find the area of the region that lies inside the curve r = 1 costheta and outside the curve r = 2-costheta
Answers
The area of the region that lies inside the curve r = 1 cosθ and outside the curve r = 2-cosθ is 6π square units.
To find the area of the region that lies inside the curve r = 1 cosθ and outside the curve r = 2-cosθ, we need to follow the given steps.
Step 1: Determine the points of intersection of the curves
To determine the points of intersection of the curves, we equate the two curves and solve for θ.
r = 1 cosθ and r = 2-cosθ1
cosθ= 2-cosθ
2 cosθ = 2cosθ = 2/2cosθ
a = 1θ = π/4, 7π/4
So, the curves intersect at the angles θ = π/4 and θ = 7π/4.
Step 2: Determine the area bounded by the two curves
To determine the area bounded by the two curves, we need to integrate the difference of the outer curve and the inner curve with respect to θ between the limits π/4 and 7π/4.
∫(2-cosθ)² - (1 cosθ)² dθ, π/4 ≤ θ ≤ 7π/4
Using the formula (cosθ)² = (1 + cos2θ)/2, we can simplify the expression:
(2-cosθ)² - (1 cosθa)² = (4-4cosθ + cos²θ) - (1-2cosθ + cos²θ)= 3 - 2cosθ
The integral becomes
∫(3-2cosθ) dθ, π/4 ≤ θ ≤ 7π/4
= 3θ - 2 sinθ, π/4 ≤ θ ≤ 7π/4
= 3(7π/4) - 2 sin(7π/4) - 3(π/4) + 2 sin(π/4)
= 21π/4 + √2 + 3π/4 - √2= 6π
So, the area of the region that lies inside the curve r = 1 cosθ and outside the curve r = 2-cosθ is 6π square units.
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Related Questions
a) 25.8
b) 36.8
c) 64.2
d) 42.0
Answers
Answer:
y = 25.8
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos y = adjacent/ hypotenuse
cos y = 18/20
Take the inverse cos of each side
cos ^-1 (cos y) = cos^-1(18/20)
y =25.84193276
Rounding to the nearest tenth
y = 25.8
stanley has one-half of a cake in the fridge. he divided it equally among his three children miriam, joe, and paul. what part of the entire cake did each child get?
Answers
Each child, Miriam, Joe, and Paul, received one-sixth (1/6) of the entire cake.
To determine what part of the entire cake each child got, we need to divide the one-half of a cake that Stanley has equally among his three children, Miriam, Joe, and Paul.
Step 1: Identify the fraction of the cake that needs to be divided, which is one-half (1/2).Step 2: Divide the fraction by the number of children, which is 3.Step 3: Perform the division by multiplying the fraction by the reciprocal of the divisor: (1/2) * (1/3) = (1*1)/(2*3)The result is (1/6), which means that each child, Miriam, Joe, and Paul, received one-sixth (1/6) of the entire cake.
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Ramesh lent a loan of rs 1800 to suresh at a simple rate of interest for 2 years. At the end of period. suresh returned him total of rs 2232.At what rate of interest had ramesh lent the loan
Answers
Answer:
The rate is 12%
Step-by-step explanation:
Minus the loan from the amount. That will be your interest then use the formula: interest = principle(loan) ×rate ×time ÷ 100 to get the rate
i need atleast 5 volunteers for the magic trick
Answers
What magic trick??
Are you gonna do a magic??
Sorry for a lot of questions.
Watch help video
Find the length of the third side. If necessary, round to the nearest tenth.
Answers
Answer:
5.3
Step-by-step explanation:
Using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) with the length of the two legs of the right triangle for a and b and the hypotenuse length for c, you can solve this equation.
First, lets call the unknown side x. Plugging in all of the value we have into the equation we get \(x^{2} +6^{2}=8^{2}\). This is the same as \(x^{2} +36=64\).
The next step is to solve for x. Subtract 36 from both sides of the equation to get \(x^{2} =28\). Then, take the square root of both sides to get \(x=\sqrt{28}\).
Finally, since you need a rational answer, put \(\sqrt{28}\) into a calculator and round to the nearest tenth for 5.3
A company plans to spend $8,000 in year 2 and $10,000 in year 4. At an interest rate of 10% per year, compounded semiannually. The equation that represents the equivalent annual worth A in years I through 4 is: A) A-8,000(P/F, 10%,2) * ( A/P, 10%, 4)+ 10,000(A/F, 10%,4) B) A 8,000(P/F, 10.25%,2) * (A/P, 10%, 4)+ 10,000 (A/F, 10.25%,4) C) A-8,000(P/F,5%,2) * (A/P,5%, 4) + 10,000(A/F,5%,4) D) A-8,000(P/F, 10.25%,4)*(A/P, 10.25%, 8) + 10,000(A/F, 10.25%,8)
E) A-8,000(A/P, 10 %,4) + 10,000(A/F,10%,4)
Answers
Option (B) is the correct answer.
A company plans to spend $8,000 in year 2 and $10,000 in year 4. At an interest rate of 10% per year, compounded semiannually. The equation that represents the equivalent annual worth A in years I through 4 is given by option (B).That is;Option (B) represents the equation that represents the equivalent annual worth A in years I through 4.
The formula for equivalent annual worth is given by;A = PW (A/P, i, n) + F(A/F, i, n)where,PW = Present WorthF = Future WorthA/P = Present Worth FactorA/F = Future Worth Factori = interest raten = number of yearsSo,A = 8000(P/A, 10/2,2) + 10000(F/A, 10/2,4)A = 8000(3.1051) + 10000(0.6848)A = 24,840.80 + 6848A = $31,688.80The equation that represents the equivalent annual worth A in years I through 4 is represented by the option (B);A = 8000(P/A, 10.25/2,2) + 10000(F/A, 10.25/2,4).
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You are shopping for your favorite candy, horseradish-flavored gummy slugs, at a supermarket. a 12-ounce bag costs $5.16 while a 9-ounce bag costs $4.14. which bag is the better buy? pick the correct bag and cost per oz.
Answers
The 12-ounce bag costs $5.16 is better bag than 9-ounce bag costs $4.14.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
A 12-ounce bag costs $5.16 while a 9-ounce bag costs $4.14.
According to given question we have
A 12-ounce bag costs $5.16 means
12-ounce=$5.16
1 -ounce=$5.16 /12
1 -ounce=0.43 $
Another bag is
9-ounce bag costs $4.14 means
9-ounce= $4.14
1 -ounce=$4.14/9
1 -ounce=0.46 $
So, 12-ounce bag costs $5.16 is better than 9-ounce bag costs $4.14.
Therefore, the 12-ounce bag costs $5.16 is better bag than 9-ounce bag costs $4.14.
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-36-(-40)
Please I need this ASAP
Answers
Answer:
4
Step-by-step explanation:
-36 - (-40) = -36 + 40-36 + 40 = 4I hope this helps!
Answer:
4
Step-by-step explanation:
because -36+ 40 =4 you take the subtraction and give it to the 40
an unbiased coin is tossed four times. what is the probability that coin lands heads up at least once? (round your answer to three decimal places.)
Answers
The probability of getting at least one head is 15/16.
What is probability?
The ratio of positive outcomes to all possible outcomes of an event is known as the probability.
Formula for probability = favourable outcomes/ total outcomes
Main body:
if 4 coins are tossed , total no. of outcomes = 2⁴ = 16
In a toss there are 2 outcomes T or H
so, Probability of getting Head = 1/2
The probability of getting at least 1 head = 1- probability of getting no heads
⇒1 - Probability of getting tail in 4 tosses
⇒ 1 - (1/2)⁴
⇒ 1 - 1/16
⇒ 15/16
So the probability of getting at least one head is 15/16.
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draw a graph of the rose curve
Answers
Looking through the options, the answer is option D.
Your friend Frans tells you that the system of linear equations you are solving cannot have a unique solution because the reduced matrix has a row of zeros. Comment on his claim. The claim is right. The claim is wrong. Need Help?
Answers
Answer: Incorrect
Step-by-step explanation:
Your friend Frans' claim is incorrect. A row of zeros in the reduced matrix means that the corresponding equation in the system is redundant and does not provide any additional information. This does not necessarily mean that the system does not have a unique solution. In fact, a row of zeros in the reduced matrix is common when solving systems of linear equations using Gaussian elimination, and it can still lead to a unique solution or even an infinite number of solutions. Therefore, Frans' claim is wrong.
HELP PLLSS
92;69
work included!
Answers
Answer:
92/69 cannot be simplified
Step-by-step explanation:
add 16k to the quotient of 4m divided by 11
Answers
Answer:
\(\Large \boxed{\frac{4m}{11}+16k}\)
Step-by-step explanation:
The quotient is the result from division.
4m divided by 11 is:
\(\displaystyle \frac{4m}{11}\)
16k is added to the result.
\(\displaystyle \frac{4m}{11}+16k\)
In 2022 the 56 th Super Bowl was played in Inglewood, California. I started to make a data set on the Super Bowl for each year and added a number of variables. For each variable, tell me if the level of measurement is Nominal, Ordinal, or Continuous. Which league won the Super Bowl, either AFC or NFC. Nominal Could not tell from the information given Continuous Ordina
Answers
In your data set on the Super Bowl, the level of measurement for the variable "Which league won the Super Bowl, either AFC or NFC" is Nominal.
Nominal level of measurement is used for variables that have categories or names with no inherent order or numerical meaning. In this case, the categories are AFC and NFC, and there is no numerical or hierarchical order between them.
As for the other variables in your data set, you have not provided any information or variables to determine their level of measurement. It is important to provide more details or specific variables for me to assess whether they are Nominal, Ordinal, or Continuous.
In conclusion, the level of measurement for the variable "Which league won the Super Bowl, either AFC or NFC" is Nominal, as there is no inherent order or numerical meaning between the categories. Please provide more information if you want to determine the level of measurement for other variables.
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please help!! it’s due asap
Answers
Answer:
x = -4 and 2
Step-by-step explanation:
When x = -4 and 2, y = 0 so -4 and 2 are the roots
The equation below gives the height, H, of a stack of n textbooks in centimeters.H = 3n Which equation would give the number of textbooks in a stack if it's height is known? A. n=H+3 B. n=H-3 C. n= 3/H D. n=H/3
Answers
Answer:
Explanation:
The height of
how many years to double investment if interest rate is .10%
Answers
Answer:
How the Rule of 72 Works. For example, the Rule of 72 states that $1 invested at an annual fixed interest rate of 10% would take 7.2 years ((72/10) = 7.2) to grow to $2. In reality, a 10% investment will take 7.3 years to double ((1.107.3 = 2). The Rule of 72 is reasonably accurate for low rates of return.
Step-by-step explanation:
For example, if you invest $10,000 at 10 percent compound interest, then the “Rule of 72” states that in 7.2 years you will have $20,000. You divide 72 by 10 percent to get the time it takes for your money to double. The “Rule of 72” is a rule of thumb that gives approximate results
1+1+2+3+4+5+6+7+8+9=?
Answers
Answer:
The answer is 46
Step-by-step explanation:
Self explanatory i just added them together
hope i helped :D
What is the equation to find the radius of a cylinder? (Just the radius)
Answers
Answer:
divide the diameter by 2
Step-by-step explanation:
Simplify the expression. Write your answer as a power. (−3)^4(−3)^1
Answers
Answer:
-243
Step-by-step explanation:
results of regression analysis are often abused in the following ways:
a.Using the model without understanding the context in which the model was developed and recommended for use
b.Predicting outside the region of the data without noting the predictions are an extrapolation of the model
c.Ignoring known scientific and economic theory regarding the model and its variables
d.All of the above
e.None of the above
Answers
The correct answer is d) All of the above. Regression analysis results are often abused by using the model without understanding its context, predicting outside the data range without acknowledging extrapolation, and disregarding known scientific and economic theories related to the model and its variables.
Regression analysis is a statistical method used to examine the relationship between variables and make predictions based on the observed data. However, the misuse and misinterpretation of regression analysis can lead to erroneous conclusions.
Firstly, using the model without understanding its context can be problematic. The development and recommendation of a regression model are typically based on specific assumptions and limitations, as well as the data used in its construction. Applying the model to a different context without considering these factors may lead to inaccurate predictions or interpretations.
Secondly, predicting outside the region of the data without recognizing that it involves extrapolation is another common misuse of regression analysis. Extrapolation involves making predictions beyond the observed data range, which can be risky since the relationship between variables may not hold true outside the data range. Extrapolation should be approached cautiously and accompanied by a clear acknowledgement of its inherent uncertainties.
Lastly, ignoring known scientific and economic theory related to the model and its variables can also lead to misuse. Regression analysis should be interpreted in the context of existing theories and domain knowledge. Disregarding established theories can result in flawed conclusions or invalid interpretations of the regression model's results.
In conclusion, regression analysis should be used with care and understanding. It is crucial to consider the context, acknowledge the limitations of extrapolation, and incorporate relevant scientific and economic theories to ensure the appropriate use and interpretation of regression analysis results.
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What Gets Wetter The More It Dries?
Write the letter of each answer in the box containing the exercise number
Complete the sentence.
1. If two angles of one triangle are congruent to two angles of another
triangle, then the two triangles are A
Use the diagram.
р н
Answers
K 73°
L. 17°
U. false
T. 62°
A. congruent
2. If mC = 36°, then mZH = 54. True or false?
O
M. right angle
W. similar
3. AEDC - AA
E. 43
4. If mZE = 73°, find m2K.
LEDC
Use the diagram and the glven Information to find the Indicated
measure
0. true
D. 42
A. HGK
B. KGH
C с
E
A
5. MZA = 42°, m.ZD = 95°, mZE = 42°, ZB - ZD;
Find mZACB
6. MZA = MZE = m ZACB = MZECD = 59°; Find m2D.
Answers
Answer:
A “Towel”
Step-by-step explanation:
What is the area of trapezoid DEFG?
PLEASE SO THIS ASAP!!!
MUST SHOW WORK
Answers
Answer:
Area = 35 cm^ 2
Step-by-step explanation:
Area = 1/2(a+b) x h
1/2 (5+9) x 5
= 35 cm^ 2
Answered by G a u t h m a t h
Answer:
A = 35 cm²
Step-by-step explanation:
The area (A) of a trapezoid is calculated as
A = \(\frac{1}{2}\) h (b₁ + b₂)
where h is the perpendicular height between the bases and b₁, b₂ are the bases.
Here h = 5 , b₁ = 9 and b₂ = 5 , then
A = \(\frac{1}{2}\) × 5 × (9 + 5) = 2.5 × 14 = 35 cm²
The area of a square can be represented by the expression x10. which monomial represents a side of the square?
Answers
The side of the square is x^5 .
What is the Area of the square?Area of a square = (side)² = a²,
Given;
area of a square = \(x^{10}\)
Equating it with the general formula of square
Area of a square = a²,
a² = \(x^{10}\)
Taking square root on both sides,
\(a = \sqrt{x^{10}} \\\\a = x^5\)
Hence, the side of the square is x^5.
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How are evidence and counterexamples used in proofs?
In a direct proof, evidence is used to
. On the other hand, a counterexample is a single example that
.
Answers
In a direct proof, evidence is used to support a claim, On the other hand, a counterexamples is a single example that show the contradictions in a claim.
What is difference between evidence and counterexamples in a proof?Evidence means any piece of information that supports the argument being made in a proof which could include mathematical formulas, logic, or theorems that have been previously proven.
Counterexamples are specific examples that disprove a statement made in a proof and are used to show that a proof is not valid and that the argument being made is flawed.
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which inequality is represented on the number line shown?
Answers
Answer:
A
Step-by-step explanation:
b/ of shaded region can make to closed inequality & it's not closed to make open inequality.
If J=91 ,L=16 , and K=73 , list the sides of triangle JKL in order from smallest to largest
A. JL, KJ, LK
B. LK, JL, KJ
C. KJ, JL, LK
D. KJ, LK, JL
Answers
JL, LK, JK are the smallest angle of a triangle is located across from its smallest side. The biggest side is on the other side of the biggest side.
How are the angles arranged, from greatest to smallest?JKL, where K is the specified angle, is an example.Acute Angles are the smallest angles. An acute angle is a particular kind of angle that measures less than 90°.an acute angle. The planar surface typically produces obtuse angles.Straight angle. Right angle.Subtract the squares of the other sides, then calculate the square root to determine the shorter side.Reflex angle at its widest point.JL, LK, JK are the smallest angle of a triangle is located across from its smallest side. The biggest side is on the other side of the biggest side.To learn more about smallest angle refer to:
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aleksander buys some martenisi bracelets that are worn by bulgarians in march to welcome spring
Answers
The equation that can be used to determine the number of bangles (y) made in certain days (y) is y = 6x+3
What is an equation of a line?The equation of a straight line is y=mx+c y = m x + c m is the gradient and c is the height at which the line crosses the -axis, also known as the y -intercept.
Given that, Alexander draws a graph of the number of bangles he made,
We need to write an equation for the same,
The line passes through two points (2, 15) and (3, 21)
We know that, an equation of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by :-
y-y₁ = (y₂-y₁) / (x₂-x₁) (x-x₁)
Here, (2, 15) and (3, 21) are (x₁, y₁) and (x₂, y₂),
y-15 = 21-15 / 3-2 (x-2)
y-15 = 6(x-2)
y-15 = 6x-12
y = 6x+3
Here, x is the number of days and y is the number of bangles made.
Hence, the equation that can be used to determine the number of bangles (y) made in certain days (y) is y = 6x+3
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The complete question is attached:-
WRAP-UP Menu Subtracting Fractions . please help
Answers
Answer:
5/24 more
Step-by-step explanation:
1/3 turns into 8/24
and
1/8 turns into 3/24
so eric has read 5/24 more
Answer:
5/24
Step-by-step explanation:
1/8×3=3/24
1/3×8=8/24
8/24-3/24=5/24.
Becca made 2 trays of rolls and bisouits. Each tray had 12 folls and 6 biscuits. How many total rols and bisouits did Beca make?
Answers
Becca made a total of 24 rolls and 12 biscuits.
Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product.
Becca made 2 trays of rolls and biscuits, with 12 rolls and 6 biscuits in each tray. To find the total number of rolls and biscuits, we need to multiply the number of rolls and biscuits per tray by the number of trays, and then add them together:
Total rolls = 2 trays × 12 rolls per tray = 24 rolls
Total biscuits = 2 trays × 6 biscuits per tray = 12 biscuits
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