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 x=9, the value of x2−2 is
Answer:
16
Step-by-step explanation:
x= 9
x×2=2x
9×2=18
18-2= 16
Question 5 Multiple Choice Worth 1 points)
(06.03)
What is the axis of symmetry for f(x) = -5x2 – 20x - 10?
Ox = 6
Ox= -6
Ox=2
Ox= -2
Answer:
a
Step-by-step explanation:
I really need help.... i am doing k12 online and i have SO much overdue and i need help, I MIGHT FAIL 6th GRADE!! i know thats not ur problem but i really need help I will mark brainliest if it lets me.
Answer:
Table 1(red)
Step-by-step explanation:
A proportional relationship will have a constant of proportionality between y and x all through the data given.
Constant of proportionality, k = y/x
Table 1 (red):
y/x = 5/1 = 10/2 = 20/4 = 5
k = 5 all through, therefore, this table show a proportional relationship between x and y
Table 2 (blue):
y/x = 1/6 ≠2/9 ≠ 4/15
This doesn't have a constant of proportionality, k, that is the same all through in the given table of values. Therefore, it doesn't show any proportional relationship between x and y
Sullivan’s boss has 5 eyes total. Three of his eyes are smaller than the other two. What percentage of his eyes are larger?
Answer:
40%
Step-by-step explanation:
3/5 are small so we have to find 2/5 which is 40%
2/5=x/100
cross multiply
you'll get: 5x=200
divide and thats how u get 40 %
Help! Tysm in advance :)
ASAP
-will mark brianist
Answer:
C typing 210 words in 5 min
Step-by-step explanation:
We know that in one minute 42 words can be done. So in 5 minutes how much can be done?
I multiplied 42x5 which gave me 210.
I hope this helps
PLEASE PLEASE HELP YA'LL 3RD TIME POSTING AND REALLY NEED HELP!!!! NO LINKS ALLOWED!!
What are the resulting coordinates of triangle X′Y′Z′ after rotating triangle XYZ counterclockwise 90° about the origin? Question options:
A) X′ (1, 1), Y′ (1, 4), Z′ (–4, 4)
B) X′ (1, 1), Y′ (4, 1), Z′ (4, 4)
C) X′ (1, 1), Y′ (1, 4), Z′ (4, 4)
D) X′ (–1, 1), Y′ (1, 4), Z′ (4, –4)
Answer:
C
Step-by-step explanation:
Rotation 90 degrees counter clockwise rule (x,y) -----> ( -y , x )
In order to find the answer we must first find the coordinates of the pre image
The coordinates are...
x (1,-1)
y (4,-1)
z (4,-4)
Now we apply the rule stated previously
( The rule explanation: the x and y values swap and the y values sign changes. So if the y value was previously positive, after a 90° counter clockwise rotation, the y value will then be negative)
x (1,-1) -----> swap x and y values ( -1,1) ------> flip sign of new x value ( 1 , 1 )
y (4,-1) ------> swap x and y values ( -1,4) -----> flip sign of new x value ( 1 , 4 )
z (4,-4) -----> swap x and y values ( -4,4) ------> flip sign of new x value ( 4,4)
the new coordinates are X' (1,1) , Y' (1,4) , Z (4,4)
Hence the answer is C
Rewrite each expression: 2^4 x 2^6 x 2^2
Answer:
16 x 64 x 4
Step-by-step explanation:
2 x 2 x 2 x 2 = 16
2 x 2 x 2 x 2 x 2 x 2 = 64
2 x 2 = 4
The perimeter of a rectangular table is 12 1/3 ft. If the length of the table is 4 ft, what is the area of the table?
Answer:
1/3 is what you are saying for
Write an equation for the line graphed.
A. y=2
B. y=2x
C. y= -2x
D. y=2x+1
Answer:
b
Step-by-step explanation:
the y intercept is zero and there is a positive slope
please help with this.
thanks sm!
Answer:
x= 5cm
5 is the missing side
Find X segment of circles
Answer:
x = 88/45
Step-by-step explanation:
square of tangent segment = produce of entire secant and segment of secant outside circle
(GH)² = GS × GW
(13)² = 9(5x + 9)
169 = 45x + 81
45x = 88
x = 88/45
The tables show the number of hours students
studied and the number of questions answered
correctly on a quiz. Which table shows a
proportional relationship?
beau completed 2/5 of his science project on Friday and 1/3of the project on Saturday what fractional part of his project did she complete during these two days
Answer:
beau completed 2/5 of his science project on Friday
beau completed 1/3 of his science project on Friday
Now
he completed during these two days=1/3+2/5=11/15 part of his project
alot of poins pleas help
Answer:
48 yd
Step-by-step explanation:
19+19+5+5
Answer:
perimeter is length + length + width + width so 19+19+5+5= 48
What is the axis of symmetry for the quadratic equation 4x^2-16x+5 plz help
Answer:
x=2
Step-by-step explanation:
use completeting the square
[tex]4x^2-16x+5=4(x-2)^2-11[/tex]
To convert Celsius to F&nrenheit, multiply the Celsius temperature by 9/5 and
then add 32. The temperature outside is 5 degrees Celsius, what is the
temperature in degrees Fahrenheit?*
66 degrees
20 degrees
63 degrees
41 degrees
Answer:
41
Step-by-step explanation:
9/5 x 5 = 9
9 +32= 41
look at the picture
Answer:
1) √10 units
A=(-1, 0) let us assume (x1, y1)
B=(2, 1) let us assume (x2,y2)
distance= √(x2-x1)^2 + (y2-y1)^2
=√(2+1)^2 + ( 1-0)^2
=√3^2 + 1^2
= √10 units
Solve for the missing angle:
Answer:
47
Step-by-step explanation:
they are corresponding
PLEASE HELP
WILL GIVE BRAINLIEST!!!
Answer:
5/4
Step-by-step explanation:
The problem tells us that 4 equal sections stacked together is 5 feet tall. Thus, we have to find how tall each section is while all sections are equally tall. So, we have to divide 5 feet by 4 equal sections, which is just 5 divided by 4, which is just 5/4 feet tall.
help, please!
A rectangle has a a perimeter of 68 ft. The length and width are scaled by a factor 1.5.
The perimeter of the resulting rectangle is ___ ft.
Answer and Step-by-step explanation:
Answer and Step-by-step explanation:
Here is the equation for finding the sides (just to show):
68 = (2L + 2W)
We multiply L and W by 2 because there are two of the lengths and 2 of the widths.
Now, we add the scale factor to the outside, but on both sides of the equation.
68 × 1.5 = 1.5(2L + 2W)
Multiply 68 by 1.5.
102 = 1.5(2L + 2W)
The answer is 102.
The perimeter of the resulting rectangle is 102 ft.
#teamtrees #WAP (Water And Plant)
Drag each equation to show if it could be a correct first step to solving the equation 3(6+x)=24.
Answer:
Here you go
Step-by-step explanation:
Hope this helps :)
In the diagram, point C represents the center of the sphere. Diego says that the part of the sphere labeled D is the radius. Gregoire says that the part of the sphere labeled D is the diameter of the sphere.
A sphere. C is the center and D is the diameter.
Who is correct and why?
Gregoire is correct; the diameter is a chord that passes through the center of the sphere.
Gregoire is correct; the diameter is a chord that is from the center to the surface of the sphere.
Diego is correct; the radius is a chord that passes through the center of the sphere.
Diego is correct; the radius is a chord that is from the center to the surface of the sphere.
Answer:A
Step-by-step explanation: edg 2021
Gregoire is correct; the part of the sphere labeled D is the diameter of the sphere.
What is a sphere?It is a three-dimensional figure where the volume is given as 4/3 πr³
We have,
The diameter of a sphere is a chord that passes through the center of the sphere and has endpoints on the surface of the sphere.
Therefore, the part of the sphere labeled D in the diagram is the diameter, not the radius.
The radius of a sphere is a chord that is from the center to the surface of the sphere, and it is half the length of the diameter.
Thus,
Gregoire is correct; the part of the sphere labeled D is the diameter of the sphere.
Learn more about Sphere here:
https://brainly.com/question/12390313
#SPJ7
Factor Each Polynomial 18h^4– 27h^2 + 18h
Answer:
[tex]9h(2h^{3} -3h+2)[/tex]
Step-by-step explanation:
Factor 9h out of 18h^4 - 27h^2 + 18h.
Find the length of the hypotenuse of the triangle.
1mm 4/5mm c
Answer: 169/225 (0.75 2d.p)
Step-by-step explanation:
c²=a²+b² as C is Hypotenuse (largest side)
c²=(1/3)² + (4/5)²
c²= 1/9 + 16/25
c=169/225
Find the average of the bowling scores 135, 185, 160, and 148
Answer:
157
Step-by-step explanation:
135+185+160+148 =628
628÷4 = 157
Which line segment is congruent to BC?
GEOMETRY HELP PLS!!!
Answer:
PR
Step-by-step explanation:
find the area of the kite.
A. 27 square units
B. 40 square units
C. 18 square units
D. 36 square units
Answer:
36 unit^2.
Step-by-step explanation:
The area is the sum of the 2 triangles with each having base between the points (-2,4) and (-2,-4).
The base is4 - -4 = 8.
Area of a triangle = 1/2 * base * height.
Area of the kite = 1/2 * 8 * 3 + 1/2 * 8 * 6
= 12 + 24
= 36.
11. Simplify 3/ 2 - /2
answer:
you can't simplify that
step-by-step explanation:
3/2- /2 isn't a proper equation, therefore it cannot be simplified
please let me know if the issue is that you forgot the numerator, and in the instance that this is the case please type in the comments the numerator and i'll gladly change my answer
have a nice day!
You have no more than 15 hours this week to spend reading a book and
writing in your journal. Write and graph an inequality describing the
possible amounts of time you can spend reading and writing this book.