64. 85%.
Answers
The percentage of actual yield is 60.66%.
What is the percentage?The percentage of a number is the hundredth part of that number.
Given that the total yield is 872.7 grams and the actual yield is 529.4 grams.
The percentage is calculated by the formula given below.
[tex]Percentage\; of\; Yield = \dfrac {Actual \;Yield }{ Total\; Yield}\times 100[/tex]
Substituting the values, we get the percentage,
[tex]Yield \;\% = \dfrac {529.4}{872.7}\times 100[/tex]
[tex]Yeils\;\%=60.66\;\%[/tex]
Hence we can conclude that the percentage of actual yield is 60.66%.
To know more about the percentage, follow the link given below.
https://brainly.com/question/8011401.
i need help w this it’s gonna count as a test grade
Answers
Answer:
C
Step-by-step explanation:
< open circle, not ≤
A clothing store is having a sale: buy one shirt at
regular price, and get a second shirt of equal or lesser
value for 35% off. Jason buys two shirts at the sale.
The regular price of the first shirt is $32.00, and the
regular price of the second shirt is $20.00. Including
sales tax, Jason pays $48.60 for the two shirts.
Answers
Using proportions, it is found that the sales tax is of 8%.
What is a proportion?A proportion is a fraction of a total amount.
In this problem, he buys a shirt for $32.00, then the second at 35% off, hence the price of the second shirt is:
P = (1 - 0.35) x 200 = 0.65 x 20 = $13.
The total price of the shirts is:
T = $32.00 + $13.00 = $45.00.
Hence, he pays $3.60 in taxes, and the sales tax is given by:
Tax = (3.6/45) x 100% = 8%.
More can be learned about proportions at https://brainly.com/question/24372153
If someone has two bottles (12 fl. oz. each) of 7.7% beer AND 3 fl. oz. of vodka, how many standard drinks has that person consumed? Select the most accurate answer.
about 2
about 3
about 4
about 5
about 6
Answers
Answer:
about 5
Step-by-step explanation:
One 12 fl oz bottle of 7.7% beer ≈ 1.5 standard drinks
1.5 fl oz vodka ≈ 1 standard drink
Therefore,
Two 12 fl oz bottle of 7.7% beer ≈ 3 standard drinks
3 fl oz vodka ≈ 2 standard drinks
So, 2 bottles of beer and 3 fl oz of vodka ≈ 3 + 2 = 5
The picture below shows the graph of which inequality?
Answers
Answer:
[tex]x^{2} < 1[/tex]
Step-by-step explanation:
45.15  divided by 21 step by step
Answers
EXPLANATION: put your decimal up 21 can’t go into 4 but in 45 2 times 45-42=3 put down your 1 21 goes into 31 one time 31-21 is 10 put down your five 21 can go into 105 5 times 105-105 is zero
Please help just this anyone who answers this gets their answer marked brainliest
Answers
Answer:
It's the third option . it's the right ans .
pls mark my ans as brainliest.
Answer:
Option C.
Step-by-step explanation:
Let us begin by redrawing the quadrilaterals so that the congruent sides and angles become more obvious in the attachment:
From the diagrams, we have the congruent angles to be:
∠F, ∠K, ∠S
∠ I, ∠L, ∠T
∠G, ∠N, ∠R
∠H, ∠M, ∠Q
We can conclude that the correct option is:
∠M and ∠Q
What’s the answer to this? Find 1/8 of 88
Answers
Answer:
11
Step-by-step explanation:
[tex]\frac{1}{8}[/tex] of 88
= [tex]\frac{88}{8}[/tex]
= 11
In which quadrant does the point (-2,5) lie?
A. Quadrant I
B. Quadrant ll
C. Quadrant lll
D. Quadrant lV
Answers
Because negative 2 goes to the left and positive five goes up
It is now five past six. What time will it be in 11 hours and 32 minutes?
Answers
help please i don't Know how to answer this
Answers
Answer:
a line of symmetry is a line divide an object in to two equal parts. answer is A
A hummingbird lives in a nest that is 8 meters high in a tree. The hummingbird flies 10 meters to
get from its nest to a flower on the ground. How far is the flower from the base of the tree?
Answers
Help please
Brainlest
Answers
Answer:
2
Step-by-step explanation:
The image has all the steps. Remember PEMDAS
HELLP PLEASE BRAINLIEST AND LOTS OF POINTS
Which of the following equations shows the linear relationship between the x and y variables shown in the table of ordered pairs?
A. y = x - 5
B. y = x + 5
C. y = 5 - x
D. y = 5x
Answers
Answer:
x+5
Step-by-step explanation:
Hope this helps
Hi! I hope you're enjoying your day!
The linear relationship between x and y is
y=x+5
So we take a number x, add 5 to it, and that is equal to y.
Let's try and see if it works.
Let's take 2.
Add 5:
y=5+2
That should be equal to 7.
y=7
Yeah! It worked :)
Let's try another one.
Let's take 3.
y=3+5
y=8
Woo-hoo! It worked again :)
Hence, the answer is
[tex]\boxed{\boxed{\bold{Option~B~-y=x+5}}}[/tex]
Hope everything is clear.
If you have any questions, please comment.
#LearningIsFun
[tex]\rule{250}{2}[/tex]
If you put 90ml of concentrate in a glass, how much water should be added?
Answers
Question wasn't clear, but I hope this helps!
→⭐Question:Lemon Squash If you put 90ml of concentrate in a glass, how
2 parts concentrate water should be added?
to 5 parts water x ml.
→⭐Answer:
Ratio: 2:5 or 2/5
Now, if this ratio is maintained then the amount of water to be added to 90 ml concentrate in a glass can be calculated as:
2/5 = 90/x ( x = the unit (ml)/ how many ml of water)
Cross multiplication of the above equation will give us:
2x = 90 x 5 = 450
Dividing both sides by 2 we will get:
x = 450/2 = 225
Therefore, if we put 90ml of concentrate in a glass, the amont of water to be added is 225ml.
I hope this answer helps!
Yours Faithfully,
Damian. / Bright_SCR.
please help!!!!!!!!!!!!
Will mark brainliest
Answers
Answer:
○ [tex]\displaystyle 25[/tex]
Step-by-step explanation:
[tex]\displaystyle 4 = 2\sqrt{25} - 6 \\ 4 = 2[5] - 6 \\ \\ 4 = 10 - 6[/tex]
I am joyous to assist you at any time.
A cast iron pipe used as a water main for a home has an outer diameter of 8 in. If the pipe has a thickness of 0.6 in, what volume of iron does 29 in of pipe contain? Answer in cubic inches. Round your answer to the nearest hundredth if necessary. (Note: diagram is not drawn to scale.)
Answers
The volume of cast iron pipe is 1053.19 in³.
Volume of CylinderThe volume of a cylinder can be calculated by: [tex]\pi *r^2*h[/tex], where:
r = radius
h= height
In this question, the cylinder is represented for a pipe, where:
r = inner diameter= [tex]inner\;diameter=outer\;diameter-2*thickness[/tex]
h= length of pipe
From this, you should apply the volume of the pipe. See the steps:
Step 1 - Find the inner diameterinner diameter=outer diameter-2*thickness
inner diameter=8-2*0.6
inner diameter=8-1.2=6.8 in
Step 2 - Find the volume of the pipe[tex]V_{pipe}=\pi *r_{internal}^2*h\\ \\ V_{pipe}=\pi *(\frac{6.8}{2} )^2*29\\ \\ V_{pipe}=\pi *(3.4)^2*29=1053.19\;in^3[/tex]
The volume of cast iron pipe is 1053.19 in³.
Read more about the volume of pipe here:
https://brainly.com/question/906588
i need help with these before 12 am
Answers
Answer:
1. factored form is - 5/2, 3, 2 solutions 2. - 1/2 , -5 2 solutions 3. -2, 3 2 solutions 4. -2 , 5, 2 solutions
Step-by-step explanation:
Question 1:
[tex]2x^{2} -x-15=0\\(2x+5)(x-3)=0[/tex]
Solutions are x = -5/2 and 3
Question 2:
[tex]2x^2+11x =-5\\2x^2 + 11x +5 = 0\\(2x+1)(x+5)= 0[/tex]
Solutions are x = -1/2 and x =-5
Question 3:
[tex]x^2-x-6=0\\(x-3)(x+2)=0[/tex]
Solutions are x = 3 and -2
Question 4
[tex]x^{2} -3x-10 = 0\\(x-5)(x+2)=0[/tex]
Solutions are x = 5 and x = -2
An individual head of a sprinkler system covers a circular area of grass with a radius of 25 feet. The yard has 3 sprinkler heads that each cover a circular area with no overlap. What is the approximate total area that will be watered? 1963. 5 ft 1963. 5 ft² 5890. 5 ft 5890. 5 ft².
Answers
The total area covered by the yard by the 3 sprinkler heads such that each covers a circular area with no overlap is 5892.857 ft².
What is the area of a circle?The area of a circle is the area covered by the circle with radius r. It is given by the formula,
[tex]\text{Area of circle} = \pi r^2[/tex]
As it is given that the area covered by a single sprinkler system is of the radius of 25 feet, therefore, the area covered by a singular sprinkler system can be written as,
Area of sprinkler = Area of a circle with radius 25 feet
[tex]\begin{aligned}\text{Area of sprinkler}&= \pi r^2\\&=\pi (25^2)\\&= 1964.2857 \approx 1964.286\rm\ ft^2\end{aligned}[/tex]
Now, as we know that the yard has three such sprinkler systems, therefore, the area covered by the sprinkler will be thrice the area covered by a single sprinkler,
The total area covered by the sprinkler = 3 x Area of sprinkler
= 3 x 1964.286
= 5892.857
Thus, the total area covered by the yard by the 3 sprinkler heads such that each covers a circular area with no overlap is 5892.857 ft².
Learn more about the Area of Circle:
https://brainly.com/question/1238286
The derivation for the equation of a parabola with a vertex at the origin is started below. = startroot (x minus 0) squared (y minus p) squared endroot = startroot (x minus x) squared (y minus (negative p)) squared endroot (x)2 (y – p)2 = (0)2 (y p)2 x2 y2 – 2py p2 = y2 2py p2 if the equation is further simplified, which equation for a parabola does it become? x2 = 4py x2 = 2y2 2p2 y2 = 4px y2 = 4py
Answers
The equation of parabola it becomes will be x²= 4py.The y-axis passes through (0, -a), and the directrix of the parabola x² = 4ay has the equation y + a = 0
What is a parabola?A parabola is a curve in which all points are at the same distance from two fixed points: the focus and a fixed straight line (the directrix ).
The given expression in the problem is;
[tex]x^2 +y^2-2py +p^2= y^2+2py+p^2[/tex]
On simplifying the gIven expression we get;
[tex]x^2- 2py = 2py \\\\ x^2= 2py+2py \\\\x^2=4py[/tex]
The y-axis passes through (0, -a), and the directrix of the parabola x²= 4ay has the equation y + a = 0. The y-axis passes through (0, a), and the center of the parabola x2 = -4ay has the equation y - a = 0.
Hence the equation of parabola it becomes will be x²= 4py
To learn more about the parabola refer to the link;
https://brainly.com/question/8495504
a box contains 576 marbles of six different colors . if there are 254 boxes, how many marbles are in all the boxes
Answers
Answer:
To answer this, we would first have to divide 576 by 6. Next, take that answer and put it in the next division problem including the number 254. Whatever the answer is that is you final answer
Step-by-step explanation:
Sorry I couldn't tell you the answer. My sisters woke me up at 1 in the morning, so I didn't get much sleep. Please forgive me if the answer you come up with is wrong. If it is, please report my answer. If it is right, please mark me as brainliest because I really want to level up
what is standard form for -1/2k^3+3/4k^5
Answers
Answer:
3/4k^5+-1/2k^3
Step-by-step explanation:
You put the numbers in order from the largest exponent to the smallest.
on monday three hundred sixty one students went On a trip to the zoo seven buses were filled and four students had to travel separately.. how many students were in each bus?
Answers
1. Solve the following inequality on your own paper and select the best answer below.
Answers
Answer:
Hope this helps you........