Find the area of the region inside the circle r=4cos(theta) and outside the circle r=2.
Answers
Area of the region inside the circle r=4cos(theta) and outside the circle r=2 is 4π/3 + 2√3
What is the polar curve?A form created using the polar coordinate system is called a polar curve. Points on polar curves have varying distances from the origin (the pole), depending on the angle taken off the positive x-axis to calculate distance. Both well-known Cartesian shapes like ellipses and some less well-known shapes like cardioids and lemniscates can be described by polar curves.
r = 1 − cosθsin3θ
Polar curves are more useful for describing paths that are an absolute distance from a certain point than Cartesian curves, which are good for describing paths in terms of horizontal and vertical lengths. Polar curves can be used to explain directional microphone pickup patterns, which is a useful application. Depending on where the sound is coming from outside the microphone, a directional microphone will take up sounds with varied tonal characteristics. A cardioid microphone, for instance, has a pickup pattern like a cardioid.
The area between two polar curves can be found by subtracting the area inside the inner curve away from the area inside the outer curve.
The figure attached shows the bounded region of the two graphs. The red curve is r=4cos(θ) and the blue curve is r=2.
The points of intersection of the two curves are
θ = π/3 and 5π/3
The area is calculated as follows:
Since the bounded region is symmetric about the horizontal axis, we will find the area of the top region, and then multiply by 2, so as to get the total area.
A = 2 [tex]\(\int_{0}^{\pi /3}[/tex] ½ (4 cos (θ)² − ½ (2)² dθ
= [tex]\(\int_{0}^{\pi /3}[/tex] 16 cos2 (θ) − 4dθ
= [tex]\(\int_{0}^{\pi /3}[/tex] 8 (1+cos(2θ)) − 4dθ
=[tex]\(\int_{0}^{\pi /3}[/tex] 4 + 8 cos (2θ) dθ
= [4θ + 4sin (2θ)] [tex]\(\int_{0}^{\pi /3}[/tex]
= 4π/3 + 2√3
To learn more about the, polar curve visit:
https://brainly.com/question/27548409
#SPJ4
Related Questions
The length of a rectangle is three more than double the width. if the perimeter is 78 inches, find the dimensions.
Answers
The length of a rectangle is 27 inches and the width of a rectangle is 12 inches.
Given that, the length of a rectangle is three more than double the width and the perimeter of a rectangle = 78 inches.
We need to find the dimensions of the rectangle.
What is the perimeter of a rectangle?The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).
Let the width of the rectangle be x.
Then, length=2x+3
Now, perimeter=2(2x+3+x)
⇒ 78=2(3x+3)
⇒ 3x+3= 39
⇒ 3x=36
⇒ x=12 inches
So, width=12 inches and length=2x+3=27 inches
Therefore, the length of a rectangle is 27 inches and the width of a rectangle is 12 inches.
To learn more about the perimeter of a rectangle visit:
https://brainly.com/question/2142493.
#SPJ4
Reasoning true or false: if an augmented square matrix in row-echelon form has a row of zeros as its last row, then the corresponding system of equations has no solution. explain your reasoning.
Answers
False, if an augmented square matrix in row-echelon form has a row of zeros as its last row, then the corresponding system of equations has no solution.
A square matrix with a row of zeroes means that one variable can be written as a linear combination of the other variables.What does the term "echelon form" mean?
If a matrix in linear algebra has the shape that comes from a Gaussian elimination, it is said to be in echelon form. When a matrix is in row echelon form, Gaussian elimination has been applied to the rows, and when it is in column echelon form, Gaussian elimination has been applied to the columns.What purpose does echelon matrix serve?
By reducing a complex matrix to a simple matrix, the Echelon Form of a matrix can be utilized to solve a linear equation. If a matrix meets certain criteria, which we'll go over in this post, it is said to be in an echelon form.Learn more about echelon form
brainly.com/question/14693506
#SPJ4
A is the midpoint of segment ST. Point A is located at (7,-1) and point S is located at (5,0). What are the coordinates of point T?
Answers
The coordinates of point T is (9,-2)
Given that A is the midpoint of segment ST. midpoint A has coordinates (7,-1) and point S has coordinates ( 5,0 ) and asked to find the coordinates of the point T
Let's assume the coordinates of the point T as(a,b)
Midpoint formula for a line segment having endpoints (x1,y1) and (x2,y2)
Let's assume the midpoint as (X,Y)
(X,Y)=([tex]\frac{x1+x2}{2}[/tex],[tex]\frac{y1+y2}{2}[/tex])
Here the endpoints of the linesegment ST are S(5,0) and T(a,b) and the midpoint of the linesegment ST is A and has coordinates (7,-1).
⇒(7,-1)=([tex]\frac{5+a}{2}[/tex],[tex]\frac{b}{2}[/tex])
⇒7=[tex]\frac{5+a}{2}[/tex]⇒14=5+a⇒a=9
⇒-1=[tex]\frac{b}{2}[/tex]⇒b=-2
Therefore,The coordinates of point T is (9,-2)
Learn more about coordinates here:
https://brainly.com/question/27749090
#SPJ9
Solve the equation, and enter the solutions from least to greatest. If there is only one solution, enter "n.a." for the second solution. or Reset Nextelect the correct answer from each drop-down menu. Consider this expression. The simplest form of the expression has in the numerator and in the denominator. 1/x+1/x-10=x-9/x-10
Answers
We need to know how to solve quadratic equation for this problem. The solution of the equation is x=1 and x=10.
An equation that has a variable with maximum degree two is called a quadratic equation. A quadratic equation can be solved by factorization method. Factorization method is a method where we group the variables together to find common factors among them. The common factors give the solution of the equation. Since a quadratic equation has variable of degree two it has two solutions. The roots of a quadratic equation can be real and unequal, real and equal or imaginary. If we solve the given equation we get a quadratic equation.
[tex]\frac{1}{x} +\frac{1}{x-10} =\frac{x-9}{x-10} \\\frac{x-10+x}{x(x-10)} =\frac{x-9}{x-10} \\2x-10=x(x-9)\\2x-10=x^{2} -9x[/tex]
[tex]x^{2} -9x-2x+10=0\\x^{2} -11x+10=0\\x^{2} -10x-x+10=0\\x(x-10)-1(x-10)=0\\(x-1)(x-10)=0\\[/tex]
Therefore the solution of the equation is x=1 and x=10.
Learn more about quadratic equation here:
https://brainly.com/question/1214333
#SPJ1
A pilot flew a jet from City A to City B, a distance of 2000 mi. On the return trip, the average speed was 20% faster than the outbound speed. The round-trip took 9 h 10 min. What was the speed from City A to City B?
Answers
A pilot flew a jet from City A to City B, a distance of 2000 mi. On the return trip, the average speed was 20% faster than the outbound speed. The round-trip took 9 h 10 min. What was the speed from City A to City B?
Find the product of 2√/18 and 2√5 in simplest form. Also, determine whether the
result is rational or irrational and explain your answer.
Answers
2√10/3 is irrational number
The term "rational number" refers to any number that can be stated as a fraction, as well as a positive, negative, or zero. If q is not equal to zero, it can be expressed as p/q.
The word "rational" is derived from the word "ratio," which is a fraction and really refers to a comparison of two or more values or integer numbers. It is the ratio of two integers, to put it simply.
Consider the rational integer 3/2. It denotes that the integer 3 is divided by the number 2.
Irrational numbers are those that are not rational in nature. Let's explain; irrational numbers can be expressed as decimals but not as fractions, hence they cannot be expressed as the ratio of two integers.
After the decimal point, irrational numbers have an infinite amount of non-repeating digits. Here's an illustration of an irrational number:
For instance, 8 = 2.828
MULTIPLYING THE TWO NUMBERS,
2/√18 x 2√5
= 2 /3√2 x 2√5
= 4√5/3√2
= 2√2 x √5 /3
= 2√10/3
rational number multiplied by an irrational number is always a irrational number.
Since √10 is a irrational number, therefore, 2√10/3 is irrational number.
To learn more about rational and irrational number, refer to https://brainly.com/question/12088221
#SPJ9
Please help me! I am so confused
Answers
Theoretical probability is what might happen, but the experimental probability is definitely happens in trials. The probability in these cases is 0.25.
What is the difference between theoretical and experimental probability?Theoretical probability is based on the total outcomes vs the desired outcomes; due to this, this is just the expectation of what will hapen. However, as this is mainly based on expectations, it is not completely accurate.
On the other hand, the experimental probability is based on the observation of reality as the probability is tested, which makes it more accurate.
What are the probabilites in the cases presented?Desired outcomes /total outcomes
Probability of getting red in the spinner:
4/10 0.25 or 25%Probability of getting a 4 in a dice
3/120.25 or 25%Learn more about probability in: https://brainly.com/question/11234923
#SPJ1
What is the area of this tile?
6 in.
8in.
Answers
Answer:that would be 24
Step-by-step explanation: A triangle is a three side shape so after you multiply 6 and 8 thats 48 but then you multiply by 1/2 which is the same as dividing by 2 so (48/2)=24 and thats your answer hope this helps
you multiply the numbers together!:)
which of the following pairs of ratios form a proportion? a. 9 boys to 5 girls and 12 boys to 8 girls
Answers
Answer:
12 to 8
Step-by-step explanation:
cuz i am smart pls mark me brainliest
For which value of a does 4 = a +| x – 4| have no solution?
-6
0
4
6
Answers
Answer:
a = 6
Step-by-step explanation:
Hello!
First, let's isolate the Absolute Value bracket.
4 = a + |x - 4|4 - a = |x - 4|Based on the definition of Absolute value, the outcome should always be a positive number. Therefore, if the product, 4 - a, is a negative number, it will have no solutions.
That means a has to be greater than 4 for it to be negative. a should be 6.
a = 6
If f ( x ) = 3 x + 2 and g ( x ) = x 2 − x , find the value. f ( 4 )
Answers
We have been given
f(x) = 3x+2
g(x) = x²-x
And we have to find f(4).
What is f(x)
f(x) is the value of the function. m is the slope of the line. b is the value of the function when x equals zero or the y-coordinate of the point where the line crosses the y-axis in the coordinate plane. x is the value of the x-coordinate.
We have been given
f(x) = 3x+2
And we have to find the value of f(4)
So, putting x=4 in f(x)
f(4)= 3×4+2
f(4)=12+2
f(4)=14.
To know more about limits continuity
and differentiability
Visit:. brainly.in/question/22006066
#SPJ9
Please help me out with 3 questions..
Answers
Each part of the question is plotted on the number line as an image with the solution.
How are rational numbers represented on the number line?
On the number line, rational numbers could be represented. Origin refers to the numeric line's center (O). The illustration of rational numbers shows positive numbers here on the right side of zero, or the origin, and negative numbers on the left. Depending on the kind of fraction, rational numbers are represented differently on the number line.(1) [tex]\frac{-3}{8} , 1\frac{1}{5} = \frac{6}{5} = 1.2 , \frac{-3}{4}[/tex] are plotted on the number line as an image with the solution.
(2) -13+15+(-8) = -6 is plotted on the number line as an image with the solution.
(3) [tex]\frac{3-(-14)}{7} = \frac{17}{7} = 2.429, \frac{-36+58}{-11} = -2[/tex] are plotted on the number line as an image with the solution.
Learn more about number line here:
https://brainly.com/question/24644930
#SPJ9
TASK 2-Percentages (34 Marks)
Topic: Finding Percentages
1. Suppose you have a grandmother who gives you one cent on your first birthday. The
next year she gives you 3 cents, the following year 9 cents. Each year she triples the
amount she gave the year before until you are 13.
How much money would you have on your 12 birthday? you would have
$154
72
(a) Complete the table below (BMarks)
Birthday
1
2
3
4
5
6
7
8
9
10
11
12
13
Total
Money
1c
3c
9c
27c
81c
$2.43
34 86
39 72
$19 34
338 68
377 36
$154 72
Percentage
3309-44
$309 44
(b) What percentage is the amount of money on your 12th birthday to the total money
given by your grandmother. Your percentage need to be corrected to two decimal
places. You need to show all the steps for your percentage calculation.
Answers
Answer:
1; 1
2:3
3:9
4:27
5:81
6:243
7:729
8:2,187
9:6,561
10:19,683
11:59,049
12:177,147
6. The value of a car is gradually declining in such a way that at the end of each year it is worth in January 2002 6 of its value at the beginning .it was worth 36000,000 in January 2000. What was its worth in January 2002?
Answers
Answer:
the value of a car is gradually declining in such a way that at the end
Step-by-step explanation:
I don't know what to say
Regular insulin is ordered iv at 7 units/hour. the iv bag contains 100 units of regular insulin in 100ml of d5w. the iv rate should be how many ml/hr? (round to the nearest whole number
Answers
The iv (insulin rate) rate should be 7 ml/hr.
Here,
Regular insulin is ordered iv at 7 units/hour.
The iv bag contains 100 units of regular insulin in 100ml of d5w.
We have to find the iv rate.
What is insulin rate?
Basal insulin rate is the rate at which an insulin pump provides small, “background” doses of fast-acting insulin.
Now,
Regular insulin is ordered iv at 7 units/hour.
The iv bag contains 100 units of regular insulin in 100ml of d5w.
The insulin rate in ml/hr = ( 7 units / 1 hr ) * (100 ml / 100 units) = 7 ml/hr
So, The iv (insulin rate) rate should be 7 ml/hr.
Learn more about the insulin rate visit:
https://brainly.com/question/17424490
#SPJ4
Shifting data, by adding a constant to each data value, does not change the _________.
A. quartiles
B. mean
C. standard deviation
D. median
Answers
The standard deviation is a measure of a collection of values' variance or dispersion. The correct option is C, standard deviation.
What is a standard deviation?The standard deviation is a measure of a collection of values' variance or dispersion. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.
Shifting data, by adding a constant to each data value, do not change the standard deviation. This is because the standard deviation is a measurement of how much a group of values varies or is dispersed.
Hence, the correct option is C, standard deviation.
Learn more about Standard Deviation here:
https://brainly.com/question/16555520
#SPJ4
Eight families live on abbie's street. she asks each family how many pets they have. abbie's data set is: 0, 0, 1, 1, 2, 2, 2, 5. the modal number of family pets on abbie's street is:__________
Answers
Answer:
Step-by-step explanation:
It is asking for the "mode" which is the data element you see the most, therefore it is 2.
12. FIND THE ERROR A student is finding the
total cost c, including sales tax, of a book
that costs $9.95. The sales tax rate is 9%.
Find the student's mistake and correct it.
Answers
Here is what the student wrote (re-pasting for clarity)
C = 1.9 x 9.95
C = 18.91
C = $18.91
The error happens in the 1st line
Why? Because the 1.9 should be 1.09
The 1.9 represents a tax of 90% when we want a 9% tax instead
In other words, 9% = 9/100 = 0.09 while 90% = 90/100 = 0.9
-----------------
This is what the steps should look like
C = 1.09 x 9.95
C = 10.8455
C = 10.85
Don't forget to round to the nearest hundredth, aka nearest penny.
The total cost, after sales tax, is $10.85
6. You just had surgery on your knee. As part of rehabilitation your physical
therapist wants you to walk 1 minute on day 1 and double your time every day. How
many minutes will you be walking on day 7?
Answers
64 minutes
Step-by-step explanation:
1x2=2 it day one
2x2=4 it day two
and more
32x2=64 it day 7
which expressions below equal a rational number? select all that apply.
Answers
The expressions that are equal to a rational number are [(2/3)+(4/5)], [(√3) - (√3)], and [(√49)(√1)].
A rational number is one that can be stated as the ratio of two numbers, with the denominator not equal to zero.All real numbers that are not rational numbers are referred to as irrational numbers. The ratio of two integers cannot be used to express irrational values.(a) π√4π√4 is equal to 2π, which is an irrational number.(b) (2/3)+(4/5)(2/3)+(4/5) = (22/15), which is a rational number.(c) (√36)-(√5)(√36)-(√5) = 6-√5, which is an irrational number.(d) (√3)-(√3)(√3)-(√3) = 0, which is a rational number.(e) (√49)(√1)(√49)(√1) = 7*1 = 7, which is a rational number.To learn more about real numbers, visit :
https://brainly.com/question/551408
#SPJ9
What is the decimal number 34.567 written in expanded form?
A: An expression that reads three times ten, plus one times one, plus five times one-tenth, plus seven times one-hundredth, plus four times one-thousandth
B: An expression that reads three times ten, plus three times one, plus six times one-tenth, plus seven times one-hundredth, plus five times one-thousandth
C: An expression that reads three times ten, plus four times one, plus five times one-tenth, plus six times one-hundredth, plus seven times one-thousandth
D: An expression that reads three times ten, plus seven times one, plus five times one- tenth, plus four times one-hundredth, plus six times one-thousandth
Answers
Answer:
option 3
Step-by-step explanation:
C: An expression that reads three times ten, plus four times one, plus five times one-tenth, plus six times one-hundredth, plus seven times one-thousandth
-1/2 is equivalent to 1/2
Answers
Answer: No
Step-by-step explanation:
No because its off by 1 point, -1/2, 0, 1/2
Write an algebraic expression to represent how much money Max has saved.
Max is saving to buy a car. He already has $700 saved. He will continue to earn money by cutting lawns; he earns $15 for each lawn. Let x represent the number of lawns Max cuts.
Answers
Answer: x=700+15
Step-by-step explanation: an educated guess
Answer:
y = 15x + 700
Explanation:
In this sentence said Max already has $700 which means it should be constant value in the equation. Max earns $15 for each lawn he cuts.
Linear equation:
y = mx + bwhere 'm' is rate of change, 'b' is constant value
So, the equation should be (for total money Max saved):
y = 15x + 700where y represents total money Max saved and x = number of lawns cut.
Evaluate
4(x+3)(x+1)
(x+5)(x-5)
for x = 3.
Answers
Answer: -1536
Step-by-step explanation:
1: 4(3+3) (3+1) (3+5) (3-5)
2: 4(6) (4) (8) (-2)
3: 24 (4) (8) (-2)
4: 96 (8) (-2)
5: 768 (-2)
= -1536
x^5y^5z^3 =?
A. bases are different, so this can't be done.
B. xy5z3
C. (xy)5z3
Answers
To simplify the indices expression x⁵y⁵z³, we can conclude that; A. bases are different, so this can't be done.
How to simplify Indices?We want to simplify the indices given as;
x⁵y⁵z³
Now, we can see that the bases are different and as such it means they cannot be simplified using laws of indices on the exponents.
This is because when the bases are different, the expression cannot be factored with the exponents being added, subtracted, divided or multiplied.
Thus, we will conclude that the bases are different, so this can't be done.
Read more about Indices at; https://brainly.com/question/15361818
#SPJ1
Multiply:
-2x(3x - 4)
Enter the correct answer
Answers
Answer:
- 6x² + 8x
Step-by-step explanation:
- 2x(3x - 4) ← multiply each term in the parenthesis by - 2x
= - 6x² + 8x
EASY LOOKING FOR ANSWER HELP
Answers
Answer:
I forgot the answer
Step-by-step explanation:
3.2*10^8, 1.2*10^8, 7*10^5, 5*10^3
(3x-5)/4 is less than or equal to -1
How to solve for x?
Answers
Step-by-step explanation:
[tex] \frac{3x - 5}{4} \leq1[/tex]
[tex]3x - 5 \leq1 .4[/tex]
[tex]3x - 5 \leq4[/tex]
[tex]3x \leq4 + 5[/tex]
[tex]3x \leq9[/tex]
[tex]x \leq \frac{9}{3} [/tex]
[tex]x \leq3[/tex]
x = {3,2,1,0,...}
<6 and <7 form a linear pair. Twice the measurement of <6 is twelve more than four times the measurement of <7. Find the measurement of each angle.
Answers
A linear pair , m∠7 = 58°, m∠6 = 122° are the measurement of each angle.
What is Linear Pair?
When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°.
Linear Pairs add up to equal 180°.
Step 1: Define
m∠6 + m∠7 = 180°
2m∠6 = 4m∠7 + 12
Step 2: Rewrite systems of equations
I will set m∠6 = x and m∠7 to y
x + y = 180°
2x = 4y + 12
Step 3: Rewrite 2nd equation
2x = 2(2y + 6)
x = 2y + 6
Step 4: Use Substitution
2y + 6 + y = 180
3y + 6 = 180
3y = 174
y = 58°
Step 5: Find x by plugging y back into an original equation
x + 58 = 180
x = 122°
Step 6: Rewrite
x = m∠6
y = m∠7
m∠6 = 122°
m∠7 = 58°
Learn more about Linear Pair
brainly.com/question/17525542
#SPJ9
Isabella needed to get her computer fixed. She took it to the repair store. The
technician at the store worked on the computer for 4.25 hours and charged her $144
for parts. The total was $547.75. Which equation or tape diagram could be used to
represent the context if a represents the cost of labor per hour?
Answers
The equation is 547.75 = 4.25a + 144 so the tape diagram in option D is the correct answer.
What is an equation?A mathematical equation that represents the relationship of two expressions on either side of the sign.
It has one or more variables and equal to symbol.
Example: 3x – 5 = 5
We have,
Time spent fixing the computer = 4.25 hours
Cost of parts = $144
Total cost = $547.75
Cost of labor per hour = a
Since the cost of labor per hour is 'a' cost of labor for 4.25 hours is:
= 4.25 x a
= 4.25a
We can write an equation as:
547.75 = 4.25a + 144
Thus the tape diagram in option D is the correct answer.
Learn more about equations here:
https://brainly.com/question/28532602
#SPJ1