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:
what's the circumference of a circle with the radius of 7 ft use 3.14 for π
Answer:
7 x 3.14 x 2 = 43.96 ft
Step-by-step explanation:
Formula of Circumference:
pi(3.14 or 22/7 depending on what they tell you to use for pi) x 2 x r(given radius or half your diameter
Pls help is it; (1.5, 2) or no solution
Answer:
no solution?
Step-by-step explanation:
Solve to get the value of h
To the nearest tenth, which is the BEST estimate for the volume of the given pyramid?
Answer:
4.2 cubic inches
Step-by-step explanation:
Find the diagram attached
Volume of the rectangular pyramid = BH/3
B is the base area
H is the height of the pyramid
Given
Base area = 3.2in * 1.4in
Base area = 4.48sq. in
Height = 2.8in
Volume of the rectangular pyramid = 4.48*2.8/3
Volume of the rectangular pyramid = 12.544/3
Volume of the rectangular pyramid = 4.2 cubic inches
PLEASE HELP ME I REALLY NEED THE ANSWER
1 tickets
2 tickets
3 tickets
4 tickets
Answer:
2 adult tickets
Step-by-step explanation:
we have two relations
[tex]a + c = 5[/tex]
[tex]9a + 4c = 30[/tex]
first rearrange the top equality for one of the variables
[tex]a = 5 - c[/tex]
now substitute into the second equation
[tex]9(5 - c) + 4c = 30[/tex]
perform the distribution and combine like terms
[tex]45 - 9c + 4c = 30[/tex]
[tex]45 - 5c = 30[/tex]
[tex] - 5c = - 15[/tex]
[tex]c = 3[/tex]
place this 3 into our first equation and solve for a
[tex]a + (3) = 5[/tex]
[tex]a = 2[/tex]
Im doing an extra practice and need help with this one problem
Answer:
it might be this 8.74777778 im not sure if it is tho so if im wrong then im sorry
Step-by-step explanation:
What is the slope of the line?
please help i put the picture here
what is the mean of the following data values? 53,71,89,10,87
Answer:
63
Step-by-step explanation:
Mean=Sum of all values/number of observation
=53+71+89+10+87/5
=310/5
=62
It's 62
Just took test
Julie is playing a game where she must flip 3 coins. If Julie flips all 3 coins and gets heads all three times, she wins. If Julie does not get heads all three times, she loses.
1/8
1/2
1/4
Answer:
1/8
Step-by-step explanation:
[tex](\frac{1}{2})^{3}[/tex]
Can someone help with this, i don’t know how to do it
Answer:
X=12
Step-by-step explanation:
In all Triangle, the sum of the interior angles =180
180-86-46=4x
4x=48
x=12
Can someone please show me how you get it and the answer
Answer:
m is the slope and b is the y intercept
Question 7
Which set of side lengths can be used to form a right
triangle?
Answer:
D.30,40,50
Step-by-step explanation:
A.4,5,6
B.2,3,4
C.10,20,30
D.30,40,50
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
4² + 5² = 25 is not equal to the square of 6 which is 36
2² + 3² = 10 . 10 is not equal to the square of 4 which is 16
10² + 20³ = 500. 500 is not equal to the square of 30 which is 900
30² + 40² = 2500. this is equal to the square of 50
Drag expressions into order to show a way to find 4 × 3/8
Step-by-step explanation:
[tex]4 \times \frac{3}{8} [/tex]
[tex] \frac{4}{1} \times \frac{3}{8} [/tex]
=12/8
=1 4/8=
= 1 1/2
If 40% of x + 20% of x + 1/10 = 75% of x, then find the value of x. Please give answers with steps
Answer:
x = 13/12
Step-by-step explanation:
explain on image
3 Simplify 3e - e + 4e
Which angles are adjacent angles?
Answer:
<KLN and <MLN
Step-by-step explanation:
adjacent angles have a common vertex and a common side
What type of data distribution is shown on the graph? A bar graph has x on the x-axis, from 0 to 4, and P x (x) on the y-axis, from 0 to 0.5 in 0.1 increments. The probability of 0 is 0.01, the probability of 1 is 0.25, the probability of 2 is 0.3, the probability of 3, is 0.4, and the probability of 4 is 0.02.
Answer:
1.A
2.B
3.A
Step-by-step explanation:
edge 2021 yw :)
Answer:
1. a
2. b
3. a
Step-by-step explanation:
Which angles are vertical angles?
Answer:
It would be Angles GFC and EFH.
Think of it like I'm drawing a capital X. Would you consider the top and bottom parts of the X to be the same? Or would you consider the top and left parts to be the same?
The correct answer for this would be that the top and bottom parts of X are the same size. Now, remember that whenever two lines are making an X. this is because the two angles only touch each other in the center point and don't share a side.
5.) Tiffany is building a model of her bedroom. She is using a scale factor of 1 foot in her room to 0.5 inch in the model. if her bed is 3 feet wide, six and a half feet long, and one and a half feet tall, what size should she make the model of her bed?
1. If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then find the polynomial.
Answer:
[tex] {x}^{2} + 6x + 5[/tex]
Step-by-step explanation:
Required polynomial
[tex] {x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ \\ = {x}^{2} - ( - 6)x + 5 \\ \\ = {x}^{2} + 6x + 5[/tex]
Find the value of x.
Answer:
5
Step-by-step explanation:
Using pythagoras theorem
Answer:
4056 is the correct answer I think
Step-by-step explanation:
13×13×24=4056
What percent of data is less than 20?
Answer:
100%
Step-by-step explanation:
The answer is 100% because all of the numbers in the data are less than 20. Therefore 100% of the data is less than 20.
Workers load 5 identical large crates and 3 identical small crates onto a freight elevator. The crates have a combined weight of 1375 pounds. Later
that day, the workers load 3 more identical large crates and 6 more identical small crates onto the freight elevator. These crates have a combined
weight of 1350 pounds.
Answer: The total would be 40.53
Step-by-step explanation:
The power generated by an electrical circuit (in watts) as a function of its current ccc (in amperes) is modeled by: P(c)=-20(c-3)^2+180P(c)=−20(c−3) 2 +180
Answer:
The current that produces maximum power is 3A
Step-by-step explanation:
Given
[tex]P(c) = 20(c - 3)^2[/tex]
Required [Missing from the question]
The current that produces maximum power
First, we represent the function in standard form
[tex]P(c) = 20(c - 3)^2[/tex]
[tex]P(c) = 20(c - 3)(c - 3)[/tex]
Open bracket
[tex]P(c) = 20(c^2 -6c+ 9)[/tex]
[tex]P(c) = 20c^2 -120c+ 180[/tex]
The maximum value of c is:
[tex]Max(c) = \frac{-b}{2a}[/tex]
Where:
[tex]f(x) = ax^2 + b^2 + c[/tex]
By comparison: [tex]P(c) = 20c^2 -120c+ 180[/tex]
[tex]a = 20[/tex]
[tex]b = -120[/tex]
[tex]c = 180[/tex]
So, we have:
[tex]Max(c) = \frac{-b}{2a}[/tex]
[tex]Max(c) = \frac{-(-120)}{2 * 20}[/tex]
[tex]Max(c) = \frac{120}{40}[/tex]
[tex]Max(c) = 3[/tex]
Uh plz help ;-;
Plzzzzz
Answer:
B)
the (8+7) x (10 + 7) x (6 + 4)
Step-by-step explanation:
Answer:
D- (8×10×6) + (7×7×4)
Step-by-step explanation:
The formula for volume is Length×Width×Height.
So you have to find the volume for each one individually then add them up together.
(You can give the other person brainliest if u want.)
Hope it Helps!:)
Solve 5.x + 6 = 20.
The solution is x
Answer:
2.8
Step-by-step explanation:
5x = 20 - 6
5x/5 = 14/5
x = 2.8
b.r.uh. these ch.a..t links be t.ripping
Answer: Ok so that is a fact for sure
Answer:
yup
Step-by-step explanation:
According to a town's census a household's number of visits to a gas station has a mode of 3 visits per week. Jane surveys 20
homes in her neighborhood and finds the mode to be 6 visits. How can she get her survey statistics to more closely approximate
the population parameters?
A)
Choose some different houses to survey.
B)
Get a more random sample from the town.
C
Increase the number of houses that she surveys.
D)
Recalculate because she must have made a mistake.
Answer:B Get a more random person sample from the town
Step-by-step explanation:
What's the gradient of y=3x+1
Answer:
3
Step-by-step explanation:
y = 3x + 1
This is in slope-y-intercept form: y = mx + c
Gradient = m = 3