By Green's theorem, the line integral
[tex]\displaystyle \int_C f(x,y)\,\mathrm dx + g(x,y)\,\mathrm dy[/tex]
is equivalent to the double integral
[tex]\displaystyle \iint_D \frac{\partial g}{\partial x} - \frac{\partial f}{\partial y} \,\mathrm dx\,\mathrm dy[/tex]
where D is the region bounded by the curve C, provided that this integrand has no singularities anywhere within D or on its boundary.
It's a bit difficult to make out what your integral should say, but I'd hazard a guess of
[tex]\displaystyle \int_C \left(3y+5e^{-x}\right)\,\mathrm dx + \left(10x+3\cos\left(y^2\right)\right)\,\mathrm dy[/tex]
Then the region D is
D = {(x, y) : 0 ≤ x ≤ 1 and x ² ≤ y ≤ √x}
so the line integral is equal to
[tex]\displaystyle \int_0^1\int_{x^2}^{\sqrt x} \frac{\partial\left(10x+3\cos\left(y^2\right)\right)}{\partial x} - \frac{\partial\left(3y+5e^{-x}\right)}{\partial y}\,\mathrm dy\,\mathrm dx \\\\ = \int_0^1 \int_{x^2}^{\sqrt x} (10-3)\,\mathrm dy\,\mathrm dx \\\\ = 7\int_0^1 \int_{x^2}^{\sqrt x} \mathrm dy\,\mathrm dx[/tex]
which in this case is 7 times the area of D.
The remaining integral is trivial:
[tex]\displaystyle 7\int_0^1\int_{x^2}^{\sqrt x}\mathrm dy\,\mathrm dx = 7\int_0^1y\bigg|_{y=x^2}^{y=\sqrt x}\,\mathrm dx \\\\ = 7 \int_0^1\left(\sqrt x-x^2\right)\,\mathrm dx \\\\ = 7 \left(\frac23x^{3/2}-\frac13x^3\right)\bigg|_{x=0}^{x=1} = 7\left(\frac23-\frac13\right) = \boxed{\frac73}[/tex]
What is the cardinal number of the set {-1,3,7,52,36,19,-6}
Answer:
can you please send me another one
How many pounds are in 2 tons, 800 pounds
Answer:
4,00 pounds
Step-by-step explanation:
Answer:
4,800 pounds
Step-by-step explanation:
2 tons = 4,000 pounds
800 pounds
4,000 + 800 =
4,800 pounds
25% of £90
Work it out
Answer:
22.5
Step-by-step explanation:
percent is any number over 100, so 25% is 25 over 100, this means that 25% can be written as:
25100
Now, any number in fractional form (a number over a number) is the same as division so 25% can also be written as a decimal, we just move the decimal point 2 places to the right of 25, like this:
25100=0.25
Now we have two ways that we can solve this problem! I'll start with the fractional method of solving.
I’m having trouble finding the answers to this problem
Step-by-step explanation:
Solve by Subsitution
[tex]x = 50 - y[/tex]
Replace this into the second equation
[tex]y(50 - y) = 300[/tex]
[tex]50y - {y}^{2} = 300[/tex]
Write in standard form
[tex] - {y}^{2} + 50y = 300[/tex]
Use the quadratic formula, and our answer will be
(6.97,43.02)
(43.02,6.97)
Anyone good with calculus? Please help.
First take a time derivative of a function describing motion,
[tex]\frac{d}{dt}h(t)=\frac{d}{dt}-4.9t^2+19.6t-14.6=-9.8t+19.6[/tex].
Finding the maxima of the function is obtained by determining where the critical points are. You can find the critical points by equating the derivative with 0 and solving for t,
[tex]\frac{d}{dt}h(t)=0[/tex]
[tex]-9.8t+19.6=0\implies t=\frac{19.6}{9.8}=\boxed{2}[/tex].
So at 2 seconds the ball peaks in height.
To find out the height feed 2 to the function h.
[tex]h(2)=-4.9\cdot2^2+19.6\cdot2-14.6=\boxed{5}[/tex].
So at 2 seconds the ball reaches maximum height of 5 meters.
Hope this helps :)
A canoeist traveling with the current traveled the 24 miles between two riverside campsites in 2 hours. The return trip against the current took 3 hours. Find the speed of the canoeist in still water and the speed of the current, both in miles per hour.
Answer:
Speed of canoiest is 10 miles/hour.
Speed of current is 2 miles/hour.
Step-by-step explanation:
Let the speed of canoiest is v and the speed of current is u.
distance = speed x time
24 = (v + u ) x 2
v + u = 12 ..... (1)
Now
24 = (v- u) x 3
v - u = 8 .... (2)
By solving (1) and (2)
2 v = 20
v = 10 miles/hour
u = 2 miles/hour
A telephone pole has a wire attached to its top that is anchored to the ground. The distance from the bottom of the pole to the anchor point is 49 feet less than the height of the pole. If the wire is to be 14 feet longer than the height of the pole, what is the height of the pole?
9514 1404 393
Answer:
105 ft
Step-by-step explanation:
Let x represent the height of the pole. Then (x -49) is the distance from the pole to the anchor point, and (x+14) is the length of the wire from the top of the pole to the anchor point.
The Pythagorean theorem gives us the relation ...
(x +14)² = x² +(x -49)²
x² +28x +196 = x² +x² -98x +2401 . . . . eliminate parentheses
x² -126x +2205 = 0 . . . . . . . . put in standard form
x² -126x +3969 -1764 = 0 . . . . "complete the square)
(x -63) = ±√1764 . . . . . . add 1764, take the square root
x = 63 +42 = 105 . . . . . . highest value root. The pole must be higher than 49 feet
The height of the pole is 105 feet.
Which expression is equivalent to this polynomial? 9x^2 + 4
A. (3x+2i)(3x-2i)
B. (3x+2)(3x-2)
C. (3x+2i)^2
D. (3x+2)^2
f(x)=-2x^2+x-5 find f(5)
f(5) = -50
Hope it helps you...
What is the length of Line segment A C? Round to the nearest tenth.
Triangle A B C is shown. Angle A C B is 90 degrees and angle B A C is 55 degrees. The length of C B is 15 meters.
10.5 m
12.3 m
18.3 m
21.4 m
Answer:
10.5
Step-by-step explanation:
In the picture if you think about it, it has to be a number less than 15 since CB is 15. I picked 12.3 and got it wrong therefore it has to be 10.5.
Answer:
A) 10.5
Step-by-step explanation:
1. Find the equation of each of the straight line graphs that passes through the given
points.
(i) (1, 7) (2, 10)
(ii) (3, -1) (-2, 9)
(iii) (4, 3) (8,4)
(iv) (2, -5) (-2, 7
(v) (-1, -8) (3, 12)
(vi) (-5, 1) (10, –5)
(viii) (2, 2) (0, -4)
Answer:
25.987957
Step-by-step explanation:
Eileen is reading a novel for her library’s summer reading program. Which question can Eileen ask herself to best form a personal connection with the text?
A. What symbolism does this novel share with other novels I have read?
B. How do the facts in the text add to what I already know about my research topic?
C. What connections can I build between the themes in this text and other modern stories?
D. How do the struggles of the characters compare with challenges I have faced in my own life?
Answer:
Step-by-step explanation:
To begin with the answer. This is very personal, but I would choose D. I think you have to relate things to what you know. How do other people live through the same problem? Does the author believe that the best path has been chosen, or does he/she believe that the central character is doomed to failure? And how do these comments relate to me. You are going to get the most out of any novel when you can relate to the central character or any of the characters for that matter.
I'm not concerned with C. You can read trash and what they say is likely consistent but that only means that trash is pandering to a clientele that does not want to think much. Whatever spin you put on C, agreement is not a terrific thing. It does not make you think.
I suppose B is important if you are reading non fiction. I'm not answering it that way.
A: not the answer. This is a very remote connection. Most of the time symbolism is not the main attraction of any novel nor especially of any non fiction writing. Moby D*ick is not a great novel because of its symbolism of which there is a huge amount. It is a great novel because the conflict is between man and nature and although that is symbolic, it is not as important as the character study of Ahab (who is himself a symbol). Nor or Ishmael for that matter. I will admit you have to have a Bible in one hand and Moby Di*ck in the other, but it is not critical. The theme is.
Find the intersection of the line and the circle given below
2x+y=-5
x^2+y^2=10
Answer:
There are two intersections.
(-3,1) and (-1,-3)
Step-by-step explanation:
Answer:
They intersect at (-3,1), and also (-1,-3)
Step-by-step explanation:
Graph:
Find the volume of the figure. Round to the nearest tenth if necessary.
Answer:
Volume = 204 m³
Step-by-step explanation:
The figure is a triangular prism
Volume of the triangular prism = ½ × a × c × h
Where,
a = 8 m
c = 5.1 m
h = 10 m
Plug in the known values and solve
Volume = ½ × 8 × 5.1 × 10
Volume = 4 × 5.1 × 10
Volume = 204 m³
Can someone plz solve this for me
Answer: [tex]y^\frac{1}{8}[/tex]
Step-by-step explanation:
Ok so when taking roots the number in the little corner at the left of the radical sign (if there is one) is the root you take. It could be the 4th root, 6th root, or the x root. You don't have to use the radical sign though, you can use an exponent to write it. All you have to do is take the reciprocal of the number to find what to write for the exponent. So for those examples it would be [tex]\frac{1}{4}, \frac{1}{6} ,\frac{1}{x}[/tex]. The number in the top left of the radical sign is 8 so the answer would be [tex]y^\frac{1}{8}[/tex]
A precise statement of the qualities of an idea, object, or process is called a
O A. theorem
O B. proof
C. definition
D. common notion
Answer:
C. definition
Step-by-step explanation:
A precise statement of the qualities of an idea, object, or process is called a definition. Hence, option (C) is answer.
Can someone help please
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Answer:
(b) f(x) = (-x)^(1/2)
Step-by-step explanation:
The square root is only defined for argument values that are non-negative. Hence the domain of ...
f(x) = (-x)^(1/2)
is all values of x less than or equal to zero. This is not "all values of x."
Ayúdenme con esta multiplicación de polinomio por favor
(2×+3y)(-4ײy-2×y²)
Answer: welcome to brainly
Step-by-step explanation:
Hello there! My name is agenthammerx, a Master Answerer and Engagement Team Member here on Brainly. I am here to welcome you to the site! Thank you for taking initiative to check out Brainly and for posting your first question! The Brainly Community welcomes you. If you have any questions regarding anything about the site, please don’t hesitate to reach out to me! I will try my best to help you and answer your question or check out our help center at https://faq.brainly.com/
The length of a ladder leaning against a building is 60 feet. The ladder hits the building at the top of the building. The distance to the building from where the ladder touches the ground is 15 feet. What is the height of the building to the nearest foot?
A. 38ft
B. 48ft
C. 58ft
D. 68ft
Answer:
C. 58ft
Step-by-step explanation:
An imaginary triangle is described here. The hypotenuse is 60, and one of the other sides is 15.
60*60=3600
15*15=225
3600-225=3375
sqrt3375=58.09
round that to get 58ft
This is the question I am stuck on
Answer:
a^ 8 / b^12
Step-by-step explanation:
We know that x^y / x^z = x^ (y-z)
a^-5 b^-4
----------------
a^ -13 b^8
a^ (-5 - -13) b ^ (-4 -8)
a^ (-5+13) b^ (-4-8)
a^ 8 b^ (-12)
We know that x ^ - y = 1/ x^y
a^ 8 / b^12
Water is leaking out of an inverted conical tank at a rate of13400cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height8meters and the diameter at the top is6meters. If the water level is rising at a rate of24centimeters per minute when the height of the water is5meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.
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Answer:
2,664,118.8 cm³/min
Step-by-step explanation:
The diameter at the water level of 5 m is (5/8)(6 m) = 3.75 m, so the area of the water surface is ...
A = (π/4)d² = (π/4)(3.75 m)² ≈ 11.044662 m²
When rising at the rate of 24 cm/min, the volume is increasing at the rate ...
(110,446.62 cm²)(24 cm/min = 2,650718.8 cm³/min
The input volume must be sufficient to accommodate this increase as well as the leakage. Then the input volume is ...
2,650718.8 cm³/min + 13,400 cm³/min = 2,664,118.8 cm³/min
when it is transformed to
What is the effect on the graph of f (2)
g(x) = 1 +112
A. The graph of f(x) is shifted 11 units to the left.
B. The graph of f(x) is shifted 11 units to the right.
C. The graph of f(x) is shifted 11 units up.
D. The graph of f(x) is shifted 11 units down.
Answer:
C. The graph of f(x) is shifted 11 units up.
Step-by-step explanation:
Given
[tex]g(x) = f(x) + 11[/tex]
Required
Interpret g(x)
When a function is shifted up in b units, the rule is:
[tex](x,y) \to (x,y+b)[/tex]
Replace b with 11
[tex](x,y) \to (x,y+11)[/tex]
Replace y with f(x)
[tex](x,f(x)) \to (x,f(x)+11)[/tex]
So, we have:
[tex]g(x) = f(x) + 11[/tex]
Hence; f(x) is shifted 11 units up.
Given the function f(x) = 7x^2 − 2x + 5. Calculate the following values:
We have that the Fuction's result for the given values are
f(-2) =37f(-1) =14f(0) =5 f(1) =10f(2) =29
From the Question we are told that
Function
[tex]f(x) = 7x^2 -2x + 5.[/tex]
Generally
For -2
[tex]f(-2) = 7(-2)^2 − 2(-2) + 5.[/tex]
f(-2) =37
For -1
[tex]f(-1) = 7(-1)^2 − 2(-1) + 5.[/tex]
f(-1) =14
For 0
[tex]f(0) = 7(0)^2 − 2(0) + 5.[/tex]
f(0) =5
For 0
[tex]f(1) = 7(1)^2 − 2(1) + 5.[/tex]
f(1) =10
For 2
[tex]f(2) = 7(2)^2 − 2(2) + 5.[/tex]
f(2) =29
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factor the polynomial
-x5+36x3-22x2-147x-90
Answer:
-(x+6)(x+1)^2(x-3)(x-5)
Step-by-step explanation:
Which statements about the relationship between the two triangles below are true? Check all that apply,
Answer:
I don't know, because i really don't know
i will give brainliest!
Given a rhombus has a side length of 15 and one diagonal has a length of 2x. Find the length of the second diagonal in terms of x. Show all work and leave your answer in radical form.
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Answer:
2√(225 -x²)
Step-by-step explanation:
Let 2y be the length of the second diagonal. The half-diagonals and the side of the rhombus form a right triangle. The Pythagorean theorem tells us the relationship between sides and hypotenuse is ...
x² +y² = 15²
y² = 225 -x²
2y = 2√(225 -x²2) . . . . the length of the second diagonal
Expand the following: 4(a + 3b - 5c).
Please help, I'm really struggling with expanding equations
Answer:
4a+12b-20c
Step-by-step explanation:
Use the distributive property, multiply the number on the outside to everythign on the inside.
4*a=4a
4*3b=12b
-5c*4=-20c
Two vectors m and n are defined by 3i+4j and n=2i-j. find the angle between m and n
Answer:
[tex]{ \tt{m.n = |m| |n| \cos( \theta) }} \\ { \tt{ (3 \times 2) + (4 \times - 1) = (5)( \sqrt{5}) \cos( \theta) }} \\ { \tt{ \cos( \theta) = \frac{0.4}{ \sqrt{5} } }} \\ \theta = 79.7 \degree[/tex]
Consider the following data representing the price of refrigerators (in dollars).14051405, 11211121, 13391339, 10961096, 12991299, 14011401, 11381138, 11491149, 12231223, 10711071, 13991399, 14001400, 12421242, 13181318, 11011101, 10651065, 14281428, 12251225, 13501350, 13581358, 13121312Copy DataPrice of Refrigerators (in Dollars)Class Frequency Class Boundaries Midpoint Relative Frequency Cumulative Frequency1049–1118 1119–1188 1189–1258 1259–1328 1329–1398 1399–1468 Step 2 of 7 : Determine the frequency of the fifth class.
Answer:
3
Step-by-step explanation:
Given the data:
1405, 1121, 1339, 1096, 1299, 1401, 1138, 1149, 1223, 1071, 1399, 1400, 1242, 1318, 1101, 1065, 1428, 1225, 1350, 1358, 1312
Using the intervals:
Class interval ___ Frequency
1049–1118 ________ 4
1119–1188 ________ 3
1189–1258 ________3
1259–1328 _______ 3
1329–1398 _______ 3
1399–1468 _______ 5
From the table ; the fifth class is the interval :
1329 - 1398 and it has a frequency of 3
I’m in summer school can y’all plz help me
Answer: Choice A. [tex]-x^2+2x+8[/tex]
Work Shown:
[tex](f - g)(x) = f(x) - g(x)\\\\(f - g)(x) = (2x+1) - (x^2-7)\\\\(f - g)(x) = 2x+1 - x^2+7\\\\(f - g)(x) = -x^2+2x+(1+7)\\\\(f - g)(x) = -x^2+2x+8\\\\[/tex]
which shows the answer is choice A.
Side note: be sure to distribute the negative to every term inside the second set of parenthesis. So you wouldn't say -(x^2-7) = -x^2-7. If you did this error, then you'd get to the wrong answer choice C.
Answer:
hope it helps u plz mark me brainliest mate
Step-by-step explanation:
(f-g)(x)=2x+1-(x^2-7)
(f-g)(x)=2x+1-x^2+7
(f-g)(x)= -x^2+2x+8
this is the correct answer
