Split up the boundary of C (which I denote ∂C throughout) into the parabolic segment from (1, 1) to (0, 0) (the part corresponding to y = x ²), and the line segment from (1, 1) to (0, 0) (the part of ∂C on the line y = x).
Parameterize these pieces respectively by
r(t) = x(t) i + y(t) j = t i + t ² j
and
s(t) = x(t) i + y(t) j = (1 - t ) i + (1 - t ) j
both with 0 ≤ t ≤ 1.
The circulation of F around ∂C is given by the line integral with respect to arc length,
[tex]\displaystyle \int_{\partial C}\mathbf F\cdot\mathbf T \,\mathrm ds[/tex]
where T denotes the tangent vector to ∂C. Split up the integral over each piece of ∂C :
• on the parabolic segment, we have
T = dr/dt = i + 2t j
• on the line segment,
T = ds/dt = -i - j
Then the circulation is
[tex]\displaystyle \int_{\partial C}\mathbf F\cdot\mathbf T\,\mathrm ds = \int_0^1 (7t^3\,\mathbf i+5t^4\,\mathbf j)\cdot(\mathbf i+2t\,\mathbf j)\,\mathrm dt + \int_0^1 (7(1-t)^2\,\mathbf i+5(1-t)^2\,\mathbf j)\cdot(-\mathbf i-\mathbf j)\,\mathrm dt \\\\ = \int_0^1 (7t^3+10t^5)\,\mathrm dt - 12 \int_0^1 (1-t)^2\,\mathrm dt =\boxed{-\frac7{12}}[/tex]
Alternatively, we can use Green's theorem to compute the circulation, as
[tex]\displaystyle\int_{\partial C}\mathbf F\cdot\mathbf T\,\mathrm ds = \iint_C\frac{\partial(5y^2)}{\partial x} - \frac{\partial(7xy)}{\partial y}\,\mathrm dx\,\mathrm dy \\\\ = -7\int_0^1\int_{x^2}^x x\,\mathrm dx \\\\ = -7\int_0^1 xy\bigg|_{y=x^2}^{y=x}\,\mathrm dx \\\\ =-7\int_0^1(x^2-x^3)\,\mathrm dx = -\frac7{12}[/tex]
The flux of F across ∂C is
[tex]\displaystyle \int_{\partial C}\mathbf F\cdot\mathbf N \,\mathrm ds[/tex]
where N is the normal vector to ∂C. While T = x'(t) i + y'(t) j, the normal vector is N = y'(t) i - x'(t) j.
• on the parabolic segment,
N = 2t i - j
• on the line segment,
N = - i + j
So the flux is
[tex]\displaystyle \int_{\partial C}\mathbf F\cdot\mathbf N\,\mathrm ds = \int_0^1 (7t^3\,\mathbf i+5t^4\,\mathbf j)\cdot(2t\,\mathbf i-\mathbf j)\,\mathrm dt + \int_0^1 (7(1-t)^2\,\mathbf i+5(1-t)^2\,\mathbf j)\cdot(-\mathbf i+\mathbf j)\,\mathrm dt \\\\ = \int_0^1 (14t^4-5t^4)\,\mathrm dt - 2 \int_0^1 (1-t)^2\,\mathrm dt =\boxed{\frac{17}{15}}[/tex]
12.5% of it is 6 hrs
Answer:
48 hours
Step-by-step explanation:
12.5/100 = 6/x
1. cross-multiply
12.5 × x = 12.5x
100 × 6 = 600
2. divide
12.5x/12.5 = x
600/12.5 = 48
3. answer
x = 48
How many 1.5 ft
pieces of pipe can you cut from a 12ft pipe
Answer:
8 pieces.
Step-by-step explanation:
12 / 1.5
= 24 / 3
= 8.
pls help ill give brainleist
what number is 11 less than the other number if there's some is increased by 8 the result is 71 find the numbers
Answer:
26,37
Step-by-step explanation:
m=n-11
m-n=-11-------(1)
m+n+8=71--------(2)
(1)+(2)
(m-n)+(m+n+8)=-11+71
m-n+m+n+8=-11+71
2m+8=60
2m=52
m=26
by substitute in (1)
26-n=-11
-n=-11-26
n=37
Identifying properties used to solve liner equation.
Options are:
Addition property of Equality
subtraction property of Equality
multiplication property of Equality
division property of Equality
simplifying
distributive
Need a better explaination
-3x^5y^7/6xy^8
PLEASE HELP
9514 1404 393
Answer:
-x^4/(2y)
Step-by-step explanation:
Perhaps you want to simplify ...
[tex]-\dfrac{3x^5y^7}{6xy^8}=-\dfrac{3}{6}x^{5-1}y^{7-8}=-\dfrac{x^4y^{-1}}{2}=\boxed{-\dfrac{x^4}{2y}}[/tex]
__
The applicable rules of exponents are ...
(a^b)/(a^c) = a^(b-c)
a^-b = 1/a^b
_____
Comment on notation
When writing a fraction in plain text, any denominator that includes an arithmetic operation must be enclosed in parentheses. Your given expression is properly written as ...
-3x^5y/(6xy^8)
Without the parentheses, the product xy^8 is in the numerator. This is demanded by the order of operations, which requires you evaluate your expression as (-3x^5y^7/6)·xy^8
sequence 32,52,72,92 simplified
Step-by-step explanation:
the common increment is 20
Answer:
8, 13, 18, 23
Step-by-step explanation:
Find the lengths of AD, EF, and BC in the trapezoid below.
Answer:
Step-by-step explanation:
Segment EF is mid-segment of ABCD ⇒ ( 2x - 4 ) + ( x - 5 ) = 2x
x - 9 = 0
x = 9
AD = 4
EF = 9
BC = 14
The length of segments AD, EF, and BC in the trapezoid are 4, 9 and 14 respectively
What is Coordinate Geometry?A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.
We have to find the lengths of AD, EF, and BC in the trapezoid
Segment EF is mid-segment of ABCD
So ( 2x - 4 ) + ( x - 5 ) = 2x
Now let us solve for x
2x-4+x-5=2x
Combine the like terms
x-9=0
x=9
So AD =x-5
=9-5= 4
EF = 9
BC = 2x-4
=18-4
=14
Hence, the length of segments AD, EF, and BC in the trapezoid are 4, 9 and 14 respectively
To learn more on Coordinate Geometry click:
brainly.com/question/27326241
#SPJ2
Solve each equation for the given variable?
Answer:
1. x = 20 2. n = 50
Step-by-step explanation:
1/4x - 2 = 3
1/4x = 5
x = 20
2. 8 = 1/5n - 2
10 = 1/5n
n = 50
Answer:
Question 1
Original equation:
1/4x-2=3
Add 2 to both sides:
1/4x=5
Multiply both sides by 4/1:
x=20
Question 2
Original equation:
8=1/5n x 2
Divide both sides by 2
4 = 1/5n
Multiply both sides by 5/1
n=20
Let me know if this helps!
find the square root of 121/225
Answer:
11/15 or .73333333...
Step-by-step explanation:
heres how i went about it:
think of it as a fraction,
121
------
225
to find the sqyare root of a fraction you would find the square root of each number individually
√121=11
√225=15
then you divide them and get .73333333333333333...
bad at explaining but hope this helped <3
what are two examples of acute angle
Answer:
Ex. 45° & 89°
Step-by-step explanation:
Acute angles are angles less than 90°. Therefore, any angle less than 90° will do.
Answer:
acute angles are angles which are less than 90° .
For example . A angle with 50°.
more examples of acute angels are : 78° , 60° , 45° , 30 ° .
hope this helps you
mrk me braniliest
if the value of a any quadratic function f (x)=ax^2 + BX + C is -8, the function will
Answer:
The parabola will open downward
Step-by-step explanation:
f (x)=ax^2 + BX + C
Since a = -8
The parabola will open downward
When a< 0 the graph opens downwards
a>0 the graph opens upwards
Please help me with 19 and 20 please
9514 1404 393
Answer:
19. B -- continued, but modest ...
Step-by-step explanation:
19. There is no decline or decrease indicated on this graph. If growth were exponential, the graph would be concave upward, which it is not. There is continued growth indicated.
__
20. The percentage change from 2005 to 2010 is ...
(60 -20)/20 × 100% = 2 × 100% = 200%
One might compute an average rate of change per year of ...
200%/(5 yr) = 40%/yr
_____
Additional comment
As with any statement of percentage, you need to be very clear about what the base is.
Here, 100% is the number of farms in 2005, so an increase of 40% per year is an increase by 40% of the number in 2005. That is very different from 40% of the number in the previous year, which is how an annual percentage increase is usually interpreted. (The average annual rate of change is closer to 24% with respect to the previous year's number.)
Find the slope of the line passing through the pair of points or state that the slope is undefined. Then indicate whether the line
through the points rises, falls, is horizontal, or is vertical
(2,9) and (-2,9)
56÷(7-9)^3 -24/23-5×4
Answer:
= −28.043478261
Step By Step Explanation
Answer From Gauth Math
The sum of 3x2 +x+8 and x- 9 can be expressed as
Answer:
2x + 5
Step-by-step explanation:
((3x2)+x+8) + (x-9)
= ((6) + x +8) + (x -9)
= (14 +x) + (x-9)
= 14 + x + x -9
= 2x + 5
answered by g a u t h m a t h
Choose a variable to isolate and what it is equal to in the
system of equations below.
16x = 2y + 18
4y = 3x - 1
A. X = -8y + 9
B. y = X-9
C. y = 8X-9
O D. y = 8x + 9
Answer:
С. y=8x-9
Step-by-step explanation:
Solve the system of equations
3x=4y+1
16x=2y+18 (multiply by -2)
-32x= -4y-36
3x-32x= 4y+1-4y-36
-29x= -35
x=35/29
4y= 3*35/29-1= 105/29-29/29=76/29
y= 76/29: 4/1= 19/29
You know x and y, then attempt to replace x,y in every equation (from A to D) on 35/29 and 19/29 respectively. If the left and right part in some equation are equal after replacing that's the correct answer.
In C 19/29= 8*35/29- 9
19/29=19/29
It is correct.
John has a cylindrical propane tank that measures 8" in diameter and 8" tall If John
buys a new cylindrical propane tank that is twice as wide and half as tall as his
current tank, how much larger will the volume of the new tank be?
Answer:
2 times as large
Step-by-step explanation:
For the original cylinder, we can say that the volume of a cylinder is equal to V= πr²h. For this cylinder, we can say that V = π * radius² * height. The radius is equal to 1/2 of the diameter, so the original radius is 8/2 = 4. Therefore, the volume of the original cylinder is V = π * radius² * height = π * 4² * 8 = π * 16 * 8 = π * 128
For the new cylinder, "twice as wide" means that the diameter is twice as big as the original one. Half the height means that the height is halved. The new diameter is therefore 8 * 2 = 16 (meaning that the new radius is 16/2=8) while the new height is 8/2 = 4. The new volume is thus
V = π * radius² * height = π * 8² * 4 = π * 64 * 4 = π * 256
To see how much larger the new tank volume is, we can divide (new tank volume) by (old tank volume), resulting in
π * 256 / (π *128) = 2
59 less than twice Mabel's score
Answer:
Mabel's score = s
2s-59
Step-by-step explanation:
I HOPE MABEL HAS A NICE GRADE
Is it Mabel from Gravity Falls?
lol
13. Solve for m. Assume that none of the denominatons are equal to 0
Plz help me
Answer:
m = (ps - b - uxs/t) / ux/t - p
Step-by-step explanation:
ux/t +b/m+s =p
multiplying throughout by (m+s) we get:
ux/t(m+s) + b = p(m+s)
open the brackets:
uxm/t + uxs/t + b = pm + ps
bring on one side of the equal sign all terms containg m, to make it the subject:
m(ux/t - p) = ps - b - uxs/t
m= (ps - b - uxs/t) / ux/t - p
4 + 1n(x-1)=3 solve for x
[tex]\\ \sf \longmapsto 4+10(x-1)=3[/tex]
[tex]\\ \sf \longmapsto 4+10x-10=3[/tex]
[tex]\\ \sf \longmapsto 10x-6=3[/tex]
[tex]\\ \sf \longmapsto 10x=3+6[/tex]
[tex]\\ \sf \longmapsto 10x=9[/tex]
[tex]\\ \sf \longmapsto x=\dfrac{9}{10}[/tex]
Help me Please I need this
there are 7 vertices in this shape
Answer:
7.
Step-by-step explanation:
The vertices are the points where the lines meet.
help asap!!
Find the length of AB
A. 2.89
B. 33.13
C. 378.63
D. 377.19
Answer:
C
Step-by-step explanation:
[tex] \sin( 5 ^{o} ) = \frac{33}{ab} \\ ab = 378.63[/tex]
*WILL GIVE BRAINLIEST* Find the length of side xx in simplest radical form with a rational denominator.
Answer:
[tex]x = \frac{4 \sqrt{3} }{3} [/tex]
Step-by-step explanation:
The explanation is in the picture!❤
-7x-17=2x+10
Show work
-7x-17=2x+10
2x+7x= -17 -10
9x= - 27
x = – 27/ 9
x= –3
I hope I helped you^_^
Jane has 200 feet of fencing to enclose a rectangular vegetable garden. One side of the garden will be alongside Jane's house so only three sides will need to be fenced. What is the largest area that can be enclosed by the 200 feet of fencing?
Answer:
10,000 ft^2
Step-by-step explanation:
Let x represent length alongside Jane’s house and y represent width of garden.
We have been given that Jana has 200 feet of fencing to enclose a rectangular vegetable garden. One side of the garden will be alongside Jane’s house so only three sides will need to be fenced.
The fencing on 3 sides of garden will be equal to perimeter of garden on three sides.
p = x + 2y
200 = x + 2y
We know that area of rectangle is equal to length times width that is A = xy .
From perimeter equation, we will get:
x = 200 - 2y
Substituting this value in area equation, we will get:
A(y) = (200-y)y
Now, we need to find derivative of area of function.
A(y) = 200y - y^2
A'(y) = 200 - 2y
Now, we will set derivative equal to 0 to find critical points.
200 - 2y = 0
200 = 2y
y = 100
So thus the area will be maximum when 100.
A(y) = 200y - y^2
Substituting y for 100 we get A(100) = 10,000
find x on the lines plz and thanks
Answer:
x = 9
this is a ratio problem. You can see that 12/6 = 2, so you can also take 18/2 to get 9.
Answer:
the answer is 6
Step-by-step explanation:
Because 6 and x are corresponding angle so that means no matter what ( if u want the answer to how long the line is or what degree the angle is ) the answer is always going to be the same as the one above ( which is 6 )
Hop this helpssss
X(x+7)=0, what’s the answer, please help
Answer:
x=0 and x=-7
Step-by-step explanation:
Since the answer is 0, one of the 2 parts in the equation has to be 0:
x(x+7)=0 either the "x" has to be 0 or the "x+7"
With this you can create 2 equations:
x=0 and x+7=0
These simplify to x=0 and x=-7
Use the discriminant to determine the number of real solutions to the equation 3m ^ 2 = - 6
Hi,
no need to use discriminant for that.
3(m)^2 = -6
m^2 = -6/3
m^2= -2
in R, there is no
solution as a square can not be negative.
Im confused I dont know hoow to reduce
Answer:
[tex] \frac{5}{6} - \frac{1}{6} [/tex]
[tex] \frac{5 - 1}{6} [/tex]
[tex] \frac{4}{6} [/tex]
[tex] \frac{2}{3} [/tex]
hope this helps you
