Answer:
How do I ask a question on here?
Step-by-step explanation:
Answer: 12
Step-by-step explanation: you welcome
PLEASE HELP! WILL MARK BRAINLIEST!
The path of a seat on a new Ferris wheel is modeled by x = –25sin(StartFraction pi Over 30 EndFraction t) and y = –25cos(StartFraction pi Over 30 EndFraction t) + 30, where distances are measured in feet. What is the maximum height a rider will experience?
50 feet
55 feet
60 feet
80 feet
Answer:
The maximum height a rider will experience is 55 feet.
Step-by-step explanation:
Let's start writing the function that defines the path of a seat on the new Ferris wheel. This function will depend of the variable ''t'' which is time.
[tex]X(t)=(x,y)[/tex]
In which [tex]X(t)[/tex] are the coordinates of the seat (the x - coordinate and the y - coordinate) that depend from time.
[tex]''x''[/tex] and [tex]''y''[/tex] are functions that depend from the variable ''t''.
For this exercise :
[tex]X(t)=[-25sin(\frac{\pi}{30}t);-25cos(\frac{\pi}{30}t)+30][/tex]
In order to find the maximum height a rider will experience we will study the behaviour of the y - component from the function [tex]X(t)[/tex].
The function to study is [tex]y(t)=-25cos(\frac{\pi}{30}t)+30[/tex]
To find its maximum, we will derivate this function and equalize it to 0. Doing this, we will find the ''critical points'' from the function.
⇒ [tex]y(t)=-25cos(\frac{\pi}{30}t)+30[/tex] ⇒
[tex]y'(t)=\frac{5}{6}\pi sin(\frac{\pi}{30}t)[/tex]
Now we equalize [tex]y'(t)[/tex] to 0 ⇒
[tex]y'(t)=0[/tex] ⇒ [tex]\frac{5}{6}\pi sin(\frac{\pi}{30}t)=0[/tex]
In this case it is easier to look for the values of ''t'' that verify :
[tex]sin(\frac{\pi}{30}t)=0[/tex]
Now we need to find the values of ''t''. We know that :
[tex]sin(0)=0\\\\sin(\pi)=0\\sin(-\pi)=0[/tex]
Therefore we can write the following equivalent equations :
[tex]\frac{\pi}{30}t=0[/tex] (I)
[tex]\frac{\pi}{30}t=\pi[/tex] (II)
[tex]\frac{\pi}{30}t=-\pi[/tex] (III)
From (I) we obtain [tex]t_{1}=0[/tex]
From (II) we obtain [tex]t_{2}=30[/tex]
And finally from (III) we obtain [tex]t_{3}=-30[/tex]
We found the three critical points of [tex]y(t)[/tex]. To see if they are either maximum or minimum we will use the second derivative test. Let's calculate the second derivate of [tex]y(t)[/tex] :
[tex]y'(t)=\frac{5}{6}\pi sin(\frac{\pi}{30}t)[/tex] ⇒
[tex]y''(t)=\frac{\pi ^{2}}{36}cos(\frac{\pi }{30}t)[/tex]
Now given that we have an arbitrary critical point ''[tex]t_{n}[/tex]'' ⇒
If [tex]y''(t_{n})>0[/tex] then we will have a minimun at [tex]t_{n}[/tex]
If [tex]y''(t_{n})<0[/tex] then we will have a maximum at [tex]t_{n}[/tex]
Using the second derivative test with [tex]t_{1},t_{2}[/tex] and [tex]t_{3}[/tex] ⇒
[tex]y''(t_{1})=y''(0)=\frac{\pi ^{2}}{36} >0[/tex] ⇒ We have a minimum for [tex]t_{1}=0[/tex]
[tex]y''(t_{2})=y''(30)=\frac{-\pi^{2}}{36}<0[/tex] ⇒ We have a maximum for [tex]t_{2}=30[/tex]
[tex]y''(t_{3})=y''(-30)=\frac{-\pi^{2}}{36}<0[/tex] ⇒ We have a maximum for [tex]t_{3}=-30[/tex]
The last step for this exercise will be to find the values of the maximums.
We can do this by replacing in the equation of [tex]y(t)[/tex] the critical points [tex]t_{2}[/tex] and [tex]t_{3}[/tex] ⇒
[tex]y(t_{2})=y(30)=55[/tex]
[tex]y(t_{3})=y(-30)=55[/tex]
We found out that the maximum height a rider will experience is 55 feet.
Answer:
B
Step-by-step explanation:
When 6 times a number, x, is added to 7, the result is equal to thirteen more than 7 times the same number, what is the value of x
Answer:
x = -7
Step-by-step explanation:
Seven times a number and seven is equal to six times a number.
Word problems can be tricky no matter what level of math or science you are in.
First look at the question for words that indicate mathematical symbols.
"times" indicates multiplication
"and" indicates addition
"a number" means we have a variable, x, to solve for
Now we can go from left to right and write it in a mathematical equation
7x + 7 = 6x
Then, solve for x
7x + 7 = 6x
7 = 6x - 7x
7 = -1x
7/-1 = x
x = -7
Finally, we check our work.
7x + 7 = 6x
7(-7) + 7 = 6(-7)
-49 + 7 = -42
-42 = -42 √
The answer is x = -7
The area of a triangular sail is given by the expression 12bh, where b is the length of the base and h is the height. What is the area of a triangular sail in a model sailboat when b = 12 inches and h = 7 inches?
Answer:
42 square inches
Step-by-step explanation:
Area of a triangle = (1/2)(base)(height)
A = 1/2(12)(7)
A = 1/2(84)
A = 42
a sleeve of golf balls is shown to the nearest inch what is the volume of the box that is not filled by the 3 balls
Clinton has a bag of Skittles. Inside the bag are 6 red, 4 orange, 7 yellow, 3 purple and 4 green Skittles. What is the probability of drawing a green Skittle, replacing it, and then drawing another green Skittle
The probability of drawing a green Skittle, replacing it, and then drawing another green Skittle is 1/36
How to determine the probability?The distribution of the Skittle is given as:
Red = 6
Orange = 4
Yellow = 7
Purple = 3
Green = 4
The total number of skittle is:
Total = 6 + 4 + 7 + 3 + 4
Evaluate
Total = 24
The probability of selecting a green skittle is:
P(Green) = 4/24
So, the probability of selecting 2 green skittles is:
P = 4/24 * 4/24
Evaluate
P = 1/36
Hence, the probability of drawing a green Skittle, replacing it, and then drawing another green Skittle is 1/36
Read more about probability at:
https://brainly.com/question/25870256
#SPJ1
A survey asked first-year college students, "How many miles is this college from your permanent home?" Students had to choose from the following options: 5 miles or less, 6 to 10 miles, 11 to 50 miles, 51 to 100 miles, 101 to 500 miles, or over 500 miles. The bar chart below shows the percent of students at public and private 4-year colleges who chose each option.
Answer:
Students who attend a private college are more likely to travel a farther distance to attend college.
Step-by-step explanation:
Find the length of each arc. Round your answers to the nearest tenth.
A) 127.2 yd
C) 102.4 yd
B) 7.1 yd
D) 56.5 yd
Answer: 7.1 yd
Step-by-step explanation:
the formula for arc length is 2πr(x/360), x being the central angle
input the values, so the equation would be 2π9(45/360), which equals 7.1
Multiples of 6 and 14
Answer:
Step-by-step explanation:
6: 6, 12, 18, 24, 30, 36, 42, 48, 54
14: 14, 28, 42, 56
the LCM (least common multiple) is 42.
what is the value of y2 -x2 when y=6 and x=5
What is the graph of the function f(x) = the quantity of negative x squared minus 2 x minus 2, all over x minus 2 ? (6 points)
Answer:
Please check my interpretation of your written equation.
Step-by-step explanation:
f(x) = (-x^2 - 2x - 2)/(x-2)
Wild. See attached graph.
Choose all the graphical displays that are best for showing numerical data.
box-and-whisker plot
bar graph
line graph
circle graph
stem-and-leaf plot
scatter plot
histogram
Answer:
box-and-whisker plot
line graph
stem-and-leaf plot
scatter plot
histogram
Step-by-step explanation:
Answer:
stem-and-leaf plot
Step-by-step explanation:
trust me this is the right one
You pick a card at random. Without putting the first card back, you pick a second card at
random.
3 4 5 6
What is the probability of picking a 5 and then picking a 3?
Write your answer as a fraction or whole number.
Answer:
4
Step-by-step explanation:
The volume of a sample of oxygen is 200.0 mL when the pressure is 3.00
atm and the temperature is 310 K. What is the new temperature if the
volume increases to 400.0 mL and the pressure decreases to 2.00 atm?*
322.3K
482.8 K
O 413.3K
686.0 K
9514 1404 393
Answer:
C 413.3K
Step-by-step explanation:
Temperature is proportional to volume and pressure. Pressure has decreased by a factor of 2/3, and volume has increased by a factor of 400/200 = 2. So, the new temperature is ...
(310 K)(2/3)(2) = 413 1/3 K ≈ 413.3 K
polynomial test
solve or simplify
-7x(11x+12)
i need help on these
Answer:
-77x^2 -84x
Step-by-step explanation:
[tex] - {77x}^{2} - 84x[/tex]
just multiply -7 by each number within the parentheses.
Chase is a contestant on a game show. His scores in each of the first four
rounds are shown below. Chase's final score is double his score after the
four rounds. What is Chase's final score? Show your work
Answer:
the final score of chase is 170
Step-by-step explanation:
Given that
The chase final score would be double his score after the four rounds
So the chase final score is
= (Round 1 score + round 2 score + round 3 score + round 4 score) × 2
= (-35 + 45 + 90 - 15) × 2
= 170
Hence the final score of chase is 170
The same would be considered and relevant
Answer: 46857578087543677536
zle
1. A shoe box manufacturer is creating a box with
the following dimensions. Calculate the volume
of the shoe box in cubic inches.
5 in
8 in
12 in
Created with DOCE
i need help
Answer: 480 in cubed
Step-by-step explanation: volume is length * width * height so 8*5*12=480
Calculate the length of line AB
Answer this if you know this
5+3-2√5±∞
Answer:
wt actual hell
Step-by-step explanation:
Answer:
answering because my account got banned
Step-by-step explanation:
another math question
Answer:
5
Step-by-step explanation: 1/2 probability, 10 / 2 equals 5
Answer:
The best prediction possible for the number of times it will land on tails is 5 times.
Step-by-step explanation:
Because there are two sides to a coin, that means there will be a 50% chance of landing on a side. Since you are flipping 10 coins, the best prediction to make is that 50% of the flips, or 5 flips, will result in tails.
-2 1/3 - (-5)=___
3 1/3
3 2/3
-7 1/3
2 2/3
Answer:
10/3 or 3 1/3
Step-by-step explanation:
-2 1/3=-5/3
-5/3-(-5)
-5/3+5
-5/3+15/3
10/3
answer : -2 1/3 - (-5) = [tex]2\frac{2}{3}[/tex]
explanation : we need to convert the mixed numbers to improper fractions, then find the LCD and combine.
step 1 : convert the mixed number to an improper fraction
ex: [tex]-\frac{7}{3}-(-5)[/tex]
step 2 : when there is a - in front of an expression in parentheses, change the sign of each term in the expression
ex : [tex]-\frac{7}{3}+5[/tex]
step 3 : calculate the sum
ex : [tex]\frac{8}{3}[/tex]
solution : [tex]\frac{8}{3}[/tex]
simplify: [tex]2\frac{2}{3}[/tex]
exact form : [tex]\frac{8}{3}[/tex]
decimal form : 2.66666666 (repeating)
mixed number form : [tex]2\frac{2}{3}[/tex]
hope this helps !
- audrey ♡
10ft/2in simplified so the units are the same
hey! i’ll give brainliest pls help.
Answer:
Hi! I'll just help qwq
The first option should be the correct answer!
Step-by-step explanation:
The sun is in the center, and all other planet orbits/goes around the sun.
The second option is a theory of which old people believed. Now we know for sure that the sun is in the center, and we orbit around it.
Which situations can be modeled by a linear function?
Answer:
A, C, E
Step-by-step explanation:
F(x) =
X+1 if x 1
-x+1 if 1
X-1 if x>3
Please help
Answer:
f ' [x] = 0
Step-by-step explanation:
Escribir un 8% como un decimal
Answer:
8% como un decimal es 0.08%
Espero que te ayude!
What is the cosine ratio of ∠Z?
Answer:
10 / 26
Step-by-step explanation:
cos <Z = adjacent / hypotenuse
= YZ / XZ
= 10 / 26
Answer:
Cos of an angle by definition of its ratio is side adjacent/hypotenuse. The side adjacent to angle Z cannot be the hypotenuse, so it has to be 10. he hypotenuse is 26. Therefore, cosZ= 10/26 = 5/13
Step-by-step explanation:
MRK ME BRAINLIEST PLZZZZZZZZZZZZz
a store charges by the pound for candy. if it costs you 10$ for 4 pounds of candy, how much will it cost you for 15 pounds?
(help! i need the work too please ! :) )
4x10=40 16 with a remainder of 1
Answer: I think it is $37.50
Step-by-step explanation: You first have to divide 10 by 4 to know how much money it was for 1 pound and I got 2.5. Then I multiplied 2.5 by 15 to get 37.5 which is $37.50.
The ratio of the number of Mary's necklaces to the number of Helen's necklaces is 25:9.Mary's has 100 necklaces. How many necklaces does Helen's have.
Answer: 36
Step-by-step explanation:
Given
The ratio of Mary's to Helen's necklaces is 25:9
Mary has 100 necklaces
Suppose Helen has x necklaces
Therefore the ratio can be written like
[tex]\Rightarrow \dfrac{25}{9}=\dfrac{100}{x}\\\\\Rightarrow x=\dfrac{100}{25}\times 9\\\\\Rightarrow x=4\times 9\\\Rightarrow x=36[/tex]
So, Helen has 36 necklaces
Ay help me and when I finish I am giving free point
but help me with this
Answer:
The correct answer is [tex]\frac{2}{16}[/tex].
Step-by-step explanation:
Since there are 8 cards and two sides to the coin, that means there will be a total of 16 different outcomes. Out of the 16 possible outcomes, 2 of them meet the requirement of picking a vowel card and landing on heads, so the fraction to represent the situation would be [tex]\frac{2}{16}[/tex].
Answer:
2/16
Step-by-step explanation:
y/8 =5
Y=?
What does y =
Answer:
the answer is y=40
Step-by-step explanation:
y/8=5
y=8*5
y=40
Answer:
5
Step-by-step explanation:
The vertical value in a pair of coordinates. How far up or down the point is. The Y Coordinate is always written second in an ordered pair of coordinates (x,y) such as (12,5). In this example, the value "5" is the Y Coordinate. Also called "Ordinate"
I hope this helped!