How do you find the exact length of the polar curve r=1+sin(θ)?
Answers
To find the exact length of the polar curve r = 1 + sin(θ), we can use the arc length formula for polar curves, which is:
L = ∫[a, b] √[r(θ)^2 + (dr/dθ)^2] dθ
where a and b are the limits of integration.
In this case, we have:
r(θ) = 1 + sin(θ)
Taking the derivative with respect to θ, we get:
dr/dθ = cos(θ)
Substituting these expressions into the arc length formula, we get:
L = ∫[0, 2π] √[(1 + sin(θ))^2 + cos(θ)^2] dθ
We can simplify this expression by expanding the square and simplifying:
L = ∫[0, 2π] √[1 + 2sin(θ) + sin(θ)^2 + cos(θ)^2] dθ
L = ∫[0, 2π] √[2 + 2sin(θ)] dθ
L = 2∫[0, 2π] √[1 + sin(θ)] dθ
To evaluate this integral, we can use the substitution u = 1 + sin(θ), du/dθ = cos(θ), which gives:
L = 2∫[1, 1+√2] 1/2 du
L = 2(2/3)(1+√2)^(3/2) - 2(2/3)
L = (4/3)(1+√2)^(3/2) - (4/3)
Therefore, the exact length of the polar curve r = 1 + sin(θ) is (4/3)(1+√2)^(3/2) - (4/3), which is approximately 6.283 units.
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Related Questions
The price of trail mix at a health food store is
$7.50 per pound. At that rate, what is the total
cost of three 8-ounce bags of trail mix?
Answers
Answer:
$3.75 every 8 oz bags.
Step-by-step explanation:
7.5 divided by 2 to get 3.75. 1 LB is equal to 16 oz so 8 is half of 16.
In a golf tournament, players competed in pairs. Joey and Melissa were partners. Joey got a score of +8, and Melissa got a score of -4. What was their combined score?
Answers
Answer:
4
Step-by-step explanation:
Use this tax table to find how much tax you need to pay on a taxable income of $40,000.
If taxable
But not
The tax ls:
income is over- ovCr
SO
$7,825
10 percent of the
amount over SO
S7,825
$31,850
$782.50 plus 15 percent
of the amount over
7,825
$31,850
$77,100
$4,386.25 plus 25
percent of the amount
over 31,850
$77,100
$160,850 $15,698.75 plus 28
percent of the amount
over 77,100
$160,850
$349,700 $39,148.75 plus 33
percent of the amount
over 160,850
$349,700
no limit
$101,469.25 plus 35
percent of the amount
over 349,7
Answers
9514 1404 393
Answer:
$6,423.75
Step-by-step explanation:
The table tells you ...
If the amount is over 31,850 but not over 77,100 the tax is 4386.25 +25% of (40,000 -31,850).
So, the tax is ...
$4,386.25 + 0.25(40,000 -31,850) = $4,386.25 + 0.25(8,150)
= $4,386.25 +2,037.50 = $6,423.75
Please help meee I need this
Answers
Answer:
TS
Step-by-step explanation:
QT≅TS because QS is bisected by PR
A bee flies at 12 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 18 minutes, and then flies directly back to the hive at 8 feet per second. It is away from the hive for a total of 21 minutes.
Answers
Answer:4
Step-by-step explanation:
Megan bought 2 1/4 pounds of bananas for $0.80 per pound and 1 1/2 pounds of strawberries for $1.10 per pound. How much more did Megan spend on bananas than on strawberries?
Answers
Answer:
$0.15
Step-by-step explanation:
Cost of each pounds of banana = $0.80
Number of pounds of banana = 2 1/4 pounds
Total cost of banana = $0.80 × 2 1/4 pounds
= 0.80 × 9/4
= 0.80 × 2.25
= 1.8
Total cost of banana = $1.8
Cost of each pounds of strawberry = $1.10
Number of pounds of strawberry = 1 1/2 pounds
Total cost of strawberry = $1.10 × 1 1/2 pounds
= 1.10 × 3/2
= 1.10 × 1.5
= 1.65
Total cost of strawberry = $1.65
How much more did Megan spend on bananas than on strawberries?
Total cost of banana - Total cost of strawberry
= $1.8 - $1.65
= $0.15
Answer:
$0.15
Step-by-step explanation:
Cost of each pounds of banana = $0.80
Number of pounds of banana = 2 1/4 pounds
Total cost of banana = $0.80 × 2 1/4 pounds
= 0.80 × 9/4
= 0.80 × 2.25
= 1.8
Total cost of banana = $1.8
Cost of each pounds of strawberry = $1.10
Number of pounds of strawberry = 1 1/2 pounds
Total cost of strawberry = $1.10 × 1 1/2 pounds
= 1.10 × 3/2
= 1.10 × 1.5
= 1.65
Total cost of strawberry = $1.65
How much more did Megan spend on bananas than on strawberries?
Total cost of banana - Total cost of strawberry
= $1.8 - $1.65
= $0.15
A bathroom in a dwelling unit has a counter space of seven feet including the sink. How many receptacles are required to serve this area
Answers
To determine the number of receptacles required for the bathroom counter space, we need to refer to the electrical code guidelines. The specific requirements may vary depending on the country or region, as well as the local electrical codes in place.
In the United States, according to the National Electrical Code (NEC), at least one 20-ampere-rated branch circuit is required to serve the bathroom receptacles. The code specifies that this circuit should be dedicated solely to the bathroom receptacles and should not serve any other areas.
The NEC also states that at least one receptacle outlet is required on the bathroom countertop. This receptacle should be located within 3 feet of the outer edge of the countertop and should be installed above the countertop surface. This means that a receptacle needs to be placed within reach of the bathroom counter space.
Considering the given information that the bathroom counter space is seven feet, including the sink, we need to install at least one receptacle outlet on the countertop within 3 feet of the outer edge. Depending on the specific layout and size of the counter space, additional receptacles may be required to meet the code's requirements for accessibility and convenience.
To ensure compliance with local electrical codes and safety standards, it is advisable to consult with a licensed electrician or refer to the specific electrical codes applicable in your area. They will be able to provide accurate guidance based on the local requirements and regulations.
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CAN YOU PLEASE HELP ME WITH THIS PROBLEM???
Answers
Answer:
Step-by-step explanation:
\(tan \ 50 =\dfrac{opposite \ side}{adjacent side}\\\\\\1.19=\dfrac{21}{MD}\\\\\\1.19*MD=21\\\\MD = \dfrac{21}{1.19}\\\\\\MD = 17.65\)
What are composite numbers
Answers
Answer:
When a number can be divided up exactly and is not a prime number , it is a Composite Number.
The first few composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16,........
Hope it helps.
Brenda is opening a savings account which compounds interest quarterly. Her banker gave her the following expression to find the amount that will be in the account, in dollars, after t years.
Which statement below best describes the coefficient, 3,700?
3700(1.05)^4t
A. the amount of the yearly earnings
B. the rate at which the account is increasing
C. the amount of the initial deposit
D. the number of times the account has compounded since it was opened
Answers
This statement best describes the coefficient, 3,700 is "the amount of the initial deposit". which is the correct answer would be option (C).
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
The exponential function is given in the question as:
3700(1.05)^4t
This expression is for the amount that will be in the account, in dollars, after t years.
As per the question,
The coefficient, 3,700 represents the amount of the initial deposit in the given exponential function
Thus, the correct answer would be an option (C).
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Explain the difference between a completely randomized experimental design and a randomized block design
Answers
A completely randomized experimental design and a randomized block design are two types of experimental designs used in research.
In a completely randomized design, subjects or experimental units are randomly assigned to different treatment groups.
Each subject has an equal chance of being assigned to any treatment group, and there is no consideration for any potential blocking factors.
This design is often used when there are no known sources of variability or potential confounding factors that need to be controlled.
On the other hand, a randomized block design involves grouping subjects or experimental units into blocks based on a certain characteristic or blocking factor that may influence the outcome.
Within each block, subjects are randomly assigned to different treatment groups.
This design allows for better control of potential confounding variables, as it ensures that each treatment group is represented equally within each block.
Overall, the main difference between a completely randomized design and a randomized block design lies in the consideration of blocking factors.
Completely randomized designs are simpler and more straightforward, while randomized block designs are more effective at controlling for potential confounding variables.
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At Pizza pizzazz the cost of a square pizza depends on the total square inches. A small
Pizza is 5 inches on each side and cost four dollars plus $0.05 per square inch. A medium pizza is 8 inches on each side and cost $3.50 plus $0.04 per square inch. What is the difference in price between a small pizza and a medium pizza?
Answers
Answer:
The difference in price between a small pizza and a medium pizza is $0.81
Step-by-step explanation:
Small pizza
Side = 5inch
Area = 25 sq.in
Cost = $4 +0.04*25
= 4 + 1.25 = $5.25
Medium pizza
Side = 8inche
Area = 64 sq.in
Cost = 3.50 + 0.04*64 = $6.06
Difference = Medium pizza - small pizza
= 6.06 - 5.25
= $0.81
Write the number in standard form. 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000)
Answers
Answer:
374.392
Step-by-step explanation:
3*100=300
4*10=40
7*1=7
3*(1/10)=0.3
9*(1/100)=0.09
2*(1/1000)=0.002
Put them together and you get 347.392
A sequence is defined by the explicit formula an=3n+4. Which recursive formula represents the same sequence of numbers?
Answers
The recursive formula that represents the same sequence of numbers as the explicit formula an = 3n + 4 is an = an-1 + 3, with the initial term a1 = 7.
A recursive formula defines a sequence by expressing each term in terms of previous terms. In this case, the explicit formula an = 3n + 4 gives us a direct expression for each term in the sequence.
To find the corresponding recursive formula, we need to express each term in terms of the previous term(s). In this sequence, each term is obtained by adding 3 to the previous term. Therefore, the recursive formula is an = an-1 + 3.
To complete the recursive formula, we also need to specify the initial term, a1. We can find the value of a1 by substituting n = 1 into the explicit formula:
a1 = 3(1) + 4 = 7
Hence, the complete recursive formula for the sequence is an = an-1 + 3, with the initial term a1 = 7. This recursive formula will generate the same sequence of numbers as the given explicit formula.
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what is the mean for the population of scores shown in the frequency distribution table? x f 5 1 4 2 3 3 2 4 1 2
Answers
The mean for the population of scores shown in the frequency distribution table x f 5 1 4 2 3 3 2 4 1 2 is 2.67. This means that the population's average score is 2.67.
The formula for calculating the mean (sometimes known as the average) of a population of scores is:
(sum of all scores) / mean (total number of scores)
We must first obtain the total of all scores in order to compute the mean of the population of scores indicated in the frequency distribution table. To do this, we multiply each score by its frequency (f) and then sum the results. For example, the product of 5 and 1 (the frequency) for the score 5 is 5. The product of 4 and 2 (the frequency) with the score 4 is 8. We repeat this process for all scores, then add up all the products to get the total score.
The sum of all scores is then divided by the entire number of scores, yielding the sum of all frequencies.
The mean is determined using the data from the frequency distribution table as follows:
(5 * 1 + 4 * 2 + 3 * 3 + 2 * 4 + 1 * 2) / (1 + 2 + 3 + 4 + 2) = (5 + 8 + 9 + 8 + 2) / 12 = 32 / 12 = 2.67
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questionkiki has 131 wheat rolls and 117 rye rolls. she places them in baskets of 9 rolls each. she divides the total number of rolls by 9 and gets 27 r 5.what is the correct interpretation of r 5 for this situation?responseskiki has 5 baskets left after filling 27 baskets.kiki has 5 baskets left after filling 27 baskets.kiki has 5 rolls left after filling 27 baskets.kiki has 5 rolls left after filling 27 baskets.kiki can fill at most 27 baskets with 5 rolls each.kiki can fill at most 27 baskets with 5 rolls each.kiki can fill 5 more baskets after filling 27 baskets.kiki can fill 5 more baskets after filling 27 baskets.
Answers
From division algorithm kiki divides total number of rolls by 9, and results 27 with remainder, r= 5, then the right interpretation is kiki has 5 rolls left after filling 27 baskets. So, option(b) is correct one.
The division algorithm tells us that when a number 'a' is divided by a number 'b' the quotient 'q' and the remainder 'r' represented by relation, a = bq + r.
Total number of wheat rolls that kiki had
= 131
Total number of rye rolls that kiki had
= 117
Total number of rolls she had = 131 + 117
= 248
Number of rolls placed by Kiki in one basket = 9
Total number of baskets she needed to place the rolls = dividing total rolls by total number of rolls in one basket, \(= \frac{ 248}{9} \)
Results, quotient =27 and remainder = 5
That means when kiki wants to put all rolls in baskets, we placed total 243 rolls in 27 baskets with 9 rolls in each and 5 rolls are remained. The rammining rolls are represented by remainder. Hence, required interpretation is that 5 rolls are left after placed in 27 baskets .
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Complete question:
question : kiki has 131 wheat rolls and 117 rye rolls. she places them in baskets of 9 rolls each. she divides the total number of rolls by 9 and gets 27 r 5.what is the correct interpretation of r 5 for this situation?responses
a) kiki has 5 baskets left after filling 27 baskets.
b) kiki has 5 rolls left after filling 27 baskets.
c) kiki can fill at most 27 baskets with 5 rolls each.
d) kiki can fill 5 more baskets after filling 27 baskets.
How many solutions does this system have? y = 5x + 1 y = -2x -8
Answers
The number of solutions of the given linear system is only one.
To determine how many solutions this linear system has, we'll analyze the given equations: y = 5x + 1 and y = -2x - 8.
1: Since both equations are already set to y, we can set the right sides of the equations equal to each other:
5x + 1 = -2x - 8
2: Solve for x by adding 2x to both sides of the equation:
7x + 1 = -8
3: Subtract 1 from both sides:
7x = -9
4: Divide both sides by 7:
x = -9/7
5: Plug the value of x back into either of the original equations to find the corresponding value of y. We'll use the first equation:
y = 5(-9/7) + 1
y = -45/7 + 1
y = -38/7
So, the solution for this system is x = -9/7 and y = -38/7. Since we found one unique solution, this system has 1 solution.
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how would you solve this?
1 - y <= x
Answers
Answer:
the answer I got is x>1-y
Help help urgently now ❤️That’splease please
Answers
Answer:
6566
Step-by-step explanation:
The answer is 6566.
what is 105 times 3?
Answers
The value of the given expression 105 times 3 is equal to 315.
Calculation of the expression 105 times 3 is equal to :
In Mathematics the word 'times' represents the multiplication.Here 105 times 3 means 105 multiply by 3.1
1 0 5
× 3
3 1 5
Explanation : 3 multiply by to unit digit 5 we 15.Write 5 below 3 and 1 carry forwarded to tens digit.Now multiply 3 by 0 we get 0 add 1 carry forwarded value write next to 5.At last multiply 3 to 1 we get 3 write next to 1.Final result is 315.Therefore, the calculated value of the expression 105 times 3 is equal to 315.
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Patel squeezed oranges so that his family could have fresh-squeezed juice for breakfast. He squeezed StartFraction 4 over 17 EndFraction cups from the first orange, StartFraction 3 over 10 EndFraction cups from the second orange, StartFraction 9 over 20 EndFraction cups from the third orange, StartFraction 3 over 11 EndFraction cups from the fourth orange, and StartFraction 7 over 15 EndFraction cups from the fifth orange. Patel estimates that he needs 3 cups of orange juice for his family. About how much more orange juice does he need to reach his estimate?
Answers
Answer:A
Step-by-step explanation:this is not true
Answer:
It A
Step-by-step explanation:
I had the question hope this helps!!!!!
For what value of k will k + 11, 2k – 1 and 2k + 7 are the consecutive terms of an A.P.?
1st answer will be marked brainliest and no glibberish answers
Answers
\(\text{For arithmetic series, the common difference will be same. }\\\\~~~~~~(2k-1)-(k+11) = (2k+7)-(2k-1)\\\\\implies 2k-1-k-11 = 2k+7-2k+1\\\\\implies k-12=8\\\\\implies k=8+12\\\\\implies k=20\)
B. {(15,0),(15,-2)}
Function?
Domain:
Range
Answers
Answers:
Function? No, it's not a functionDomain: {15}Range: {0, -2}===============================================
Explanation:
The domain consists of the set of x coordinates of each point. In this case, we only have one x value listed. The domain is {15}. Use curly braces even if there's only one item. This tells the reader we have a set.
The range is {0,-2} to indicate the y coordinates of the two points.
We don't have a function because x = 15 repeats itself. The input x = 15 leads to multiple outputs at the same time, which isn't allowed if you want a function. You can use the vertical line test as a visual way to see that we don't have a function.
Help me please i hate s
Answers
a. 20%, 5% times 4 = 20
b. 70%, 5% times 6 = 30, 30% will steal so 70% will not.
c. 10%, 5% times 2 = 10.
HELP ME PLEASE I need this now
question 1 first picture is to this question
As x decreases without bound, f(x) increases without bound.
As x increases without bound, f(x) approaches the line y = - 4.
As x decreases without bound, f(x) approaches zero.
As x decreases without bound, f(x) approaches the line y = 4.
question 2 the second picture to this question
As x decreases without bound, f(x) approaches the line y = 6.
As x increases without bound, f(x) approaches the line y = 6.
As x increases without bound, f(x) increases without bound.
As x decreases without bound, f(x) increases without bound.
Answers
Answer:
Question 1:
As x decreases without bound, f(x) increases without bound. TRUEAs x increases without bound, f(x) approaches the line y = - 4. TRUEAs x decreases without bound, f(x) approaches zero. FALSEAs x decreases without bound, f(x) approaches the line y = 4. FALSEQuestion 2:
As x decreases without bound, f(x) approaches the line y = 6. TRUEAs x increases without bound, f(x) approaches the line y = 6. FALSEAs x increases without bound, f(x) increases without bound. TRUEAs x decreases without bound, f(x) increases without bound. FALSEAs x decreases without bound, f(x) approaches the line y = 6.Step-by-step explanation:
Question 1:
options
As x decreases without bound, f(x) increases without bound.As x increases without bound, f(x) approaches the line y = - 4.As x decreases without bound, f(x) approaches zero.As x decreases without bound, f(x) approaches the line y = 4.Solving notes:
As x decreases without bound, f(x) does NOT approach zero.
As x decreases without bound, f(x) does NOT approaches the line y = 4.
_________________________________________________
Question 2:
options
As x decreases without bound, f(x) approaches the line y = 6.As x increases without bound, f(x) approaches the line y = 6.As x increases without bound, f(x) increases without bound.As x decreases without bound, f(x) increases without bound.Solving notes:
As x increases without bound, f(x) does NOT approach the line y = 6.
As x decreases without bound, f(x) does NOT increase without bound.
Solve for all values of x by factoring.
x² + 7x = 0
Answers
Answer:
(0,-7)
Step-by-step explanation:
Factor out the x^2 and the 7x.
x(x+7)
Do the zero factor
x = 0
x = -7
What are the domain and range of the relation given in the table?
Answers
Answer:
C
Step-by-step explanation:
all x values is domain, all y values are range
Answer:
Its c
Step-by-step explanation:
Domain = x value
Range = y value
what information can the chi-square goodness-of-fit test provide?
Answers
The chi-square goodness-of-fit test can provide information on categorical data match an expected distribution and which categories are contributing to any deviation from that distribution.
The chi-square goodness-of-fit test is a statistical test used to determine whether a set of observed categorical data matches an expected distribution. Specifically, the test compares the observed frequencies of each category to the expected frequencies based on a hypothesized distribution, and calculates a chi-square statistic. This statistic measures the degree of difference between the observed and expected frequencies, with larger values indicating greater deviation from the expected distribution. If the chi-square statistic is large enough to reject the null hypothesis (i.e., the observed data do not match the expected distribution), the test can provide information on which categories are contributing the most to the discrepancy. This can help identify which categories are over-represented or under-represented in the observed data, and can inform further investigation into potential causes of the deviation. In summary, the chi-square goodness-of-fit test can provide information on whether observed categorical data match an expected distribution and which categories are contributing to any deviation from that distribution.
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NEED HELP PEOPLEPOELOEOELEOEOE
Answers
Answer:
a) 210×0.10=21
b) 48×0.10=4.8
Step-by-step explanation:
210-21=189
48-4.8=43.2
help pls i really need it
Answers
Answer:
RHS
Step-by-step explanation: the hypotenuse and one side of the triangle is respectively equal to the hypotenuse and one side of the other triangle
so, its rhs