The Sea Dragon, a pendulum ride at an amusement park, moves from its central position at rest according to the trigonometric function P(t)=−10sin(pi/3t), where t represents time, in seconds. How many seconds does it take the pendulum to complete one full cycle?
A= 3
B= 5
C= 6
D= 10
Answers
Answer:T = 2*Pi / (Pi / 3) = 6 seconds
Step-by-step explanation:
The time (in seconds) that it take the pendulum to complete one full cycle is given by: Option C: 6 (seconds)
What is the period of sine function?Trigonometric functions are periodic. They repeat their values after some specific constant input interval (constant depends on the trigonometric function chosen).
For sine function, its period is 2π
Thus, we get:
[tex]y = \sin(x) = \sin(x+2\pi) = \sin(x + 2\pi n) ; n \in \mathbb Z[/tex] integer, and y is some constant at some constant value of x)
For this case, the pendulum's motion is modeled by:
[tex]P(t) = -10\sin\left(\dfrac{\pi}{3} t\right)[/tex]
Let it takes 'd' seconds to do one full cycle, then we get:
[tex]P(t) = P(t+d) = P(t+2d) = P(t + nd); n \in \mathbb Z - \mathbb Z^{-}[/tex] (n is non-negative integer).
Using the formula, we get:
[tex]-10\sin\left(\dfrac{\pi}{3} t\right) = -10\sin\left(\dfrac{\pi}{3} (t + nd)\right)\\\sin\left(\dfrac{\pi}{3} t\right) =\sin\left(\dfrac{\pi}{3}t + \dfrac{\pi}{3}nd\right)[/tex]
But we know that:
[tex]\sin\left(\dfrac{\pi}{3} t\right) =\sin\left(\dfrac{\pi}{3}t +2\pi n\right)[/tex]
Thus, we get:
[tex]2\pi n = \dfrac{\pi}{3}nd\\[/tex] (compared for non-negative values of n)
This gives:
[tex]d = \dfrac{2\pi n \times 3}{\pi n} = 6[/tex] (in seconds)
Thus, the time (in seconds) that it take the pendulum to complete one full cycle is given by: Option C: 6 (seconds)
Learn more about periodic functions here:
https://brainly.com/question/12529476
Related Questions
Henry painted a picture of his house on canvas. The actual width of
the driveway is 20 feet. If it is represented with a width of 4 inches on
the canvas, what was the scale factor used?
Answers
Answer:
The scale factor would be -5.
Step-by-step explanation:
If the driveway is 20 feet but 4 foot on the canvas. Then 20/4 is 5. But since the width is going from 20 to 4, the numbers are going down to it would be a negative scale factor. If it was going from 4 width to 20 width, the scale factor would be a positive 5.
What is the initial value?
A. -8
B. -5
C. 0
D. 7
Answers
Answer:
A. -8
Step-by-step explanation:
Given the values of the function in a table, to determine the initial value of the function, you need to determine where x = 0.
Since the function is linear, the rate of change will be constant/the same.
To find the rate of change, you need to divide the change in the y value by the change in the x value.
X Y
+2↓ -5 | 7 ↓ -6
+2↓ -3 | 1 ↓ -6
+2↓ -1 | -5 ↓ -6
1 | -11
_____________
Since y changes by -6 and x changes by +2 every time, ∆Y/∆X = -6/+2 [Reduce] = -3/+1.
Slope = -3.
This means that y will decrease by 3 units every increase of 1 unit in x.
If (-1, -5) is a point which means that -1 is x when -5 is y.
We can apply the rate of change to see where x = 0.
So -5 + 1(-3/+1) → -5 + -3 = -8
Which of the following could be a rational number
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What are the options???
the local market is selling a pound of bananas for $0.55. if you bought 8 bananas for $1.44, what is the unit rate?
Answers
Answer:
$0.18
Step-by-step explanation:
Given that :
Number of bananas purchased = 8
Cost at which the 8 bananas were purchased = $1.44
The unit price of bananas can be obtained using the relation :
Total Cost of bananas / number of bananas
Unit price = $1.44 / 8
Unit price = $0.18
Price per unit of banana = $0.18
Find the distance between the points (-8, -3) and (-2, 5). Hint: Use the Pythagorean theorem.
Answers
Answer:
1/5
Step-by-step explanation:
Use Pythagoras theorem
Carol has had a $145,000 fixed mortgage for 5 years at 5.5% and is
considering refinancing. She can now get an 80/20 mortgage with 4.5% and
9.5% interest, respectively. Based only on this information, should she
refinance?
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Answer: no the two blended interest rates are the same
Step-by-step explanation:
Answer:
no, the new blended rate is higher than the old interest rate
Step-by-step explanation:
bc i said so
Enter 4/5 and 1/3 as a pair of equivalent fractions with the least common denominator between the two fractions.
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Answer:
x is 20
Step-by-step explanation:
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Sunny can read 60 pages in 5 hours how many pages can he read in 7 hours
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Answer:
i will help
Step-by-step explanation:
the answer is 91 do the math bro
you welcome
Find the area of the circle
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i think the answer is 87.82
Sandra bought a pair of leather boots that were marked down by 20%. The original cost of the boots was $150. What did Sandra pay for the boots
Answers
Answer:
130 maybe
Step-by-step explanation:
Answer:
120
Step-by-step explanation:
It is 120 because if you do 20% of 150 that's 30 so subtract that with 150 leaving you 120.
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Answer:
1. 48ft
2. 28 inches
Step-by-step explanation:
1. 6x8=48
2. 4x7=28
It cost Erica $9.75 for the ingredients to make 30 cupcakes. She sold them for $1.00 each. What was Erica’s total profit?
STEP BY STEP PLZZ PLEASE PLZZZZZ
Answers
Answer:
$30 (I think)
Step-by-step explanation:
because you have 30 cupcakes and selling 1 for a dollar but it may be $20.25 if you have to subtract the $9.75 that you used to buy the cupcakes
1 5/16 + 1 5/16=_____
Answers
Answer:
2 10/16 or 2 5/8
Step-by-step explanation:
You can add the whole numbers first, so 1+1=2
Now add the remaining fractions: 5/16 +5/16=10/16.
2+10/16=2 10/16 or 2 5/8.
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Answer:
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Step-by-step explanation:
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Answers
Answer:
84
Step-by-step explanation:
x12
Simplify ———
x14
Dividing exponential expressions :
1.1 x12 divided by x14 = x(12 - 14) = x(-2) = 1/x2
Final result :
1
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x2
If there are 48 oranges then how many apples are there?
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Answer:
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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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You want to wrap a gift shaped like the regular triangular prism shown. How many square inches of wrapping paper do you need to completely cover the prism?
length 11 in
height 8.7 in
width 10 in
Answers
Find the quotient. Write your answer in scientific notation, (3.6 x 10 to the power of 7) divided by (7.2 times 10 to the 7)
Answers
Given:
The given expression is:
[tex]\dfrac{3.6\times 10^7}{7.2\times 10^7}[/tex]
To find:
The value of the quotient.
Solution:
We have,
[tex]\dfrac{3.6\times 10^7}{7.2\times 10^7}[/tex]
It can written as:
[tex]=\dfrac{3.6}{7.2}\times \dfrac{10^7}{10^7}[/tex]
[tex]=\dfrac{1}{2}\times 1[/tex]
[tex]=0.5[/tex]
It can be rewritten as:
[tex]=5\times \dfrac{1}{10}[/tex]
[tex]=5\times 10^{-1}[/tex]
Therefore, the value of the quotient is [tex]5\times 10^{-1}[/tex].
The question is right there please read and help I’ll give u Branliest plz
Answers
Second ((-4,4)
Third (0,2)
The formula for reflection over y axis is (x,y)—-> (-x,y)
You can just change the x value to its opposite and that is the coordinate over the y axis.
A pieces of wire was 12.36 centimeters long. Thelma cut the wire into 6 pieces of equal length. What was the length of each piece of wire in centimeters?
Answers
Answer:
2.06cm
Step-by-step explanation:
Given data
Length of wire= 12.36cm
We are told that it was cut into 6 pieces
Hence, the length of a piece is
=12.36/6
=2.06cm
Therefore, the answer is 2.06cm
Emma is a professional cyclist. For the past year she has been practicing to ride as far as she can in a minute. At the beginning of the year, her personal record was 5/6 of a kilometer in one minute. After six months, she improved her record by 1/15 of a kilometer. After a year, she further improved her record by 1/12 of a kilometer. What is her best record?
Answers
Step-by-step explanation:
5/6+1/15+1/12in on minute
Emma's best record is 59/60 kilometers per minute.
Given that, Emma personal record was 5/6 of a kilometer in one minute.
What is addition of two fractions?To add fractions there are three simple steps:
Step 1: Make sure the bottom numbers (the denominators) are the same. Step 2: Add the top numbers (the numerators), put that answer over the denominator.
Step 3: Simplify the fraction (if possible)
Given, after six months, she improved her record by 1/15 of a kilometer. After a year, she further improved her record by 1/12 of a kilometer.
Now, 5/6 + 1/15 + 1/12
LCM of denominators 6, 15 and 12 is 60.
50/60 + 4/60 + 5/60
= 59/60
Therefore, Emma's best record is 59/60 kilometers per minute.
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drawing a vowel from letter tiles that spell out MATHEMATICS
chance
Blank 1:
Blank 2:
Answers
Given:
Drawing a vowel from letter tiles that spell out MATHEMATICS.
Chances = [tex]\dfrac{?}{?}[/tex]
To find:
The correct values for the blanks.
Solution:
Vowels are a, e, i, o, u.
In MATHEMATICS, the vowels are A, E, A, I.
Number of vowels = 4
We know that,
[tex]Probability=\dfrac{\text{Number of selected vowels}}{\text{Total number of vowels}}[/tex]
[tex]Probability=\dfrac{1}{4}[/tex]
So, the chance of drawing a vowel from letter tiles that spell out MATHEMATICS is [tex]\dfrac{1}{4}[/tex].
Blank 1: 1
Blank 2: 4
Therefore, the value for blank 1 is 1 and the value for blank 2 is 4.
Find the perimeter of the figure at right(picture). Use 3.14 as an estimate for π
Answers
Answer:
54.88cm
Step-by-step explanation:
For shaded region perimeter, subtract the circle perimeter from the rectangle
perimeter
= (10*8) - (2 * 3.14 * 8/2)
= 80 - 25.12
= 54.88cm
karrie was late to work 14 times last year if she worked 250 days last year what percent of the days were she late
Answers
250 days = 100%
14 days = ?%
1 day = 100/250 = 0.4%
Therefore 14days = 0.4% • 14 = 5.6 %
help please in this question?
Answers
Answer:
see explanation
Step-by-step explanation:
∠ 1 and ∠ 2 are adjacent angles and are supplementary, sum to 180° , so
5x + x + 54 = 180 ← equation to solve to find x
6x + 54 = 180 ( subtract 54 from both sides )
6x = 126 ( divide both sides by 6 )
x = 21
Then
∠ 1 = 5x = 5 × 21 = 105°
∠ 2 = x + 54 = 21 + 54 = 75°
Can someone help me?