a)[tex]\[ h(t) = 13 - 6\cos\left(\frac{2\pi}{15} t\right) \][/tex]
This formula gives the distance \( h \) from you to the ground after \( t \) seconds of riding.
b) you are 10 meters above the ground at [tex]\( t = \frac{5}{2} \)[/tex] seconds, which is \( 2.5 \) seconds after starting at the lowest point.
Let's break down this problem step by step:
a. To find a formula for the distance ( h ) (in meters) from you to the ground after ( t ) seconds of riding, we can use trigonometry and the properties of circular motion.
1. The Ferris wheel has a radius of 6 meters and is centered 7 meters above the ground. This means that at the lowest point, you are ( 7 + 6 = 13 ) meters above the ground, and at the highest point, you are ( 7 - 6 = 1 ) meter above the ground.
2. The angular speed of the Ferris wheel is given as 24 degrees per second. Since the Ferris wheel completes one full rotation (360 degrees) in[tex]\( \frac{360^\circ}{24^\circ/\text{sec}} = 15 \)[/tex] seconds, its angular velocity is[tex]\( \omega = \frac{2\pi}{15} \)[/tex]radians per second.
3. Let [tex]\( \theta \)[/tex] be the angle in radians that the Ferris wheel has rotated through at time ( t ) seconds. The height ( h ) above the ground can be expressed as:
[tex]\[ h = 13 - 6\cos(\theta) \][/tex]
To relate[tex]\( \theta \) to time \( t \)[/tex], we use the formula for angular displacement in circular motion:
[tex]\[ \theta = \omega t \][/tex]
Substitute [tex]\( \omega = \frac{2\pi}{15} \)[/tex] into the equation above to get:
[tex]\[ \theta = \frac{2\pi}{15} t \][/tex]
Now, substitute [tex]\( \theta \)[/tex]back into the equation for height \( h \):
[tex]\[ h(t) = 13 - 6\cos\left(\frac{2\pi}{15} t\right) \][/tex]
This formula gives the distance \( h \) from you to the ground after \( t \) seconds of riding.
b. To find the times when you are 10 meters above the ground, we set \( h(t) = 10 \) and solve for \( t \):
[tex]\[ 10 = 13 - 6\cos\left(\frac{2\pi}{15} t\right) \][/tex]
First, subtract 10 from both sides:
[tex]\[ -3 = -6\cos\left(\frac{2\pi}{15} t\right) \][/tex]
Divide both sides by -6:
[tex]\[ \frac{1}{2} = \cos\left(\frac{2\pi}{15} t\right) \][/tex]
Now, take the inverse cosine (arccos) of both sides:
[tex]\[ \frac{2\pi}{15} t = \cos^{-1}\left(\frac{1}{2}\right) \][/tex]
Solve for \( t \) by dividing both sides by [tex]\( \frac{2\pi}{15} \)[/tex]:
[tex]\[ t = \frac{15}{2\pi} \cos^{-1}\left(\frac{1}{2}\right) \][/tex]
Using the fact that [tex]\( \cos^{-1}\left(\frac{1}{2}\right) = \frac{\pi}{3} \)[/tex], substitute this value into the equation:
[tex]\[ t = \frac{15}{2\pi} \times \frac{\pi}{3} \]\[ t = \frac{5}{2} \][/tex]
So, you are 10 meters above the ground at [tex]\( t = \frac{5}{2} \)[/tex] seconds, which is \( 2.5 \) seconds after starting at the lowest point.
The price of a 250 dollar coat increased 7% last year. The coat is now on sale for one half off. What is the sale price?
helpppppppppppppppppppppppppp
A rectangular deck
is 12 ft by 14 ft. When the length and width are increased by the same amount very becomes 280 squares ft. By how much were the dimensions increased ?
You need to have a password with 4 letters followed by 2 even digits between 0 and 9, inclusive. if the characters and digits cannot be used more than once, how many choices do you have for your password?
The total number of possible passwords, considering the conditions that no letters or digits can be reused, and only even digits 0-9 can be used, would be 7,893,600.
Explanation:This is a question of combinations and permutations. Firstly, consider the four letters. There are 26 letters in the English alphabet. Since you have four letters and none of them can be the same, the number of possibilities is 26 * 25 * 24 * 23. Next, consider the two numbers. Since we can only choose even numbers between 0 and 9 (which gives us 5 possible selections), and they cannot be the same, the number of possibilities is 5 * 4. Therefore, to find the total number of possible passwords, you multiply the possibilities for letters and numbers together. So, the number of
possible passwords would be 26 * 25 * 24 * 23 * 5 * 4, which equals to 7,893,600.
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20 POINTS! What is the distance between the points (2, 3) and (5, -4)?
A rectangular note card has a perimeter of 18 inches and an area of 20 square inches. What are the dimensions of the note card?
Which absolute value function has a graph that is wider than the parent function when graphed represents the parent function f(x)=|x| reflected over the x-axis and translated 1 unit to the right
A. F(x) = -|x|+1
B. F(x) = -|x-1|
C. F(x) =|-x|+1
D. F(x) =|-x-1|
Answer:
B.[tex]F(x)=-\mid{x-1}\mid[/tex]
Step-by-step explanation:
We are given that a function
[tex]f(x)=\mid x\mid[/tex]
We have to find absolute value of function when parent function reflected over the x- axis and translated 1 unit to the right.
The transformation rule when the point (x,y) is reflected over x- axis is given by
[tex](x,y)\rightarrow (x,-y)[/tex]
Apply the reflection on function over x- axis then, we get
[tex]g(x)=-\mid x\mid[/tex]
Transformation rule when the point (x,y) is shifted a units towards right is given by
[tex](x,y)\rightarrow (x-a,y)[/tex]
When the graph is translated 1 units towards right then , obtained function is given by
[tex]F(x)=-\mid{x-1}\mid[/tex]
Help? Will mark Brainliest! TYSM!
Jade buys a blouse and a skirt for 34 of their original price. Jade pays a total of $31.50 for the two items. If the original price of the blouse is $18, what is the original price of the skirt? Enter your answer in the box.
Answer:
The original price of the skirt is $24
Step-by-step explanation:
The question must be 3/4 of their original price. So, I will solve this using 3/4 as 34 is unclear and does not suit the question.
Lets assume that the price of the blouse be = x
Lets say the price of the skirt is = y
Now, given is that 3/4 of the price together for both items is $31.5 0
This means,
[tex]\frac{3}{4}(x+y)=31.50[/tex] ..... (1)
The original price of the blouse is $18 so, x= 18 .............(2)
Putting x=18 in equation (1)
[tex]\frac{3}{4}(18+y)=31.50[/tex]
[tex]3(18+y)=31.50*4[/tex]
[tex]3y+54=126[/tex]
[tex]3y=72[/tex]
y=24
Hence, the original price of the skirt is = $24.
Check:
Original price of both items = [tex]18+24=42[/tex]
And 3/4 of 42 is [tex]\frac{3}{4}*42= 31.50[/tex]
So, the correct answer is $24.
viola makes gift baskets for valentine's day.she has 13 basket left over from last year, and she plans to make 12 more each day. if there are 15 work days unitl the day she begins to sell the baskets, how many baskets will she have to sell?
193 baskets
156 baskets
205 baskets
181 baskets
It has 3 more vertices than a triangle
Find the area of the triangle that has a base of 4.2 mm and a height of 1.5 mm.
Cora arrived at school at 7:55 am She left for 1 hour for a doctors appointment. She was dismissed from school at 3:15 pm. How long was Cora at school?
At the end of the first round in a quiz show, Jeremy has at most negative 20 points. Write an inequality that means “at most negative 20.”
Which sequence of transformations creates a similar, but not congruent, triangle? ((will medal for correct answer))
Dilation and rotation
Rotation and translation
Reflection and rotation
Translation and reflection,
A street promotion worker gets paid $0.10 for each flyer he hands out. His goal is to make $15 an hour. How many flyers must he hand out each hour?
A. 45
B. 1500
C. 150
D. 15
The street promotion worker must hand out 150 flyers each hour to make $15.
Explanation:To determine how many flyers the street promotion worker must hand out each hour to make $15, we need to use the equation:
Number of flyers × Payment per flyer = Total payment
Since the worker wants to make $15 an hour, the equation becomes:
Number of flyers × $0.10 = $15
To solve for the number of flyers, we divide both sides of the equation by $0.10:
Number of flyers = $15 ÷ $0.10
Number of flyers = 150
Therefore, the street promotion worker must hand out 150 flyers each hour to make $15.
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Jennifer recorded the temperature of water samples and the time it took 50g of salt to dissolve in the samples. Jennifer's data models a direct variation. Which table contains Jennifer's data?
Answer:
The answer is C.
Step-by-step explanation:
I know that its c because i literatly just tried it and it said corect it was on USA. test prep
what should you do first to simplify the expression (43 + 9) ÷ 76 + 5
prove that an isosceles trapezium is always cyclic
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Is 11p-7q polynomial
How much is in the account after year 6 ??
Daniel is planning to go camping, but he lost the pole that supports the middle point of the tent. A cross-section of the tent is shown below. The base of the tent measures 96 inches wide, and the length from the top point of the tent to the corners of the base is 102 inches.
Ramon spends 2/5 of his monthly income on rent ,1/5 of his income on utilities and 3/4 of the amount remaining on food and recreation.He saves 193.50 a month,What is Ramon’s monthly income?
The sin 215° is ____
●A positive value
●0
●A negative value
The sin 215 degrees is a positive value. (Soh Cah Toa - Sin Cos Tan)
Answer: A positive value
believe; live
Please help! 15 points!
Btw, you cannot answer in the file.....that's just a pic.....
PLEASE HELP ASAP! BRAINLIEST TO BEST/RIGHT ANSWER
Answer:
C
Step-by-step explanation:
The very first term would result in 2 having an exponent in 0 making the equation -3 * 1 which is just -3 and C is the only option.
To further prove this -3 * 2^3 is -24. n is the term that you are looking for. So finding the fourth term would mean you would take 4-1 which is 3 thus making the exponent 3.
In 1992, only 275 people owned cellphones in Metropolis. Each year, cell phone use has continuously grown by 82%. How many cellphone users were there in 2000?
If f(x) = 1 + 5x, and g(x) = x3, find (f∘g)(x)
A.
1 + 5x3
B.
1 – 3x3
C.
1 + 8x
D.
5x3
Please help, what effect does doubling the radius of a cone's base have on the cone's volume? Thank you! :),