PRECALCULUS HELP IM BEGGING YOU
Dean has built a ferris wheel in his backyard. It has a diameter of 10 feet and completes 30 revolutions per minute. Sketch a quick graph and find the period of the function that describes the height above the ground of a seat on the outside edge of this ferris wheel.
Answers
Answer: Period = 2 seconds
Graph is shown below
========================================================
Explanation:
1 minute = 60 seconds
We have 30 revolutions every 60 seconds, so we can write the ratio
30 rev: 60 sec
Divide both parts by 30 to turn that "30 rev" into "1 rev"
30 rev: 60 sec
30/30 rev: 60/30 sec
1 rev : 2 sec
This tells us that each full revolution takes 2 seconds. This is the period of the ferris wheel. The period is the length of each cycle.
The cyclic or periodic nature of this motion heavily implies we'll be dealing with a sine or cosine function of some kind. Let's go with sine.
Side note: cosine is really a sine function in disguise (it's just a phase shifted version of it).
---------------------
The general sine curve equation is
y = A*sin(B(x-C)) + D
where
|A| = amplitudeB = 2pi/T with T being the periodC handles phase shifts (left and right shifting)D handles vertical shifting, and y = D is the equation of the midline---------------------
The wheel is 10 feet in diameter, so 10/2 = 5 is the radius. This is also the amplitude because it is the distance from the midline to either the highest point (10 ft) or lowest point (0 ft). So A = 5.
Since T = 2 is the period, this means,
B = 2pi/T
B = 2pi/2
B = pi
We don't have any phase shifts to worry about so C = 0.
The midline is D = 5 since this is halfway up
----------------------
Putting all the pieces together, we get this sine equation
y = A*sin(B(x-C)) + D
y = 5*sin(pi*(x-0)) + 5
y = 5*sin(pi*x) + 5
The graph is shown below.
x = time in seconds, y = height of the seat
Related Questions
if m^1=m^2 then m^ 1 is?
Answers
Answer:
90
Step-by-step explanation:
The London School of Economics and the Harvard Business School have conducted studies of how chief executive officers (CEOs) spend their time. These studies have found that CEOs spend many hours per week in meetings that include conference calls, business meals, and public events. Suppose that the data below show the time spent per week in meetings (hours) for a sample of 25 CEOs.
14 15 18 23 15
19 20 13 15 23
23 21 15 20 21
16 15 18 18 19
19 22 23 21 12
a. What is the least amount of time spent per week on meetings? The highest?
b. Use a class width of two hours to prepare a frequency distribution, a relative frequency distribution, for the data.
Answers
Answer:
(a) The least amount of time spent per week on meetings is, 12 hours.
The highest amount of time spent per week on meetings is, 23 hours.
(b) Shown below.
Step-by-step explanation:
(a)
Arrange the data in ascending order.
S = {12 , 13 , 14 , 15 , 15 , 15 , 15 , 15 , 16 , 18 , 18 , 18 , 19 , 19 , 19 , 20 , 20 , 21 , 21 , 21 , 22 , 23 , 23 , 23 , 23}
The least amount of time spent per week on meetings is, 12 hours.
The highest amount of time spent per week on meetings is, 23 hours.
(b)
The frequency distribution table with the relative frequency distribution is as follows:
Class Interval Frequency Relative Frequency
12 - 14 3 0.12
15 - 17 6 0.24
18 - 20 8 0.32
21 - 23 8 0.32
Total 25 1.00
Jack and Jillian sell apples at a produce stand. Jillian earns $2 for each bag of apples she sells. At the end of the week, Jack has earned $8 less than Jillian. The following expression shows Jack's earnings:
2x − 8
In the expression, what does the first term represent?
Answers
Answer:
2(x-4)
Step-by-step explanation:
it's the only thing i could think of, or its one
Answer:
Jillian's earnings at the end of the week
Find the rate of change between:
(-4, 0)
(-4, 2)
Answers
Answer:
Its increasing the y value by 2 everytime
Step-by-step explanation:
-4,0 + 0,2 = -4,2
-4,2 + 0,2 = -4,4
to understand the increasing value add 2.
All of the following are rational except
Sqrt 0.49
Sqrt 19
Sqrt 900
Sqrt 100
Answers
Answer:
0.49
Step-by-step explanation:
for it to be rational there should not be no decimal nor pi .
how to graph a line with slope 2 passing through the point (2, -1)
Answers
What is 837 divided by 36?
Answers
Answer:
23.25 you will just divide it
Step-by-step explanation:
Simplify -6 to the power of 2 divided by 12- 2(-7).
Answers
Answer: 18
Step-by-step explanation: -36 / -2 simply
HELLLLLLLLPPPPPPPPPPPP!!!!!!
Answers
Answer:
3 bars of soap and 2 toothbrushes.
Step-by-step explanation:
A chef needs 60 oz of hot pepper sauce.
Which container size represents the better buy?
What will be the total cost of those containers?
Answers
Answer:
30-oz is a better buy
Total cost: $40.80
Step-by-step explanation:
The container with a lesser price per oz will be the better buy.
Let's calculate how much each container will give us per oz:
2-oz container = $1.99/2 = $0.995 per oz
5-oz container = $3.95/5 = $0.79 per oz
12-oz container = $8.76/12 = $0.73 per oz
30-oz container = $20.40 = $0.68 per oz
The 30-oz container is cheaper and would be a better buy.
In total the chef would buy 60-oz of hot pepper sauce for = 60-oz*$0.68 = $40.80
7.86÷0.2
I need you to answer with step by step explaination
Answers
2. The equation became 78.6/2
3. Divided 7/2, got 3
4. Divided 8/2, got 9
5. Put the decimal point on the preferred spot
6. Divide 6/2, got 3
7. 78.6/2 equals 39.3
A large automobile insurance company selected samples of single and married male policyholders and recorded the number who made an insurance claim over the preceding three-year period.
Single Policyholders Married Policyholders
n1 = 900 n2 = 400
Number making claims = 135 Number making claims = 24
Required:
a. Use a level of significance α = 0.05. Test to determine whether the claim rates differ between single and married male policyholders. Explain your determination.
b. Provide a 95% confidence interval for the difference between the proportions for the two populations.
Answers
Answer:
Step-by-step explanation:
Given the following :
Single policy holders (n1) = 900
Number making claims (x1) = 135
Married Policy holders (n2) = 400
Number making claims (x2) = 24
α = 0.05
a. Use a level of significance α = 0.05. Test to determine whether the claim rates differ between single and married male policyholders. Explain your determination.
Null: p1 - p2 = 0
Alternative : p1 - p2 ≠ 0
p = (n1p1 + n2p2) / n1 + n2 ;
p1 = x1/n1 = 135 / 900 = 0.15
p2 = x2/n2 = 24 / 400 = 0.06
p = (900*0.15 + 400*0.06) / (900 + 400)
p = 0.1223076
Test statistic (z):
(p1 - p2) / √p(1-p)(1/n1 + 1/n2)
(0.15 - 0.06) / √0.12231(1-0.12231)(1/900 + 1/400)
= 4.5710979
Decision:
Reject Null if P < α
Obtaining p value from z score using calculator :
P value = 0.0001
0.0001 < 0.05
Hence,
Reject Null
Quick I need help.....
Answers
Answer:
C
Step-by-step explanation:
Subtract both sides by 2
2-2 is 0
-10 - 2 is 12
-3x < 12
Divide both sides by -3
Switch signs cause dividing a negative
x > -4
decrease of 65% is the same as multiplying by what
percent?
Answers
Answer:
35%
Step-by-step explanation:
A decrease of 65% would be the same as multiplying the value by 35%.
100% - 65% = 35%
Let's use an example.
You have $150 dollars in stock and it decreases by 65%
150 - (.65*150) =
150 - 97.5 = $52.50
Now let's just multiply $150 by .35 (which is 35%)
150 * .35 = $52.50
It's the same!
rounded to the nearest thousandth, the number 0.0000741
Answers
Answer:
.000
Step-by-step explanation:
Helllllllllllllp meeeeeeee I’m an idiotttttt
Answers
Answer:
3(4 + 3x)
distribute the 3 into both numbers
3*4
3*3x
9x +12
Step-by-step explanation:
1. Lori drove 141 miles in 3 hours. What was Lori’s average rate of speed?
Answers
Answer:
47 miles per hour
Step-by-step explanation:
The average rate of speed is the miles divided by the hours
141 miles / 3 hours
47 miles per hour
Answer:
47
Step-by-step explanation:
141 / 3
Which construction is partially represented by the diagram on the baseball field? Explain the next set of instructions to correctly finish the construction.
Answers
Answer:
Construction of an angle bisector is partially represented by the diagram on the baseball field.
Step-by-step explanation:
Angle bisector of an angle bisects it into two equal angles.
Construction of an angle bisector is partially represented by the diagram on the baseball field.
Consider the figure:
From point B, draw an arc by opening the compass up to the same extend as we did while drawing arc from point A.
Take the point of intersection of both the arcs as C.
Join OC.
OC is the angle bisector of the angle.
Two dice are tossed. The probability that the total score is a prime number is:
Answers
Step-by-step explanation:
50/50 it's random I think but I learned that in science
Jonas has 20 coins, all nickels and dimes. The total value is $1.25. If n represents the number of nickels, which algebraic equation represents this situation?
A. 20n = 125
B. 5n = 1.25
C. 5n + 10(20 - n) = 125
D. 5n + 10n - 20 = 125
Answers
Answer:
a
Step-by-step explanation:
what if f(0)?
12 only
2 and 3 only
-2,-1,1 and 2 only
-2,-1,1,2 and 12
Answers
Answer:
12 only
Step-by-step explanation:
I did the test
Derek tried to solve an equation step by step.
\begin{aligned} 8d&=72\\\\ \dfrac{8d}{8}&=\dfrac{72}8&\green{\text{Step } 1}\\\\ d&=8&\blue{\text{Step } 2} \end{aligned}
8d
8
8d
d
=72
=
8
72
=8
Step 1
Step 2
Find Derek's mistake.
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
\green{\text{Step }1}Step 1start color #28ae7b, start text, S, t, e, p, space, end text, 1, end color #28ae7b
(Choice B)
B
\blue{\text{Step }2}Step 2start color #6495ed, start text, S, t, e, p, space, end text, 2, end color #6495ed
(Choice C)
C
Derek did not make a mistake.
Answers
Answer:
Step-by-step explanation:
[tex]\begin{aligned} 8d&=72\\\\ \dfrac{8d}{8}&=\dfrac{72}8&\green{\text{Step } 1}\\\\ d&=8&\blue{\text{Step } 2} \end{aligned}[/tex]
Derek's Mistake ;
[tex]\frac{8d}{8} =\frac{72}{8} \\\\[/tex]
Reason ;
[tex]72\div 8 =9 \\\\So ; d = 9[/tex]
Answer:
Step 2 - d=8
Step-by-step explanation:
72/8 equals 9 not 8
Which of the following expressions has the greatest value? A. 62 O B. 53 O c. 52 O D. 32
Answers
Answer:
A. 62
Step-by-step explanation:
At the beginning of the quarter there were 40 students in our class. At the final exam, there are only 32 students left. By what percent did the class size decrease? by 96
Answers
Answer:
20 % decrease
Step-by-step explanation:
First find the number of students that left
40 -32 = 8
Take the number of students that left and divide by the original number of students
8/40
1/5
.20
20%
20 % decrease
Answer:
20% decrease ._.
Step-by-step explanation:
If u could subscribe to my friend penny_pg3d on YT, that would be great :)
A basketball player scored 30 times during one game. she scored total of 50 points, two for each two point shot and one for each free throw. How many two point shots did she make? How many free throws
Answers
Answer:
it is 20
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
49 points in seven games unit rate
Answers
Answer:
7
Step-by-step explanation:
1. Do 49÷7 to get the average of 7
A farmer has a total of 7725. Corn plants he wants to plant 40 corn plants in each row how does the following work in long division
Answers
Answer:
The answer is B
Step-by-step explanation: Let me know if you need an explanation.
Which pair of triangles is congruent by ASA?
Answers
8/x = 5/9 solve for x
Answers
i gotchu, x = 14.4
8/x = 5/9 (solve for x)
first you'd cross multiply (property of multiplication)
(8)(9) = (5)x
72 = 5x
then you flip your equation (communitive property)
5x = 72
then you need to eliminate five so you'd divide by 5 (inverse operation)
5x/5 72/5
x = 72/5
so x would be 14.4 since 72/5 is 14.4
(or just 14 since if you rounded it your answer would be 14)
A bag has 5 yellow marbles, 3 red marbles and 2 blue marbles. Quinn randomly picks a marble from the bag and returns it before another is picked. How many times would Quinn expect to pick a blue marble if he picks a marble 200 times?
Answers
Answer:
Quinn can expect to pick blue 40 times
Step-by-step explanation:
the probability of picking blue is stated as 2/10 which can be reduced to 1/5
multiply the number of times they pick a marble ( shown as 200) by the probability of picking a blue one ( 1/5)
200 x 1/5 = 200 / 5 = 40
Quinn can expect to pick blue 40 times
Answer:40 blue marbles
Step-by-step explanation:
First find the probability of a blue marble
P (blue) = number of blue marbles / total marbles
= 2 blue/ ( 5+3+2) total
= 2/10
=1/5
We can use this since we return the marble to the bag each time
We multiply this by 200 for the number of times it is picked
200 * 1/5 = 40
We should expect to pick 40 blue marbles