Green's theorem in vector calculus connects a line integral around a simple closed curve C to a double integral over the plane area D limited by C.
What is Green's Theorem?Green's theorem in vector calculus connects a line integral around a simple closed curve C to a double integral over the plane area D limited by C. It is a two-dimensional variant of Stokes' theorem.
The path of the particle is positively oriented so we can use Green's theorem to find the work done in moving particle along C.
The work done is given by [tex]\oint_{c}\vec F \cdot \vec{dr}[/tex]
Here, [tex]\vec F[/tex](x,y)=<x+y, y²-x>
Then [tex]\oint_{c}\vec F \cdot \vec{dr} = \oint_{c}(x+y)dx+(y^2-x)dy[/tex]
In comparison with [tex]\oint_{c}Pdx+Qdy[/tex] what we have,
P= x+y and Q=y²-x
Then [tex]\dfrac{\partial P}{\partial y} = 1[/tex] and [tex]\dfrac{\partial Q}{\partial x} =-1[/tex]
Using the Green's Theorem,
[tex]\oint_{c}Pdx+Qdy = \iint_{D} \left ( \dfrac{\partial Q}{\partial x}-\dfrac{\partial P}{\partial y}\right )dA[/tex]
Here D in polar Co-ordinates is given by,
D={(r,θ) : 0 ≤ r ≤ 7, 0 ≤ θ ≤ π}
Then
[tex]\oint_{c}(x+y)dx+(y^2-x)dy\\\\=-\iint_D 2dA\\\\=-\int_{\pi}^{0}\int_{0}^7 2r drd\theta\\\\=-49\pi[/tex]
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Which inequality does the graph
represent?
y
−2 O 2 x
2
−2
Answer:
Step-by-step explanation:
Estimate the product of 4.87 × 19.39 using compatible numbers.
Answer:
95
Step-by-step explanation:
you will approximate 4.87 which will be 5, the same as 19.39 which will be 19. Then you will multiply and your answer is 95If f(x)=√4x+9+2, which inequality can be used to find the domain of f(x)?
O √4x 20
O4x+920
4x20
√4x+9+220
Answer:
[-11/4, ∞)
Step-by-step explanation:
Given :
y = √(4x + 9 + 2)
Simplifying :
y = √(4x + 11)
Now, the term in the bracket has to be greater than or equal to 0 to be real.
Hence,
⇒ 4x + 11 ≥ 0
⇒ 4x ≥ -11
⇒ x ≥ -11/4 [Lower limit]
Infinity will be the upper limit as the numbers increase indefinitely.
The domain will be :
⇒ [-11/4, ∞)
I need help understanding this question
Answer: what question i don't see it but you can try reading it again and writing it down
4x = 20
How can I solve it quickly?
I don’t want only the results.
Answer:
5
Step-by-step explanation:
You need to do 4 divided by 4 on 1 side and 20 divided by 4 on the other side
4÷4= 1 so we are left with x
20÷4= 5 so we are left with 5
Therefore x=5
Hi student, let me help you out!
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We are asked to solve the equation 4x=20.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Remember, we need to get x all by itself.Is x all by itself? No, there's a 4 multiplied by it.
So, we do the opposite operation.
The opposite of multiplication is..?
Division.
Thus, we divide both sides by 4.
x=5
[tex]\ddot\bigstar[/tex] Remember this...
[tex]\fbox{When\;solving\;equations\;,\;our\;goal\;is\;to\;find\;the\;value\;of\;the\;variable,\;which\;in\;this\;case\;was\;x}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
~Just a smiley person helping fellow students :)
The function f(t) represents the cost to connect to the Internet at an online gaming store. It is a function of t, the time
in minutes spent on the Internet.
$0
0
f(t) = $5
30 < 1 ≤ 90
$10
> 90
Which statement is true about the Internet connection cost?
It costs $5 per hour to connect to the Internet at the gaming store.
The first half hour is free, and then it costs $5 per minute to connect to the Internet.
It costs $10 for each 90 minutes spent connected to the Internet at the gaming store.
Any amount of time over an hour and a half would cost $10.
The true statement about the Internet connection cost is D. Any amount of time over an hour and a half would cost $10.
How to explain the cost?In this situation, the function is f (t), when t is a value between 0 and 30. The cost is $0 for the first 30 minutes
When t is a value between 30 and 90, the cost is US$ 5 if the connection takes between 30 and 90 minutes.
Here, the true statement about the Internet connection cost is D. Any amount of time over an hour and a half would cost $10.
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answer the question please
Answer:
(d) 108°
Step-by-step explanation:
An inscribed angle is half the measure of the arc it subtends. Conversely, the arc is twice the measure of the inscribed angle it subtends.
__
using the relationWe can define the vertex of the marked angle as point Q. Arc XY is twice the measure of inscribed angle XQY:
arc XY = 2(54°) = 108°
1. Use rectangle ABDC below for parts a through d.
15 cm
B
8 cm
C
(a) Calculate the length of each side of the dilated image using a scale factor of 3. Show your work!
(2 pts)
A'B' = |
B'D' =
I
(b) Does the scale factor of 3 create an enlargement or reduction? (1 pt)
(c) Calculate the length of each side of the dilated image using a scale factor of Show your workl
(2 pts)
A'B' =
B'D' =
(d) Does the scale factor of create an enlargement or reduction? (1 pt)
Answer:
see the attachment photo!
Which of the following equations will produce the graph shown below?
+10
10-9-8-7-6-5-4-3-2-1-1 2 3 4 5 6 7 8 9 10
O A. 20x²-20y² = 400
OB.
B. 6x² + 6y² = 144
လ -
7 PTT || | |||||||||
ܚ ܐ ܕܬ ܘ ܟ ܗ ܗ ܙܪ ܣ ܣ
-3
-5
-7
-8
-9
-10
The equation that produces the circle in the given graph is; x² + y² = 16. The correct answer is option B.
The complete graph is attached with the answer below.
How to interpret the equation of a Circle?A circle is a two-dimensional geometry on the plane having a centre point and the circular line is drawn equidistant from the centre point.
The general form of the equation of a circle is;
(x - h)² + (y - k)² = r²
where;
h, k are coordinates of the circle centre r is the radius
From the graph, we can see that the coordinates of the centre are; (0, 0).
Also, the radius is;
r = √(4² - 0²)
r = √16
Thus, our equation of the circle in the graph is;
(x - 0)² + (y - 0)² = (√16)²
⇒ x² + y² = 16
Therefore the equation that produces the circle in the given graph is; x² + y² = 16. The correct answer is option B.
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(-11x^2 + 1.4x - 3) + (4x^2 - 2.7x + 8)
[tex]\underline{\boxed{\sf{-7x^2 - \frac{13}{10} x +5}}}[/tex]
Solution :-[tex]\sf{(-11x^2 + 1.4x - 3) + (4x^2 - 2.7x + 8)}[/tex]
Remove the parentheses:
[tex]\sf{-11x^2 + 1.4x - 3 + 4x^2 - 2.7x + 8}[/tex]
Convert decimal to fraction:
[tex]\sf{-11x^2 + \frac{14}{10} x - 3 + 4x^2 - \frac{27}{10} x + 8}[/tex]
Reduce fraction to the lowest term by canceling the greatest common factor:
[tex]\sf{-11x^2 + \frac{7}{5} x - 3 + 4x^2 - \frac{27}{10}x + 8}[/tex]
Combine like terms:
[tex]\sf{-7x^2 - \frac{13}{10} x +5}[/tex]
What is the surface area of this shape(step by step if possible)
Answer:
Step-by-step explanation:
((8 x 10) x 3) + ((9 x 8)/2) x2 = (80 x 3) + (72/2) x 2
= 240 + (36 x 2)
= 240 + 72
= 312
a company makes these biscuits at a cost of $1.35 per packet. these biscuits are sold for $1.89 per packet. calculate the percentage profit the company makes on each packet
Answer:
They Make 50 cents profit a pack
Step-by-step explanation:
1.89-1.35
What is the equation of the horizontal line through
(-7,-3)?
A catapult hurls a pumpkin from a height of 32 feet at an initial velocity of 96 feet per second. the function h(t)=-16t^2+96t+32 represents the heights of the pumpkin h(t) in terms of time t. what is the max height the pumpkins will reach and what time will it reach that height?
The maximum height of the pumpkin is 3 feet
We have given that,
A catapult hurls a pumpkin from a height of 32 feet at an initial velocity of 96 feet per second.
The function h(t)=-16t^2+96t+32 represents the heights of the pumpkin h(t) in terms of time t.
We have to determine the maximum height.
What is the maxima?
At the point of maxima f'(x)=0
first, find the maxima
Therefore differentiate the given function with respect to t we get,
[tex]h'(t)=-32t+96[/tex]
h'(t)=0
Then we get,
[tex]0=-32t+96\\-32t=-96\\t=\frac{-96}{-32} \\t=3[/tex]
Therefore the maximum height of the pumpkin is 3 feet.
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pls help... Prove (1+tanx)/(1+cotx)=tanx by algebra
[tex]\text{L.H.S}\\\\=\dfrac{1+\tan x}{ 1+ \cot x}\\\\\\=\dfrac{1+ \tan x}{ 1+ \tfrac 1{\tan x}}\\\\\\=\dfrac{1+\tan x}{\tfrac{\tan x+1}{\tan x}}\\\\\\=(1+\tan x) \times \dfrac{\tan x}{1+ \tan x}\\\\=\tan x\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]
7x+16=8x+15 solve for x and y
Answer:
x = 1
Step-by-step explanation:
7x + 16 = 8x + 15
Step 1 : Subtract 15 on both sides
7x + 16 - 15 = 8x
7x + 1 = 8x
Step 2 : Subtract 7x on both sides
1 = 8x - 7x
1 = 1x
x = 1
1 over 3b = 4 over 5 . Which of the following equals b in this equation? (4 points)
2 2 over 5
1 1 over 8
2 over 5
1 over 4
Answer:
none of the answers listed are equivalent to b (22/5, 11/8, 2/5, 1/4)
Step-by-step explanation:
[tex]\frac{1}{3b} = \frac{4}{5}[/tex]
to simplify, cross multiply
(1 · 5 = 3b · 4)
(5 = 12b)
divide both sides by 12 to isolate b,
[tex]\frac{5}{12} =\frac{12b}{12}[/tex]
[tex]\frac{5}{12} = b[/tex]
None of the answers listed are equivalent to 5/12
[tex]\frac{5}{12}[/tex] [tex]\neq[/tex][tex]\frac{22}{5}[/tex]
[tex]\frac{5}{12} \neq[/tex][tex]\frac{11}{8}[/tex]
[tex]\frac{5}{12} \neq[/tex][tex]\frac{2}{5}[/tex]
[tex]\frac{5}{12} \neq[/tex][tex]\frac{1}{4}[/tex]
Her house is at (-4, 10). Her school is at (-4, 3). The community center is at (2, 3) The grocery store is at (-4, -6) Part A: Use absolute values to calculate the distance in units from Nina's house to her school. Show your work. (4 points) Part B: Is the total distance from Nina's house to the school to the grocery store greater than the total distance from Nina's house to the school to the community center? Justify your answer. (6 points)
For part A, we will see that the distance is 7 units. For part B, the distance from Nina's house to the school to the grocery store is larger.
How to find the distances?
Remember that the distance between two points (a, b) and (c, d) is:
[tex]D = \sqrt{(a - c)^2 + (b - d)^2}[/tex]
A) Her house is at (-4, 10), and her school is at (-4, 3), so the distance is:
[tex]D = \sqrt{(-4 - (-4))^2 + (10 - 3)^2} = \sqrt{7^2} = 7[/tex]
The distance is 7 units.
B) In the first case, the distance between the school and the grocery store is:
[tex]D' = \sqrt{(-4 - (-4))^2 + (3 - (-6))^2} = 9[/tex]
So the total distance is 9 + 7 = 16
And the distance between the school and the community center is:
[tex]D'' = \sqrt{(-4 - 2)^2 + (3 - 3)^2} = 6[/tex]
So the total distance is 6 + 7 = 13
So we can see that the total distance from Nina's house, to the school, to the grocery store is larger than the other.
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A set of 15 students took a math test. The test was out of 50 points and the scores were as followed: 23, 28, 29, 30, 30, 32, 33, 36, 36, 40, 41, 43, 45, 46, 48 1.
Find the Mean test score of the test
2. Find the Standard Deviation of the test 3. Using a Normal Distribution, what is the probability a student scores higher *than a 35 on the test
4. Using a Normal Distribution, what is the probability a student scores between a 30 and 40 on the test?
Answer:
1. 33.6
Step-by-step explanation:
1. Mean = total score/number of tests
= (23+28+29+30+30+32+33+36+36+40+41+43+45+46+48)/15
=33.6
I don't know any of the others, but I hope that this will be helpful :)
Rewrite using a single positive exponent. 3-6 -5
Answer:
[tex]1 \div {3}^{( 30)} [/tex]
Step-by-step explanation:
There are exponent rules I posted above that are being used here.
We have (3^-6)^-5
Since we have a power times a power, we multiply 6 and 5 to get -30. Look at the first example in the photo.
So, we're left with 3^-30.
If you look at the photo, there's a rule for negative exponents.
Take the inverse of the base number, so 3 in this case:
1 / 3
and then make the exponent positive after taking the inverse.
So, we should get 1 / 3^30
Hope this helps!
13. a) Write 2 solutions of the equation 2x - 3y = 6
b) Write the equations two lines passing through the point (-3, 2)
Answer:
y=4/3x+6
Step-by-step explanation:
The graph of y = f(x) is shown on the grid.
Both graph M and N are translations of the graph y = f(x).
a) Write down the equation of graph M.
b) Write down the equation of graph N.
Both M(x) and N(x) are translations of f(x), the equations are:
N(x) = f(x + 4).
M(x) = f(x) + 4.
How to find the equations for the translations?Remember that for a function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N
If N > 0, the translation is upwards.If N < 0, the translation is downwards.And for a function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N).
If N > 0, the translation is to the left.If N < 0, the translation is to the right.First, we can see that N is a translation of 4 units to the left, then:
N(x) = f(x + 4).
And M is a translation upwards of 4 units, then:
M(x) = f(x) + 4.
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Which are rational numbers?
Check all that are true. 3/10 3/1 0/3 -191/32 3/456
Check all that are true
NEED ANSWER ASAPPPPP
3/0 and -191/32
lmk if this is wrong, I might be.
25 is added to the product of a number and 2
Answer:
2x + 25
Step-by-step explanation:
Let that number be x.
Step 1 : Multiply x and 2.
x * 2 = 2x
Step 2 : Add 25 and 2x.
2x + 25
Hence,
25 is added to the product of a number and 2 is 2x + 25.
HELP
Select the correct answer from each drop-down menu.
12 cm
12 cm
12 cm
12 cm
12 cm
12 cm
12 cm
12 cm
12 cm
12 cm
12 cm
12 cm
12 cm
12 cm
12 cm
12 cm
The three-dimensional shape that this net represents is a
The surface area of the figure is
12 cm
12 cm
12 cm
square centimeters.
Reset
Next
The net represents a cube.
The net shows a cube with a side length of 12 cm, meaning its surface area is [tex]6(12)^{2}=\boxed{864 \text{ cm}^{3}}[/tex]
Answer:
cube864 cm²Step-by-step explanation:
The Platonic solid with six (6) square faces is the cube. Its surface area is the sum of the areas of the square faces. Each of those is the square of its edge length.
__
The 3-dimensional shape represented by the net is a cube.
The area of the cube is ...
6 × (12 cm)² = 6 × (144 cm²) = 864 cm²
IM IN NEED OF HELP ASAP!!
Answer:
B. [tex]\frac{14}{625}[/tex]
Step-by-step explanation:
Total paper in the hat:
2 blue + 6 red + 10 yellow + 7 purple = 25 total pieces of paper
P(AB) = 7 / 25 x 2 / 25
A is the probability of pulling a purple paper
B is the probability of pulling a blue paper
Answer:
14/625
Step-by-step explanation:
probability = favorable outcomes/total number of outcomes
First find the probability of drawing a purple piece of paper.
There are 7 pieces of purple paper.
Add all the amounts of colored paper together to get the total number of outcomes.
2 + 6 + 10 + 7 = 25
The probability of drawing purple is 7/25
Now find the probability of drawing blue. There are 2 blue pieces of paper. Since he replaces the purple paper the total stays at 25.
The probability of drawing blue is 2/25
This is a compound probability problem, so multiply the two probabilities together.
7/25 x 2/25
14/625
help me thank u if u do
Answer:
Choice 4^th
Step-by-step explanation:
Given:
1/2+3/4+7/16 = __
To Solve:
Addition equation by finding a common multiple.
Solution:
Let the blank _ be x.
Then,
1/2+3/4+7/16 = x
Flip this equation:
x = 1/2+3/4+7/16Now solve for x.
x = (1/2+3/4)+7/16 x = 5/4+7/16x = 27/16Hence,
1/2+3/4+7/16 = 27/16
4^th Choice is accurate.
PLS HELP FAST
Points X and Y lie on (circle)P so that PX = 5 meters and m∠XPY = 90. Find the length of XY to the nearest hundredth.
Step-by-step explanation:
P means the center of the circle.
any point on the circle has therefore a constant distance from the center : the radius r.
r = 5 m
what we need to find is the length of the circle arc between the 2 points that represents 90° of the overall circle (360°).
90/360 = 1/4
so, we are looking for 1/4 of the overall circle circumference :
2×pi×r × 1/4 = 2×pi×5 × 1/4 = pi×10/4 = pi×5/2 =
= 7.853981634... m ≈ 7.85 m
Solve triangle abc round your answers to the nearest hundredth if necessary.
Step-by-step explanation:
where are the pictures ? or diagram?
URGENT
A watch keeps exact time, but it has only an hour hand. When the hour is is of the distance between the 4 and the 5, the correct time is???
Answer:
It will be 4 30
Step-by-step explanation:
Mark me as a brainliest.