find the area of the specified region. inside the six-leaved rose r2 = 8 cos 3θ
Answers
The area of the region inside the six-leaved rose r^2 = 8 cos(3θ) is (4/9)(5√2 + 8√3).
The equation of the six-leaved rose in polar coordinates is given by r = 2\sqrt{2}\cos(3\theta), where r is the distance from the origin to a point on the curve, and θ is the angle between the positive x-axis and the line segment connecting the origin to the point. The region inside the curve can be found by integrating over the area enclosed by the curve.
Using the formula for area in polar coordinates, we have:
A = (1/2) ∫[α,β] (r(θ))^2 dθ
where α and β are the angles where the curve intersects itself.
Since the six-leaved rose has six petals, it intersects itself at angles of π/6, π/2, and 5π/6. Therefore, we have:
A = (1/2) ∫[π/6,π/2] (r(θ))^2 dθ + (1/2) ∫[π/2,5π/6] (r(θ))^2 dθ
Substituting r(θ) = 2\sqrt{2}\cos(3\theta), we get:
A = (1/2) ∫[π/6,π/2] [2\sqrt{2}\cos(3\theta)]^2 dθ + (1/2) ∫[π/2,5π/6] [2\sqrt{2}\cos(3\theta)]^2 dθ
Simplifying and evaluating the integrals, we obtain:
A = (1/2) [8√2/9 sin(6π/9) - 8√2/9 sin(2π/9)] + (1/2) [8√2/9 sin(10π/9) - 8√2/9 sin(4π/9)]
A = (4/9)√2 [sin(2π/9) - sin(6π/9) + sin(4π/9) - sin(10π/9)]
Since sin(6π/9) = sin(4π/3) = -√3/2 and sin(10π/9) = sin(8π/3) = √3/2, we have:
A = (4/9)√2 [sin(2π/9) + sin(4π/9) + √3]
Using the trigonometric identity sin(2θ) + sin(4θ) = 2sin(3θ)cos(θ), we can simplify further:
A = (8/9)√2 [sin(3π/9)cos(π/9) + √3]
Simplifying again, we get:
A = (8/9)√2 [sin(π/3)cos(π/9) + √3]
A = (8/9)√2 [(√3/2)(√2/2) + √3]
A = (4/9)(5√2 + 8√3)
Therefore, the area of the region inside the six-leaved rose r^2 = 8 cos(3θ) is (4/9)(5√2 + 8√3).
To know more about polar coordinates refer here:
https://brainly.com/question/11657509
#SPJ11
Related Questions
write the equation of line with slope of -3/8 and the y-intercept of (0,-1)
Answers
The equation of the line with slope -3/8 and passing through point (0, -1) is y = -3/8x - 1
What is Slope of a Line?
The slope is defined as the ratio of "rise" divided by "run" between two points on a line, or the ratio of altitude change to horizontal distance between any two locations on the line.
Solution:
We are provided with the value of Slope that is -3/8
And the intercept point of line is (0, -1)
Equation of Line will be
y - y1 = m(x - x1)
we are given that x1, y1 = (0, -1)
putting the values
y + 1 = -3/8 (x)
y = -3/8x - 1
To learn more about Slope of a Line from the given link
https://brainly.com/question/16949303
#SPJ1
Help pls help pls help pls help pls help pls
Answers
Answer:
Domain: -2 < x ≤ 3
General Formulas and Concepts:
Algebra I
Domain is the set of x-values that can be inputted into function f(x)Step-by-step explanation:
Since domain encompasses x values only, we are looking at the x-values of the graph. We see that our x-values span from -2 to 3. However, since x = -2 is a open dot, it is NOT included in the domain. Since x = 3 is a closed dot, it IS included in the domain:
(-2, 3] or -2 < x ≤ 3
Answer:
ramen is the true answer to lifes problems
Step-by-step explanation:
what are some effects that can occur in a country if large numbers of people are out of work?
please don't answer to get points answer the question honestly and I'll mark you on brainless
it's not maths my bad it's social studies
Answers
Answer:
It increases national debt. This happens because the unemployed don't participate in doing taxes because they do not have a job. It also effects other businesses because people with less money won't buy as many things which leads to other companies losing money.
PLEASE HELP the product of x^3 , x^5 + x
Answers
x^5= x •x •x
x •x •x •x •x •x •x •x •x= x^9
-3x + y = 7
3.x + 2y = 5
Answers
Answer:
I have no clue sorry I want to kill whoever made math
Answer:
(-1,4)
Step-by-step explanation:
-3x + y = 7
3x + 2y = 5
eliminate the "x"s
3y = 12
y = 4
-3x + 4 = 7
-3x = 3
-x = 1
x = -1
I’ll mark brainliest help please.
Answers
Answer:
7inches
Step-by-step explanation:
1x7
Answer:
7 inches
Step-by-step explanation:
Just divide 28 by 4, which is 7
paint cost $29.95 per gallon Nikki needs 12.25 gallons to complete a painting project how much will Nikki's been on paint remember to round to the nearest penny
Answers
ANSWER:
$366.89
Given:
Cost of a gallon of paint = $29.95
x gallons of paint will cost: $29.95 * x gallons
Since Nikki needs 12.25 gallon of paints, the price she would spend on paint will be:
\(\begin{gathered} 29.95\text{ }\ast\text{ 12.25 gallons} \\ =\text{ \$}366.89 \end{gathered}\)Nikki will spend $366.89 to complete the painting project
the value of the euro was $1.30 last week. during last week the euro depreciated by 5 percent. what is the value of the euro today?
Answers
If the value of the euro was $1.30 last week and during last week the euro depreciated by 5 percent, the value of the euro today is $1.235.
If the euro was worth $1.30 last week and depreciated by 5%, we can calculate the new value by multiplying the original value by (1 - depreciation rate).
Mathematically, the new value of the euro can be calculated as follows:
New Value = Original Value * (1 - Depreciation Rate)
New Value = $1.30 * (1 - 0.05)
New Value = $1.30 * 0.95
New Value = $1.235
Therefore, the value of the euro today is $1.235.
Depreciation is a term used to describe the decline in the value of a currency relative to another currency or to a basket of currencies. It can occur due to various reasons, such as changes in interest rates, inflation rates, political instability, or economic growth.
To learn more about depreciation click on,
https://brainly.com/question/15299442
#SPJ4
2. What type of association does this
graph show?
Positive
negative
none
all of the above
Answers
Determine whether each of these statements is true or false.a) 0 ∈ ∅ b) ∅∈{0}c) {0}⊂∅ d) ∅⊂{0}e) {0}∈{0} f ) {0}⊂{0}g) {∅} ⊆ {∅}
Answers
a) True, b) False, c) False, d) True, e) False, f) False, g) True
a) The statement is true. The symbol "∅" represents the empty set, which does not contain any elements. Since 0 is not an element of the empty set, the statement "0 ∈ ∅" is false.
b) The statement is false. The symbol "{0}" represents a set containing the element 0. The empty set, represented by "∅", does not contain any elements. Therefore, the empty set is not an element of the set {0}.
c) The statement is false. The symbol "{0}" represents a set containing the element 0. However, the empty set, represented by "∅", does not contain any elements. Therefore, the set {0} is not a subset of the empty set.
d) The statement is true. The empty set, represented by "∅", does not contain any elements. Every set is a subset of the empty set, including the set {0}.
e) The statement is false. The symbol "{0}" represents a set containing the element 0. In this case, {0} is not an element of itself. Therefore, the statement "{0}∈{0}" is false.
f) The statement is false. The symbol "{0}" represents a set containing the element 0. In this case, {0} is not a proper subset of itself. Therefore, the statement "{0}⊂{0}" is false.
g) The statement is true. The symbol "{∅}" represents a set containing the empty set. In this case, {∅} is a subset of itself because it contains the element ∅. Therefore, the statement "{∅} ⊆ {∅}" is true.
Learn more about empty set here: https://brainly.com/question/13553546
#SPJ11
A recipe for oatmeal cookies calls for 5 cups of flour for every 6 cups of oatmeal. How much flour is needed for a big batch of cookies that uses 18 cups of oatmeal?
Answers
Answer:
15
Step-by-step explanation:
So first you need to find out how many groups of 6 cups of oatmeal there are. So for this just do 18/6=3
So now you should be able to find the amount of flour by doing 5*3=15
The flour is needed for a big batch of cookies that uses 18 cups of oatmeal would be 15 cups.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
In order to find out how many groups of 6 cups of oatmeal there are.
So, For every 6 cups of oatmeal = 18/6=3
Now,
For 5 cups of flour = 5 x 3 = 15
The flour is needed for a big batch of cookies that uses 18 cups of oatmeal would be 15 cups.
Learn more about the unitary method;
https://brainly.com/question/23423168
#SPJ2
1. If LM = 6, what is the perimeter of APKQ?
X-6
P
3
X
M
5
Answers
Answer:
24.67
Step-by-step explanation:
6 x 3 = 18
18 plus 6 = 24
X-M=0.60
P-3=7
24.67
find the measure of the missing side
Answers
Answer:
10.3
Step-by-step explanation:
a^2 + b^2 = c^2
3.9^2 + b^2 = 11^2
b^2 = 121 - 15.21
b = 10.3
Answer:
10.3
Step-by-step explanation:
We use the pythagorean theorem. (a^2+b^2=c^2)
3.9^2 + b^2 = 11^2
3.9^2 = 15.21
11^2 = 121
15.21 + b^2 = 121
Subtract 15.21 from both sides
b^2=105.79
Take the square root of both sides
b = 10.28
10.28 is closest to 10.3 and it is also rounded to 10.3, therefore 10.3 is the answer.
Which algebraic represents this word description The product of two and the difference between a number and eleven.
Answers
Answer: 2(x-11)
Step-by-step explanation:
Disclaimer: The options are missing. They are as follows:
a. 2(11-x)
b. 11-2x
c. 2x-11
d. 2(x-11)
The algebraic expression that represents the word description: The product of two and the difference between a number and eleven is 2(x - 11). Hence, option d is the right choice.
What is an algebraic expression?An algebraic expression is a combination of variables and constants, as well as algebraic operations (addition, subtraction, etc.). Terms are the building blocks of expressions.
How do we solve the given question?We are asked to find the algebraic expression that represents this word description The product of two and the difference between a number and eleven.
We let the unknown number be x.
We are said that the expression is the product of two and the difference between a number and eleven.
The difference between a number and eleven can be written as x - 11.
Now we need the product of this and two, that can be written as:
2(x - 11).
∴ The algebraic expression that represents the word description: The product of two and the difference between a number and eleven is 2(x - 11). Hence, option d is the right choice.
Learn more about algebraic expressions at
https://brainly.com/question/4344214
#SPJ2
8 divided by 4106 long division
Answers
Answer:
513.25 or 0.001
How i got the answer:
As we that 06 + 4 = 10. 10 is not divisible by 8. It means that 4106 is also not divisible by 8. The correct answer will be 4106 divided by 8 is 513.25.
If you asking only 8 divided by 4106 the answer is 0.00194836824. In short form it is 0.001.
If you asking if 8 is divisible by 4106 the answer is 513.25. Steps are added above.
Answer: 513.25 or 0.001
Please mark me brainliest
Hope this helps.
answer is 8/4106 or 0.002
Just follow the rules for multiplication and keep going till the end
solve this please???
Answers
Answer:
5/9
Step-by-step explanation:
5/3 ÷ 3
turn them to 5/3.......1/3
multiply 5/3 × 1/3 = 5/9
Solve for r 0.5(r+2.76)=3
Answers
Answer:
r=1.43147648, −4.19147648
Step-by-step explanation:
help please tysm:)))))
Answers
According to the information, the expression that represents the number of visitors in each group is n<12.
What is a mathematical inequality?A mathematical inequality is a term that refers to a mathematical expression that has the purpose of expressing the order relationship that exists between two values when they are different. If the values in question are elements of an ordered set, such as integers or reals, then they can be compared. The notation a < b means a is less than b.
Based on the above, we can infer that the correct way to represent the inequality of visitors in each group would be:
n < 12That is, each group has less than 12 visitors.
Learn more about mathematical inequality in: https://brainly.com/question/19003099
#SPJ1
d. what is the confidence interval estimate of the difference between the two population means? (to 2 decimals and enter negative value as negative number)
Answers
The confidence interval estimate of the difference between two population means is a range of values that we can be confident contains the true difference between the means.
To calculate the confidence interval estimate of the difference between two population means, we need to use the formula:
CI = (x₁ - x₂) ± tα/2 ×SE
where x1 and x2 are the sample means, tα/2 is the critical value from the t-distribution table at a chosen level of significance α/2, and SE is the standard error of the difference between the two means.
The confidence interval estimate gives us a range of values within which we can be confident that the true difference between the two population means lies. The margin of error is determined by the critical value and the standard error.
It is important to note that a negative value for the confidence interval estimate indicates that the mean of the first population is smaller than the mean of the second population. Conversely, a positive value indicates that the mean of the first population is larger than the mean of the second population.
In summary, the confidence interval estimate of the difference between two population means is a range of values that we can be confident contains the true difference between the means. The margin of error is determined by the critical value and the standard error. A negative value indicates that the mean of the first population is smaller than the mean of the second population, while a positive value indicates the opposite.
To calculate the confidence interval estimate, we need to obtain two samples from the populations of interest, calculate the sample means and the standard deviation of each sample, and then calculate the standard error of the difference between the means. The critical value is determined based on the level of significance chosen for the test, and the degrees of freedom, which depend on the sample sizes. Once we have all the necessary values, we can use the formula to calculate the confidence interval estimate. The confidence interval is typically expressed as a percentage, with 95% being the most commonly used level of significance.
Learn more about Range:
brainly.com/question/29204101
#SPJ11
What is the product of 2x3 +9 and x3 +7?
Answers
The product of the expression is 2x⁶ + 23x³ + 63
How to determine the productFirst, we should note that algebraic expressions are described as expressions that are composed of coefficients, terms, constants, variables and factors.
These algebraic expressions are also made up of mathematical operations, such as;
BracketAdditionMultiplicationDivisionParenthesesSubtractionFrom the information given, we have that;
2x3 +9 and x3 +7?
Then,
(2x³ + 9)(x³ + 7)
expand the bracket
2x⁶ + 14x³ + 9x³ + 63
add like terms
2x⁶ + 23x³ + 63
Learn about algebraic expressions at: https://brainly.com/question/4344214
#SPJ1
If EF = 9x + 17, FG = 35. and EG= 196, find the value of x
Answers
Answer:
x = 16Step-by-step explanation:
Given:
EF = 9x + 17FG = 35EG = 196As per segment addition postulate:
EG = EF + FGSubstituting values to find x:
9x + 17 + 35 = 1969x = 196 - 529x = 144x = 144/9x = 16Choose the mixed number that is equivalent to $ 1.32.
1 32 /100
3 12/100
1 32/10
32/100
Answers
Answer:
1.32/100
Step-by-step explanation:
Address input parameters and values. Input parameters and values: The decimal number = 1.32Write it as a fraction ; 1.32/1Multiply 100 to both numerator and denominator(1.32×100)/(1×100) = 132/100
It can be written as 132%= 132/100 or 132/100
4. To simplify 132/100 to its lowest terms, find LCM for the 132 and 100
4 is LCM for 132 and 100.
5. Divide numerator and denominator by 4
132/100=(132/4)/(100/4)=33/25.
33/25 is a simplest fraction for the decimal point number 1.32.
Answer:
132/100
Step-by-step explanation:
When you multiply by 10,100,1000.... you add zero. For example:132×10=1320 132×100=13200When you devide by 10,100,1000 you decrease the number starting from the right to left. For example: 132/10=13,2 132/100=1,32. NOTE it depends on the number of zeros.Directions: Find the product and simplify
Answers
Answer:
x^4-9x^2+26x-24
Step-by-step explanation:
Answer:
\( {x}^{3} - 9 {x}^{2} + 26x - 24\)
Step-by-step explanation:
\((x - 3)( {x}^{2} - 6x + 8)\)
\( {x}^{3} - 6 {x}^{2} + 8x - 3 {x}^{2} + 18x - 24\)
\( {x}^{3} - 9 {x}^{2} + 26x - 24\)
Plz answer this im going to fail the semester :(
Answers
Answer and Explanation
__________________________________________________________
The solution of the equation is 20. ( The value of x. )__________________________________________________________
The value of x is 20.
We can figure this out by...
__________________________________________________________
\(\frac{3x}{5}-x=\frac{x}{15}-\frac{28}{3}\) but what does x equal?
\(\frac{3\cdot20}{5}-20\) = \(-8\)
\(\frac{20}{15}-\frac{28}{3}\) = \(-8\)
Since both are equal to -8, that means \(\frac{3\cdot20}{5}-20\) = \(\frac{20}{15}-\frac{28}{3}\).
Which means that...
x = 20
__________________________________________________________
Hope this helps! <3
__________________________________________________________
David wants to buy a car based on the color choices and the transmission as given below. Colors: Red, White, Blue, Yellow and Transmissions: Auto, manual. Find the probability of choosing Red car with manual transmission.
Answers
Answer:
1 of 4
Step-by-step explanation:
Solve for x
3/10 = x/7
Give your answer as an improper fraction in its simplest form!!!!!
Answers
Answer:
x = 21/10
Step-by-step explanation:
3/10 = x/7
Cross multiply.
10x = 21
x = 21/10
Answer:
x is 21/10
Step-by-step explanation:
3/10 = x/7
Multiply through by the LCM of 10 and 7 which is 70
we have
3/10 × 70 = x/7 × 70
21 = 10x
Divide both sides by 10
We have
21/10 = 10x /10
x = 21/10
Hope this helps you
1- ? divided by 3 = -7
2- -50 divided by ? =10
3- ? divided by -2 = 10
Answers
2.) 5
3.) -20
bdhdhdhfh
Please help me !
Find f(-3)
Answers
Answer:
f(- 3) = - 3
Step-by-step explanation:
locate x = - 3 on the x- axis, then go vertically down to meet f(x) at (- 3, - 3 )
Then f(- 3) = - 3
Please help, thank you!
Answers
Answer:
☑ Time is 6 years
Step-by-step explanation:
» From Simple Interest:
\({ \tt{simple \: interest = principle \times rate \times time}} \\ { \rm{S.I = P \times R \times T}} \\ { \rm{T = \frac{S.I }{ P \times R} }} \\ \\ { \rm{ = \frac{441.90}{2455 \times 3\%} }} \\ \\ { \rm{= \frac{441.90 \times 100}{2455 \times 3} }} \\ \\ { \rm{ = \frac{44190}{7365} }} \\ \\ { \rm{Time = 6 \: years}}\)
Pure copper was mixed with a 10% copper alloy to produce an alloy thát was 25% copper. How much of the pure copper and how much 10% alloy were used to produce 36 kg of 25% alloy?
Answers
Answer:
6kg pure copper and 30 kg 10% copper was mixed to give 36kg of 25% alloy
Step-by-step explanation:
Here, we want to produce 36 kg of 25% alloy
Let the Pure copper be x kg while 10% alloy be y kg
Pure copper is simply 100% copper
Thus;
x + y = 36 •••••(i)
Then;
100% of x + 10% of y = 25% of 36
= x + 0.1y = 9 •••••• ii)
From i x = 36-y
from ii, x = 9-0.1y
Equate both x
36-y = 9-0.1y
36-9 = 0.1y + y
0.9y = 27
y = 27/0.9
y = 30
x = 36-y
x = 36-30
x = 6 kg