Mary is the last person to get on a ferris wheel ride at a fair (the ride begins once she is on). The ferris wheel has a radius of 8 metres and has riders walk up stairs 2 metres off the ground to board. If Mary reaches the top of the ride after 1 minute... a.) Sketch 1 full cycle of the ferris wheel ride & determine an algebraic representation.
b.) Nearby trees obstruct people's view during the ride. The view is only enjoyable when someone is above a height of 12m. Determine for how long Mary will be able to enjoy the scenery if the ride is 4 minutes long.
Answers
Answer:
a) For sketch see attached picture.
[tex]y=-8cos(\pi t)+10[/tex]
b) Mary will be able to enjoy the scenery for a total of 1.68 min or about 101 seconds.
Step-by-step explanation:
a) In order to find the algebraic representation of the problem, we must start by drawing a sketch of what the problem looks like (see attached picture). Next, we can analyze it to see what function better fits the situation. In this case, since the ride starts at the lowest point, then we are talking about a negative cos function. A cos function has the followng general form:
[tex] y= Acos(\omega t - \phi) + C[/tex]
where:
A= amplitude
[tex]\omega[/tex]=angular speed
t=time
[tex]\phi[/tex]= phase shift
C= vertical shift.
In this case the amplitude will be the radius of the ferris wheel, so:
A=-8
it's negative because it starts at the lowest point.
the angular speed is the angle the ride will move in a given amount of time. In this case:
[tex]\omega=\frac{\pi rad}{1 min}[/tex]
[tex]\omega=\pi rad/min[/tex]
There will be no phase shift for this problem.
the vertical shift is the height of the platform, so:
C= 2
so the algebraic expression is:
[tex]y=-8cos(\pi t)+10[/tex]
b) In order to find the total time for which she will enjoy the ride we must start by building an inequality:
[tex]-8cos(\pi t)+10>12[/tex]
and solve it for t. We can start by turning it into an equation, solve it for t and find the answers that can be found into its domain, in this case D=[0,4]
so we get:
[tex]-8cos(\pi t)+10=12[/tex]
we subtract a 10 from both sides so we get:
[tex]-8cos(\pi t)=2[/tex]
and divide 8 to both sides so we get:
[tex]cos(\pi t)=-\frac{1}{4}[/tex]
Next, we take the inverse cosine to both sides and get different answers:
[tex]\pi t = 1.823+2\pi n[/tex]
and
[tex]\pi t=4.46 + 2\pi n[/tex]
we take both equations and divide them into pi so we get:
[tex]t = 0.58+2 n[/tex]
and
[tex]t=1.42 + 2n[/tex]
so now we find the possible answers that are between 0 and 4 minutes, this is for n=0 and 1, so we get the following times:
t={0.58, 1.42, 2.58, 3.42} min
we can now build our possible intervals for which the ferris wheel is higher than 12 m so we get the following intervals:
(0, 0.58) (0.58, 1.42) (1.42, 2.58) (2.58, 3.42) and (2.58, 4)
so we pick a test value for each of the intervals and test it on our equation. If the equation gives us a number that is greater than 12, then we have a valid interval. If we get a value that is less than 12, then we just discard that interval.
for (0, 0.58) we use 0.5 and get an answer of 10. We discard this interval.
for (0.58, 1.42) we use 1 and get an answer of 18. This is a valid interval.
for (1.42, 2.58) we use a 2 and get an answer of 2. We discard this interval.
for (2.58, 3.42) we use a 3 and get an answer of 18. This is a valid interval.
and finally, for (2.58, 4) we use a 3.5 and get an answer of 10. We discard this interval
So we have two valid intervals now: (0.58, 1.42) and (1.42, 2.58). So now we can use them to find the time for which Mary will enjoy the scenery.
[tex]t_{1}=1.42min-0.58min=0.85min[/tex]
[tex]t_{2}=2.58min-1.42min=0.85min[/tex]
[tex]t_{total}=0.85min+0.85min[/tex]
[tex]t_{total}=1.68min[/tex]
so:
Mary will be able to enjoy the scenery for a total of 1.68 min or about 101 seconds.
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Step-by-step explanation:
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Step-by-step explanation:
The high temperature, in ∘C, on the first day of winter was recorded in a certain city every year from 1915 to 2015. The following six temperature values were randomly selected from the data.
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Answers
Answer:
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Step-by-step explanation:
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Criteria must include lowest and highest temperature to reflect 100 years and so population standard in lower set data would reflect a reliable calculation.
As the condition has mentioned in the problem , population standard deviation would be prefer for this data set
Temperature range for year 1915 to 2015 has been given in question
= 4, 12, 6, 9, 6, 11
The standard deviation is used to calculate the spread of values in the set of data.
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mean = 8
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σ= population standard deviation
N= population size
xi= each value from the population
μ = population mean
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=8
since the range is very small difference to its extreme points on sets of temperature relative b the year difference which is a century i.e, 100 years . Though, Its implies formula that has been mentioned above which is of standard deviation for population shows the perfect calculation for this lower range of temperature gives the precise information of the spread.
Thus, Population standard deviation would be preferred for the further calculations.
Learn more about Standard deviation here:
https://brainly.com/question/14747159
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
Multiply those together and combine like terms. Then make sure you order the terms in descending powers.
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answers
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Answer:
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Step-by-step explanation:
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Answers
Answer:
x = -14Step-by-step explanation:
Given the equation
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1/4x +4 - 4 = 1/2 - 4
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Cross multiply
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Answers
Answer:
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Nth term of this quadratic sequence 2,8,18,32,50
Answers
Answer:
2n²
Step-by-step explanation:
2 , 8 , 18 , 32 , 50
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Second difference = 4 , 4 , 4
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a.
21
3
Х
4
Please hurry it’s missing
Answers
Answer:
1 7/8
Step-by-step explanation:
Convert the mixed number into an improper fraction
2 1/2 = 5/2
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Multiply across (numerator and numerator, and denominator with denominator)
5 * 3 / 2 * 4
15/8
Convert the improper fraction to a mixed number
1 7/8
Hope this helped!
Have a supercalifragilisticexpialidocious day!
One alloy is 2 parts iron and 3 parts silver and another alloy is 7 parts iron to 3 parts silver. How much of each should be combined to produce a 30 pound alloy that is one part iron to one part silver
Answers
Answer:
Let x be your first alloy
2/5x+7/10(30-x)=1/2(30)
4x+210-7x=150
3x=60
x=20
So, you need 20 lbs of the first alloy, and 10 parts of the second to make 30 lbs of half iron and half silver alloy
Answer:
20 pounds for first 10 for second.
Step-by-step explanation:
Tara ran 3 laps around her neighborhood for a total of 1 mile yesterday today she wants to run 2/3 of a mile. How many laps will she need to run around her neighborhood?
Answers
Answer:
2
Step-by-step explanation:
Huilan's age is two times Thomas's age. The sum of their ages is
72
. What is Thomas's age
Answers
Thomas age = 2x
x + 2x = 72
3x = 72
x = 24
2x = 48
Thomas is 48 years old
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Answers
Answer:
You need to add a picture
Step-by-step explanation:
But to find the vectr you basically need to count the squares from each of the shapes going up or down
For example:
- squares going down would be -x
- squares going up would be x
- squares going left would be -x
- squares goinf right would be x
Then you put it in the form of a fraction
the quadratic formula
Answers
Answer:
(-b±√(b²-4ac))/(2a)
Step-by-step explanation:
Answer:
This is my alt
Step-by-step explanation:
Question 3
(06.01 MC)
1
What is the value of the expression 10 + ( 2 )4.48? (1 point)
a
12
b
13
С
16
d
18
HELP! I will give brainliest.
Answers
Answer:
The answer is 18.96 or in your case d.18
Step-by-step explanation:
10+ (2) 4.48
10+ 8.96
= 18.96
Blank divided by 6=0.2
Answers
So the answer is 1.2
I think
Evaluate
Explain
A.5/6×10/11=
B. 9÷1/4=
D. 9/4 -2/3=
E. 1/5÷3=
Please explain your answers
Answers
Step-by-step explanation:
Multiplication of fractions is easiest operation. Simply multiple numerator to numerator and denominator to denominator. For example,
[tex]\frac{x}{y} * \frac{a}{b }= \frac{x*a}{y*b}[/tex]
Addition and subtraction requires that we find a common demoninator.
For example,
[tex]\frac{6}{4} + \frac{4}{3}[/tex]
The common denominator is 12. So I need to muliply each fraction to get the right denominator. 4*3 = 12.
[tex]\frac{6}{4}*\frac{3}{3} + \frac{4}{3} \frac{4}{4} = \frac{18}{12}+\frac{16}{12}[/tex]
Then we add the numerators
[tex]\frac{18+16}{12} = \frac{32}{12}[/tex]
Then we should reduce.
[tex]\frac{16}{6} = \frac{8}{3}[/tex]
Division is a little trickier because we have to flip-flop the second term and then multiply. For example: [tex]\frac{1}{10} \div \frac{5}{6} \rightarrow \frac{1}{10} * \frac{6}{5} = \frac{6}{50}[/tex]
use the distributive property to write an equivalent expression 3(v-9w+1)
Answers
Answer:
3v-27w+3
Step-by-step explanation:
3(v-9w+1) move the term in the parentheses by 3
then calculate 3v-3x9w+3 to get your solution which is 3v-27w+3
