Use a calculator to find the length of the curve correct to four decimal places. If necessary, graph the curve to determine the parameter interval.r = sin (6sinθ)
Answers
The length of the curve correct to four decimal place is 6.4739.
To find the length of the curve given by r = sin(6sinθ), we can use the formula:
L = ∫(a,b) √[r(θ)² + (dr/dθ)²] dθ
where a and b are the parameter values that correspond to the endpoints of the curve. In this case, we can see that r(θ) = sin(6sinθ), and we can use the chain rule to find:
dr/dθ = 6cosθcos(6sinθ)
Substituting these expressions into the formula, we get:
L = ∫(0,2π) √[sin²(6sinθ) + (6cosθcos(6sinθ))²] dθ
Using a calculator or computer program, we can evaluate this integral to find L ≈ 6.4739. Therefore, the length of the curve correct to four decimal places is approximately 6.4739.
To determine the parameter interval, we can graph the curve using polar coordinates. The curve is symmetric about the origin and has six "petals" that form a flower-like shape. The parameter interval can be taken as 0 ≤ θ ≤ 2π to cover one complete rotation of the curve.
To learn more about integrals, visit https://brainly.in/question/4630073
#SPJ11
Related Questions
A baker has 15 cups of flour. He sets aside 4 cups of flour to use tomorrow, and uses the rest of the flour for a cookie recipe that calls for 1/2 cup of flour. How many batches of cookies can the baker make
Answers
Answer:
22 I think
Hope this helps
What is the sum of the measures of the interior angles of a 10-sided figure?
A. 1,440°
B. 180°
C. 360°
D. 1,800°
Answers
The sum of the measures of the interior angles of a polygon with n sides can be found using the formula (n-2) * 180 degrees.
For a 10-sided figure, we have (10-2) * 180 = 8 * 180 = 1,440 degrees.
Therefore, the sum of the measures of the interior angles of a 10-sided figure is 1,440°.
The answer is A.
Which function has the same zeros as g(x) = -x3 + x2 + 12x?
Answers
Answer: B
Step-by-step explanation:
Angel is making dumplings. If he uses cup of dough for each dumpling, how many cups of dough does Angel need to make 7 dumplings?
Answers
Answer:
7
Step-by-step explanation:
Please tell the answer 5*25=
Answers
Answer:
5*25=125
Step-by-step explanation:
Answer:
The answer would be 125
Step-by-step explanation:
When you identify what goals are conflicting, it is a part of
a)timeline
b)analysis
c)Revision
Answers
Answer: Analysis
Step-by-step explanation:
When analysing a project, one must try to find out everything that could impart on the success of the project such that any problems can be fixed and any potential problems be made contingencies for.
This is why it is here that you check to see whether and which goals are conflicting so that they can be fixed or aligned to ensure that the project comes out as a success.
the local grocery store is running a special three dozen of eggs $1.08 what is the cost per egg
Answers
Answer:
more than 25 cents
Step-by-step explanation:
The line y= -3 is a reflection of the line y=5. What is the equation for the line of reflection?
Answers
Answer:
y = 1
Step-by-step explanation:
The line of reflection will be a parallel line midway between y = - 3 and y = 5
y = \(\frac{-3+5}{2}\) = \(\frac{2}{2}\) = 1
line of reflection is y = 1
Answer:
y=1
Step-by-step explanation:
the line of reflection will be a parallel line midway between y=-3and y=5
y=-3+5/2
=2/2=1
What does -3+x-1/3x+4 equal
Answers
\(\frac{2x+3}{3}\)
Step-by-step explanation:1. Combine multiplied terms into a single fraction-3 + x - \(\frac{1}{3}\)x + 4
-3 + x + \(\frac{-x}{3}\) + 4
2. Add the numbers-3 + x + \(\frac{-x}{3}\) + 4
1 + x + \(\frac{-x}{3}\)
3. Find common denominator1 + x + \(\frac{-x}{3}\)
\(\frac{3}{3}\) + \(\frac{3x}{3}\) + \(\frac{-x}{3}\)
4. Combine fractions with common denominator\(\frac{3}{3}\) + \(\frac{3x}{3}\) +\(\frac{-x}{3}\)
\(\frac{3 + 3x - x}{3}\)
5. Combine like terms\(\frac{3 + 3x - x}{3}\)
\(\frac{3 + 2x}{3}\)
6. Rearrange Terms\(\frac{3 + 2x}{3}\)
\(\frac{2x+3}{3}\)
Solution:\(\frac{2x+3}{3}\)
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
HELPPP
simplify the product (-8) (-6) (2)
I BEG HELP ME
Answers
Multiply left to right
48*2
=96
Answer:
96
Step-by-step explanation:
Given
- 8 × - 6 × 2 ( the product of 2 negatives is a positive )
= 48 × 2
= 96
Could someone please help me with this? thank you so so so so much :D
Answers
Answer:
I have no clue
Step-by-step explanation:
13. Gavin spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 6050 feet. Gavin initially measures an angle of elevation of 16° to the plane at point A. At some later time, he measures an angle of elevation of 37° to the plane at point B. Find the distance the plane traveled from point A to point B. Round your answer to the nearest foot if necessary.
Answers
Answer: Let's denote the distance the plane travels from point A to point B by d. We can then use trigonometry to set up two equations based on the angles of elevation and the constant altitude of the plane:
At point A:
tan(16°) = 6050 / x, where x is the distance between Gavin and the point directly beneath the plane at point A.
At point B:
tan(37°) = 6050 / (x + d), where x + d is the distance between Gavin and the point directly beneath the plane at point B.
We can solve for x in the first equation:
x = 6050 / tan(16°) ≈ 20416.6 ft
Substituting this into the second equation and solving for d, we get:
d = (6050 / tan(37°)) - x ≈ 22451.4 ft
Therefore, the distance the plane traveled from point A to point B is approximately 22,451 feet (rounded to the nearest foot).
Step-by-step explanation:
If the error bars overlap, but do not contain the mean of the other group, which of the following is true: There is no significant difference between means. There is a significant difference between means. We do not know if there is a significant difference between means. None of the statements is true.
Answers
The correct statement is: There is no significant difference between means.
There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value of a given data set. Pythagorean means consist of arithmetic mean, geometric mean, and harmonic mean
If the error bars overlap, but do not contain the mean of the other group, it means that there is no significant difference between the means. Overlapping error bars indicate that the means are within the range of uncertainty, and there is not enough evidence to conclude that the means are significantly different from each other.
Know more about means here:
https://brainly.com/question/31101410
#SPJ11
plz help me I need it urgently
Answers
Answer:
answer to the question is $600
Is Y=6x+11 a function?
Answers
Answer:
Yes
Step-by-step explanation:
y=6x+11
0=6x+11
-6x=11
x=-11/6
So its a solution
9. Look at some of the printed letters in a textbook. The small horizontal
and vertical segments attached to the ends of the letters are called
serifs. Most of the letters in a textbook are in a serif typeface. The
letters on this page do not have serifs, so these letters are in a sans-
serif typeface. (Sans means "without" in French.) The figure shows a
capital letter A with serifs. Use the given information to write a
paragraph proof that the serif, segment HI, is parallel to segment JK.
Given: 21 and 23 are supplementary.
Prove: HI || JK
Answers
By considering the given information that angles 21 and 23 are supplementary and analyzing the properties of supplementary angles and parallel lines, we have proven that segment HI is parallel to segment JK.
To prove that segment HI is parallel to segment JK based on the given information that angles 21 and 23 are supplementary, we can utilize the properties of supplementary angles and parallel lines.
First, let's examine the given figure and information.
We have a capital letter A with serifs, where segment HI represents one of the serifs, and segment JK represents a horizontal line within the letter A.
To begin the proof, we'll make use of the fact that angles 21 and 23 are supplementary.
Supplementary angles are defined as two angles whose measures sum up to 180 degrees.
We can observe that angle 21 is an interior angle of triangle AHI, and angle 23 is an interior angle of triangle AJK.
Since angles 21 and 23 are supplementary, their sum is equal to 180 degrees.
Now, let's assume that segments HI and JK are not parallel.
In this case, if we extend lines HA and JA, they will eventually intersect at point P.
Since the angles formed at the point of intersection are supplementary (angle 21 + angle 23 = 180 degrees), it would imply that angle 21 and angle PJK, as well as angle 23 and angle PHI, are also supplementary.
However, this leads to a contradiction. In the original figure, we can observe that angle 21 and angle PJK do not form a supplementary pair since angle PJK is a right angle (90 degrees) in the letter A.
Therefore, our assumption that segments HI and JK are not parallel must be incorrect.
Consequently, we can conclude that segment HI is indeed parallel to segment JK.
For similar question on angles.
https://brainly.com/question/25770607
#SPJ8
What are the domain and range of g of x equals the square root of the quantity x minus 3?
Answers
The range and domain of the square root function are:
domain: x ≥ 3
range: y ≥ 0
How to find the domain and range of the function?For any function:
y = f(x)
We define the domain as the set of the possible inputs (the possible values of x) and the range as the set of the possible outputs (possible values of y).
Here we have the following function:
g(x) = √(x - 3)
Remember that we can't evaluate a square root in an argument smaller than zero, so the smallest value on the domain is such that:
x - 3 = 0
x = 0 + 3
x = 3
So the domain is the set of all real values larger than or equal to 3:
domain: x ≥ 3
And the range has a minimum when x = 3, then:
√(3 - 3) = 0
So the range is the set of all real numbers equal to and larger than 0, so the range is:
range: y ≥ 0
Learn more about square roots:
https://brainly.com/question/428672
#SPJ1
Answer:
D: [3, ∞) and R: [0, ∞)
Step-by-step explanation:
Callie is comparing the costs of two options for her college education. option a: complete the first two years of schooling at a community college and then transfer to a university. option b: complete all four years of schooling at the university. community college financial analysis costs per year financial aid package per year tuition
Answers
After careful cost analysis, Collie will choose the option with the least financial burden.
What is cost analysis?Cost analysis refers to.the analysis between the cost of two more options for a particular goods or service
In the comparison done by Callie, the two options to obtain college education are;
Option A: complete the first two years of schooling at a community college and then transfer to a university.Option B: complete all four years of schooling at the universityTherefore, using cost analysis, Collie will choose the option with the least financial burdens.
Learn more about cost analysis at: https://brainly.com/question/4953989
#SPJ4
Are the following linear equations? If they are, put them in the form Lu linear operator L, and classify them as homogeneous or inhomogeneous:
(A) Ut = (xux)2 + (yuy)y + xy (B) uux + Uxxx = Ut (C) Utt = Uxxxx + Uyyyy
Answers
A homogeneous equation.
Yes, the following are linear equations:
(A) Ut = (xux)2 + (yuy)y + xy
This equation can be put in the form Lu linear operator L as follows: LAUt = 0, which is a homogeneous equation.
(B) uux + Uxxx = Ut
This equation can be put in the form Lu linear operator L as follows: LBu = Ut, which is an inhomogeneous equation.
(C) Utt = Uxxxx + Uyyyy
This equation can be put in the form Lu linear operator L as follows: LCT = 0, which is a homogeneous equation.
Learn more about homogeneous equation.
brainly.com/question/30504189
#SPJ11
Could someone please answer for this section I will give 20 points for all of it
Answers
Answer:
1) 2/5
2) 4/13
3) 1/8
4) 25/4 or 6 + 1/4
Step-by-step explanation:
1) 5/2 * x = 1
x = 1 / (5/2)
x = 2/5
2) (3 + 1/4) * x = 1
13/4 * x = 1
x = 1 / (13/4)
x = 4/13
3) 8 * x = 1
x = 1/8
4) (2/5)^2 * x = 1
2^2 / 5^2 * x = 1
4/25 * x = 1
x = 1 / (4/25)
x = 25/4
x = 6 + 1/4
On a certain hot summer's day, 340 people used the public swimming pool. The daily prices are $1.25 for children and $2.00 for adults. The receipts for admission totaled $537.50.How many children and how many adults swam at the public pool that day?
Answers
Answer:
190 children and 150 adults
Step-by-step explanation:
1. 1.25x + 2y = 537.5
2. x + y = 340
Here, x represents the children and y represents the adults.
Again, the first equation represent the cost of tickets, while the second represents the number of people.
From the above equation, we can solve for x and y
From equation 2,
x + y = 340
x = 340 - y
Substitute for x in equation 1
1.25x + 2y = 537.5
Then,
1.25(340 - y) + 2y = 537.5
Expand the bracket
425 - 1.25y + 2y = 537.5
Collect like terms
-1.25y + 2y = 537.5 - 425
0.75y = 112.5
y = 150.
To get the value of x, substitute for y in equation 2
x + y = 340
x + 150 = 340
x = 340 - 150
x = 190
Therefore,
There were 190 children and 150 adults at the pool that day
If f (7) = 22, then
ff-1(22)) = [?]
![If f (7) = 22, thenff-1(22)) = [?]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/wPt0BfCGWiY7ZCBNVNwTYk05JE2sJ7vR.png)
Answers
Answer:
\(f(f^{-1} (22))\) equals 22.
Step-by-step explanation:
For every input in a function, there will be one corresponding output. When taking the output of the function and inserting it as the input to the inverse function of the original, the output will be equivalent to the exact input of the original function. In this case, because \(f(7)=22\), that means \(f^{-1} (22)\) will equal 7. Using this knowledge, you can find the value of \(f(f^{-1} (22))\), which will be \(f(f^{-1} (22)) = f(7)=22\), so \(f(f^{-1} (22))\) equals 22.
The velocity of a particle can be modeled by the function v(t)=1/10(3t-8)^3+2. Which graph accurately shows the velocity of the park or at any time, t?
Answers
The graph that accurately shows the velocity of the park or at any time is as shown in the attached image.
How to draw a function Graph?Velocity is defined as the rate of change of position of object with respect to time. Velocity is also defined as the speed of an object moving in a definite direction.
Velocity is a vector quantity and so it has both magnitude and direction. Its' SI unit is in meters per second.
The velocity of a particle is modeled by the function;
v(t) = ¹/₁₀(3t - 8)³ + 2
The given velocity function is cubic function and as such the attached graph shows the velocity of the particle at any time.
Read more about Function Graph at; https://brainly.com/question/4025726
#SPJ1
Suppose the class repeats the experiment, this time with a total of only 25 trials. predict how many times the number 4 will be rolled. answer in complete sentences and be sure to include all relevant calculations.
Answers
Therefore, based on this calculation, we can predict that the number 4 will be rolled approximately 4.17 times in 25 trials.
To predict the number of times the number 4 will be rolled in the experiment with 25 trials, we need to consider the probability of rolling a 4 in each trial.
Assuming a fair six-sided die, the probability of rolling a 4 on any single roll is 1/6, as there are six equally likely outcomes (numbers 1 to 6) and only one of them is a 4.
To calculate the expected number of times the number 4 will be rolled in 25 trials, we multiply the probability of rolling a 4 (1/6) by the total number of trials (25):
Expected number of times = Probability of rolling a 4 * Total number of trials
Expected number of times = (1/6) * 25
Expected number of times = 25/6
Expected number of times ≈ 4.17
To know more about trials,
https://brainly.com/question/13351919
#SPJ11
While scuba diving ,Alex counted the number of sea turtles and jelly fish he saw
Answers
Answer:
OK what is the rest of the question i cant answer it as of right now the question is a statement.
Step-by-step explanation:
So sorry.
The number 1000 has how many factors of 10
Answers
Answer:
10³ = 1000∴ 1000 has 3 factors of 10.Hope it will be helpful!!!
My Pleasure!!!EASY GEOMETRY**
name a straight angle on the figure
Answers
How might you defend the Pardoner not as a good person but as a good preacher ? Does it matter to others that there is a difference ? Why or why not ?
Answers
We can argue that the Pardoner is a good preacher and not a good person because he is very effective in convincing people of the things he says.
This matters to others because it leads to them doubting his authenticity.
What was the Pardoner like?In the Canterbury Tales, the Pardoner goes around selling official Church pardons to people that he berates for being sinful. The pardons will then be used to absolve them of their sins.
The Pardoner is an effective preacher because he actually convinces people that they are sinners. He is not a good person because he berates people only to make profit from them as well as trying to swindle them of other possessions.
This mattered to the others who doubted his authenticity because they believed he was simply telling them stories to sell them things.
Find out more on the Canterbury Tales at https://brainly.com/question/848651.
Three friends went to a book shop the first bought three bros and four pencils for $30.00. The second bought two Bros and five pencils for $27.00 . If the third bought a bro and a pencil only how much did they pay .
Answers
Answer:
total 66$
Step-by-step explanation:
let price of bro s be x and pencil be y
according to Qn
at 1 cond
3x+4=30____(1)
2x+5y=27____(2)
solve botth and get value of each bros and pencil and then at last add,30$,27$,6$,3$
Which is the graph of the function f(x) = -√x
Answers
Answer:
1st Graph
Step-by-step explanation:
Easiest and quickest way is to graph the function in a graphing calc and then choosing the best answer.