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:
Are these two lines parallel?
y = 3x – 2
X 0 1 2 3
y3 6 9 12
Yes
No .
Answer:
Yes
Step-by-step explanation:
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.
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
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.
-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 ♡
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.
Rachel had 36 quarters. If it costs 4 quarters for each coke from a coke machine, how many could she buy?
<3 pwease help will do anything lol <3
2. A 480 Ω resistor is connected in series to a 360 Ω resistor and a 120-V power supply.
a. Draw the circuit.
b. Calculate the equivalent resistance of the circuit.
c. Calculate the current through the battery.
d. How much current is passing through each resistor?
e. Calculate the voltage drop across each resistor.
f. How does the voltage drop across each resistor compare to the voltage of the battery
I just answered a so let's start with b :
______________________________
b. The equivalent resistance of series
resistances is equal to their sum
Thus :
equivalent resistance = 480 + 360
equivalent resistance = 840
_______________________________
c.
I = V ÷ R
I = 120 ÷ 840
I = 0.1428 A
_______________________________
d. 0.1428 A
_______________________________
e. 480 ===》 120 - ( 480 × 0.1428 ) =
120 - 68.544 =
51.456
360 ===》 120 - ( 360 × 0.1428 ) =
120 - 51.408 =
68.592
_______________________________
f. 480 ===》68.544 lower than battery
360 ===》 51.408 lower than battery
hi! please help i’ll give brainliest
Answer:
third option mechanical weathering
Step-by-step explanation:
in mechanical weathering it breaks the rock into smaller pieces . these smaller pieces are just like the bigger rock , just smaller .
Answer: Mechanical weathering
Step-by-step explanation:
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:
Which characteristic does the graph display? A) Odd function
B) even function
C) neither even nor odd
Answer:
B is correct option
Step-by-step explanation:
The graph of an even function is symmetric about the y-axis. The graph of an odd function is symmetric about the x-axis. It is possible that the use of these two words originated with the observation that the graph of a polynomial function in which all variables are to an even power is symmetric about the y -axis.
ABC has vertices at A(3.2), B(1.4), and C(2.7).
What will be the new vertices after a 90° counter clockwise rotation about the origin?
Answer:
A = 1,4
B = 2,1
C = -4,-5
Step-by-step explanation:
The 90 degree anticlockwise rotation around the origin (0,0) would over lap the y axis around 1 and due to this the formation would show C point at -4,-5
Which statement is true?
A) function is a relation where each output value is assigned to exactly one input value.
B) The domain of a function is the set of all output values, or y-values, for which the function is defined.
C)The range of a function is the set of all input values, or x-values, for which the function is defined.
D)To write the equation y = ax + b in function notation, substitute f(x) for y.
Answer:
D
Step-by-step explanation:
Answer: D
Step-by-step explanation:
A function is a relation where each input value is assigned to only one output value.
The domain of a function is the set of all input values, or x-values, for which the function is defined.
The range of a function is the set of all output values, or y-values, for which the function is defined.
Which A, B, & C are wrong. So D, is the one that makes the most sense.
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:
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.
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.
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
Solve for x in the triangle. Round your answer to the nearest tenth.
Answer:
x=28.9
Step-by-step explanation:
tan(61)=x/16
10ft/2in simplified so the units are the same
Simplify 12 − 32 + (5 − 1)2.
A) 12
B) 18
C) 19
D) 97
12-32+[5-1]x2
-20+4x2
-20+8
=-12
The simplified form of the given expression is -12. Therefore, option A is the correct answer.
What is simplify?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
The given expression is 12-32+(5-1)2.
Here, 12-32+4×2
= -20+8
= -12
Therefore, option A is the correct answer.
Learn more about the simplification here:
brainly.com/question/2804192.
#SPJ6
Which situations can be modeled by a linear function?
Answer:
A, C, E
Step-by-step explanation:
Escribir un 8% como un decimal
Answer:
8% como un decimal es 0.08%
Espero que te ayude!
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:
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:
396 divided by 11. Step by step explanation
Answer: 36
Step-by-step explanation: using long division you take 11 divide into 398 so first, 11 goes into 39, 3 times
you have 6 left, so keep the 6 and drop down the other 6
next 11 goes into 66, 6 times making it 396/11= 36
hope this helps
Answer:
36
Step-by-step explanation:
396 divided by 11 is equal to 36
36
11/[tex]\sqrt{396\\}[/tex]
- 33
066
- 66
0
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
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
what is the value of y2 -x2 when y=6 and x=5
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