Answers
The area of the interior above the polar axis is -0.858 square units
The area bounded by a polar curveThe area bounded by a polar curve between θ = θ₁ and θ = θ₂ is given by
[tex]A = \int\limits^{\theta_{2} }_{\theta_{1} } {\frac{1}{2}r^{2} } \, d\theta[/tex]
Now, since we have the curve r = 1 - sinθ and we want to find the area of the interior above the polar axis, we integrate from θ = 0 to θ = π, since this is the region above the polar axis.
So, [tex]A = \int\limits^{\theta_{2} }_{\theta_{1} } {\frac{1}{2}r^{2} } \, d\theta\\= \int\limits^{\pi}_{0} {\frac{1}{2}(1 - sin\theta)^{2} } \, d\theta\\= \int\limits^{\pi}_{0} {\frac{1}{2}[1 - 2sin\theta + (sin\theta)^{2}] } \, d\theta\\= \int\limits^{\pi}_{0} {\frac{1}{2}\, d\theta - \int\limits^{\pi}_{0} 2sin\theta \, d\theta+ \int\limits^{\pi}_{0} (sin\theta)^{2} } \, d\theta\\[/tex]
[tex]A = \int\limits^{\pi}_{0} {\frac{1}{2}\, d\theta - 2\int\limits^{\pi}_{0} sin\theta \, d\theta+ \int\limits^{\pi}_{0} \frac{(1 - cos2\theta)}{2} } \, d\theta\\= \int\limits^{\pi}_{0} {\frac{1}{2}\, d\theta - 2\int\limits^{\pi}_{0} sin\theta \, d\theta+ \int\limits^{\pi}_{0} \frac{1}{2} } \, d\theta -\int\limits^{\pi}_{0} \frac{cos2\theta}{2} } \, d\theta\\[/tex]
[tex]A = \int\limits^{\pi}_{0} \, d\theta - 2\int\limits^{\pi}_{0} sin\theta \, d\theta -\int\limits^{\pi}_{0} \frac{cos2\theta}{2} } \, d\theta\\= [\theta]_{0}^{\pi} - 2[-cos\theta]^{\pi} _{0} - [\frac{sin2\theta}{4}]_{0}^{\pi} \\= [\theta]_{0}^{\pi} + 2[cos\theta]^{\pi} _{0} - [\frac{sin2\theta}{4}]_{0}^{\pi}\\= [\pi - 0] + 2[cos\pi - cos0] - \frac{ [sin2\pi - sin0]}{4}\\= \pi + 2[-1 - 1] - \frac{ [0 - 0]}{4}\\= \pi + 2[-2] - \frac{ [0]}{4}\\= \pi - 4 - 0\\= \pi - 4\\= 3.142 - 4\\= -0.858[/tex]
So, the area of the interior above the polar axis is -0.858 square units
Learn more about area bounded by polar curve here:
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Related Questions
The rectangle is rotated 180º counterclockwise about the origin. Which of the following ordered pairs is a vertex of the rectangle’s image?
A.
(-5, 1)
B.
(-4, -1)
C.
(4, -5)
D.
(4, 4)
Answers
The ordered pair is a vertex of the rectangle’s image will be (-4, -1). Then the correct option is B.
What is a transformation of a shape?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the structure and/or location of the object.
From before the refers to the object's initial condition, and Picture, after transformation, refers to the object's ultimate structure and location.
Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.
The rectangle is in the first quadrant then the coordinate of the vertices of a rectangle will be positive (x, y).
The rectangle is rotated 180º counterclockwise about the origin.
The rectangle will be in the third quadrant then the coordinate of the vertices of the rectangle will be negative (-x, -y).
Thus, the ordered pair is a vertex of the rectangle’s image will be (-4, -1). Then the correct option is B.
More about the transformation of the shape link is given below.
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HELPPPP
the last part says select 3 options
Answers
Answer:
Last three options are correct answers.
Step-by-step explanation:
Hope it helps you in your learning process.
Answer:
Last 3 ones are correct.
Step-by-step explanation:
The first one isn't it, because there needs to be 3 y's.
The second one isn't it, because the numbers equal 112, which isn't equal to 1120.
So it says to select 3, which means that the last 3 ones are correct.
(sorry if I'm incorrect, I'm bad at these questions)
I need to solve -15 (1/5w -1/3) problem for math class
Answers
-3w-5
hope that helps^^
The measure of the missing angle is
degrees.
Answers
Step-by-step explanation:
The exterior angles of a triangle is equal to the sum of two non - adjacent interior angles. Now , Set up an equation and solve for x.
[tex] \large{ \tt{x \degree = 63 \degree + 86 \degree}}[/tex]
[tex] \large{ \tt{x \degree = \boxed{ \tt{149 \degree}}}}[/tex]
Hope I helped ! ツ
Have a wonderful day / night ! ♡
# [tex] \underbrace{ \text{Carry \: On \: Learning}}[/tex] !! ✎
▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
Prices of plants: $10, $8, $20, $25, $14, $98, $11, $9, $8, $6
Which measure of center best represent the data?
A.
mean
B.
median
C.
mode
D.
range
Answers
wouldnt it be nice to have a anwers
(A)
Answer:
A
Step-by-step explanation:
Mean gives you the average, so it would give you the average of the price . Sorry if this is wrong .
13x-5 Ugh help please
Answers
[tex] \huge\bf\red{answer}[/tex]
The expression is not factorable with rational numbers.If m∠D=104°, what is m∠D'?
Answers
Answer:
m<D' = 180⁰-104⁰
m<D' = 76⁰
is the ordered pair (1, -3) a solution to
3x + 5y = -8?
Answers
Answer:
Yes give Brainliest
Step-by-step explanation:
To find y place the other terms in the equation to the right
hand side of the equation.
Thus : 5y = 7 - 3x
( now divide both sides by 5 )
⇒ 5y5=7−3x5=15(7−3x)
now will you give brainliest?
Use distributive property for 3.2= 4/5(b - 5)
Answers
Given m∥n, find the value of x.
Answers
Answer:
53°
Step-by-step explanation:
Of the two lines are parallel then x = 53°
It is important to comparison shop when purchasing a car.
What does comparison shop mean?
-Always buy from a
local dealership
-Take several photos to
use for comparison
-Compare the price &
quality from different
vendors
-Compare the true
market value of every
vehicle
Answers
Answer:
Compare price and quality
Step-by-step explanation:
I did this test
Answer:
option c
Step-by-step explanation:
comparing the price and quality from different vendors is important as we are giving a money we should be sure enough that quality is also as much the money
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
2y – 2 = -8
Answers
Answer:
[tex]y = x - 4[/tex]
Step-by-step explanation:
Given
[tex]2y - 2x = -8[/tex] -- correct expression
Required
Represent as slope intercept form
[tex]2y - 2x = -8[/tex]
Make 2y the subject
[tex]2y = 2x - 8[/tex]
Divide through by 2
[tex]\frac{2y}{2} = \frac{2x}{2} - \frac{8}{2}[/tex]
[tex]y = x - 4[/tex]
if
sin150°=1/2 fiind sin75°
Answers
Answer:
thank u for free points
Step-by-step explanation:
......
A cliff Diver jumps from 50 feet into a lake. After hitting the water he travelled 22 feet below the surface. How far did he travel?
Answers
Add both distances together:
50 + 22 = 72 feet total distance.
4x 4/4 is equal to 1 , since 4/4 is equal to 1
Answers
Answer:
False, it is equal to 4.
Step-by-step explanation:
The current question asks that 4 x 4/4 is equal to 1, since 4/4 is equal to 1, but this stems from a gross misinterpretation of mathematics.
Although it is true that 4/4 is equal to one, since the 4 parts that make up an integer are completed, when multiplying the number 1 4 times this mathematical operation will result in 4, since 4 x 1 = 4.
What is the value of the expression below?
13 - (-9)
Answers
13 - 9 = 4
Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (negative 4) = 7
Negative 5 + x = negative 2
Answers
69
Step-by-step explanation:
2+ x = 5
x + 1 = 4
9 + x = 6
x + (negative 4) = 7
Negative 5 + x = negative 2
x + 1 = 4
-5 + x = -2
In all of these, x is positive 3.
solve and receive brain list
Answers
Answer:
it is called COLD DRANK
Step-by-step explanation:
REAPEAT AFTER ME COLD DRANK OK C-O-L-D D-R-A-N-K
Answer:
Step-by-step explanation:
6x + 26 = 8x - 12 ( 1 - 3x )
6x + 26 = 8x - 12 + 36x
Doing like terms on one side,
6x -8x -36x = -12 -26
-38x = -38
x = -38 / -38
x = 1
Hope this helps you. Do vote my answer.
Thanks
Calculate the slope of the graph using (4,8) and (1, 10) using the Slope Formula. Write your answer in simplest form
Answers
Answer:
y=x+11
the slope is 2/2 or 1/1, which equals 1. Your y-int is 11.
combine like terms to create an equivalent expression
3.26d + 9.75d - 2.65
Answers
Answer:
13.01d - 2.65
Step-by-step explanation:
DON'T IGNORE THIS PART!!!
Hmmm... in order to be able to solve these type of expressions and more complex ones, we need to know what like terms are in the first place.
Well, the best definition of like terms is: Terms that have the same exact variables.
Let's see the terms that have the same exact variables! They are 3.26d and 9.75d.
By the way, before we continue--I would like to mention something extremely important: 3.26d and 9.75d are positive, whereas -2.65 is negative (you know, the negative sign appears right before it).
Now, let's add 3.26d and 9.75d. It equals 13.01d.
TIME TO COMBINE!!!
13.01d - 2.65
Is borrowing money a
Delegated power
Reserved power
Concurrent power
Answers
x to the third power =8/27
Answers
Answer:
2/3
Step-by-step explanation:
2/3
4
Jared has a collection of 90 movies on DVD. If
46 of the movies are comedies, 26 are drama,
and the rest are science fiction, what percent of
the movies are science fiction?
A) 18
B) 20
C) 28
D) 32
Answers
18/90 movies are science fiction
18/90 x 100 = 20%
So it’s B :)
Answer:
It's B but read the other person's explanation it's better than mine would be
Step-by-step explanation:
en un día de trabajo una pastelería ha producido 100 pasteles, de los cuales (2/5 en fracciones) tienen crema y (1/4 en fracciones) de la producción de pasteles no tiene crema y el resto son díbeticos ¿cuantos pasteles hay para diabéticos?
Answers
tfyhgbuhbj tctf ybubbimihbighv no
Step-by-step explanation:
tdcvyvj j ct ruv yo bb. v
..
There is a 15% off sale on a
PlayStation 5. If the original
cost is $700, what is the
sale price of the
PlayStation?
Answers
Answer:
$595
Step-by-step explanation:
equations with variables on both sides that makes the answer x=9
Answers
Answer:
x = 12
Step-by-step explanation:
Answer:
2x=18
Step-by-step explanation:
Can someone help me? I know I'm doing something wrong but I'm not sure what.
This is an example: A $624 at 5% for 3 years
This is how I solved the problem:
(624)(.05)(3)
= 93.60
Answers
Answer:
Step-by-step explanation:
CI = 624 x 1.05 ^3 =722.358 for whole investment 722.36-624 =98.36 for interest only
or for interest only do 624 x .05^3 = 98.36
Standard interest is done like this
year 1 = 624 x 1.05 = 655.20
655.20-624 = 31.20
year 2 = 655.20 + 31.20 = 686.40
year 3 = 686.40 + 31.20 = 717.60
total interest = 717.60-624 = 93.60
So standard interest is the method you have done they may be asking for either compound interest which is the first one or asking for whole investment which means you need to also add 624 at end for Standard interest.
if you need CI interest do the top one.
1. 3/4 + 1/3 =
2. 1/6 + 2/3 =
3. 3/8 + 1/4 =
4. 1/3 + 2/5 =
5. 1/8 + 3/4 =
6. 2/5 + 7/10 =
7. 1/6 + 1/3 + 3/4 =
8. 1/10 + 3/10 + 3/5 =
9. 3/8 + 5/5 + 1/2 =
Solve
10. Lisa swam 3/8 of a mile in the morning and 5/16 of a mile in the afternoon. How far did she swim?
Answers
Answer:
1. 3/4 + 1/3 = 1 1/12
2. 1/6 + 2/3 = 5/6
3. 3/8 + 1/4 = 1/4
4. 1/3 + 2/5 = 11/15
5. 1/8 + 3/4 = 7/8
6. 2/5 + 7/10 = 1 1/10
7. 1/6 + 1/3 + 3/4 = 1
8. 1/10 + 3/10 + 3/5 = 1
9. 3/8 + 5/5 + 1/2 = 7/8
10. 11/16
Step-by-step explanation:
A grocery store manager ordered 243 cases of Cheez its. Each case contains 15 boxes and each box is made up 8 packs of Cheezb its. How many packs of Cheez its did the grocery store manager order?
Answers
Answer:
29160
Step-by-step explanation:
243*15*8
Describe the slope and y-intercept of the line y = -x + 2.
Answers
Answer:
slope = -1
y intercept= 2
Step-by-step explanation:
compare the equation with the standard equation Y= MX + C
where M is the slope
to find Y intercept substitute the value of x as 0