Answers
By Green's theorem (all the conditions are met), we have
[tex]\displaystyle \int_C \sqrt y \, dx + \sqrt x \, dy = \iint_D \frac{\partial(\sqrt x)}{\partial x} - \frac{\partial(\sqrt y)}{\partial y} \, dx \, dy[/tex]
where D is the interior of the path C, or the set
[tex]D = \left\{ (x, y) : 0 \le y \le \dfrac{x^2}2 \text{ and } 0 \le x \le 2 \right\}[/tex]
So, the line integral reduces to the double integral,
[tex]\displaystyle \frac12 \int_0^2 \int_0^{\frac{x^2}2} x^{-\frac12} - y^{-\frac12} \, dy \, dx[/tex]
[tex]\displaystyle = \frac12 \int_0^2 x^{-\frac12}\left(\frac{x^2}2\right) - 2\left(\frac{x^2}2\right)^{\frac12} \, dx[/tex]
[tex]\displaystyle = \frac12 \int_0^2 \frac12 x^{\frac32} - \sqrt 2 \, x \, dx[/tex]
[tex]\displaystyle = \frac14 \int_0^2 x^{\frac32} - 2\sqrt 2 \, x \, dx[/tex]
[tex]\displaystyle = \frac14 \left(\frac25\cdot2^{\frac52} - \sqrt2\cdot2^2\right) = \boxed{-\frac{3\sqrt2}5}[/tex]
Related Questions
Freddie can mow 3 lawns in 2 hours. Tom can mow 2 lawns in 1 hour. Who should be able to mow Mr. Smith's lawn faster?
Answers
Answer:
Step-by-step explanation:
Freddie rate of mowing=3/2=1.5 lawns /hr.
Tom's rate of mowimg=2 lawns/hr
so Tom can mow Smith's lawn faster.
for 0 ≤ θ < 2 π what are the solutions to sin^2(θ) =2sin^2(θ/2)
Answers
Recall the half-angle identity for sine,
sin²(x/2) = (1 - cos(x))/2
Then the given equation is identical to
sin²(θ) = 1 - cos(θ)
Also recall the Pythagorean identity,
sin²(θ) + cos²(θ) = 1
Then we rewrite the equation as
1 - cos²(θ) = 1 - cos(θ)
Factoring the left side, we have
(1 - cos(θ)) (1 + cos(θ)) = 1 - cos(θ)
and so
(1 - cos(θ)) (1 + cos(θ)) - (1 - cos(θ)) = 0
and we factor this further as
(1 - cos(θ)) (1 + cos(θ) - 1) = 0
which gives
cos(θ) (1 - cos(θ)) = 0
Then either
cos(θ) = 0 or 1 - cos(θ) = 0
cos(θ) = 0 or cos(θ) = 1
[θ = arccos(0) + 2nπ or θ = -arccos(0) + 2nπ]
… or [θ = arccos(1) + 2nπ or θ = -arccos(1) + 2nπ]
(where n is any integer)
[θ = π/2 + 2nπ or θ = -π/2 + 2nπ] or [θ = 0 + 2nπ]
In the interval 0 ≤ θ < 2π, we get three solutions:
• first solution set with n = 0 ⇒ θ = π/2
• second solution set with n = 1 ⇒ θ = 3π/2
• third solution set with n = 0 ⇒ θ = 0
So, the first choice is correct.
Birdseed costs $0.57 a pound and sunflower seeds cost $0.87 a pound. Angela Leinenbachs' pet store wishes to make a 30 pound mixture of birdseed and sunflower seeds that sells for $0.81 per pound. How many pounds of each type of seed should she use?
Answers
Step-by-step explanation:
x = pounds birdseed
y = pounds sunflower seeds
x + y = 30
0.57x + 0.87y = 30×0.81
with this last trick (to calculate the full cost of the whole 30 pounds based on the targeted individual price per pound) we bring both constraints into the play.
from the first equation we get
x = 30 - y
and we use that in the second equation :
0.57×(30-y) + 0.87y = 30×0.81 = $24.30
17.1 - 0.57y + 0.87y = 24.3
0.3y = 7.2
y = 24
x = 30 - y = 30 - 24 = 6
she uses 6 pounds of birdseed and 24 pounds of sunflower seeds.
help now plsssssssssssssssssssssssss
Answers
cheater bro wyd ur doing a diagnostic try ur best lol
What are the odds of choosing a blue marble from a bag that contains two blue marbles, one green marble and four red marbles?
Answers
Answer:
1/3
Step-by-step explanation:
2 blue 1 green 4 red
I need help on these functions questions
Answers
Answer:
see explanation
Step-by-step explanation:
(a)
Substitute x = - 1 into f(x)
f(- 1) = 6 - 2(- 1) = 6 + 2 = 8
(b)
Substitute x = [tex]\frac{1}{3}[/tex] into g(x)
g([tex]\frac{1}{3}[/tex] ) = [tex]\frac{9}{\frac{1}{3} }[/tex] = 9 × 3 = 27
(c)
Substitute x = f(x) into h(x)
h(6 - 2x)
= 6 + (6 - 2x)² ← expand using FOIL
= 6 + 36 - 24x + 4x² ← collect like terms
= 4x² - 24x + 42
(d)
Substitute x = f(x) into g(x)
g(6 - 2x)
= [tex]\frac{9}{6-2x}[/tex]
(e)
Evaluate g(12) then substitute value obtained into f(x)
g(12) = [tex]\frac{9}{12}[/tex] = [tex]\frac{3}{4}[/tex] , then
f([tex]\frac{3}{4}[/tex] ) = 6 - (2 × [tex]\frac{3}{4}[/tex] ) = 6 - [tex]\frac{3}{2}[/tex] = [tex]\frac{9}{2}[/tex]
(f)
Evaluate f(- 9) then substitute the value obtained into h(x)
f(- 9) = 6 - 2(- 9) = 6 + 18 = 24 , then
h(24) = 6 + 24² = 6 + 576 = 582
I GIVE BRAINLEST !! PLS SLOLVE
Answers
Answer:
√6/2+1
Step-by-step explanation:
multiplying by √6/√6, we get √6(3+√6)/6=(3√6+6)/6=√6/2+1
please help quickly!!!!!!!
If y varies directly with x, determine an equation for the given direct variation. For this question, find the value of the given variable.
Find y when x = 10 if y = 8 when x = 20.
Answers
Answer:
y=K*x equation
k=constant of variation
y= 4 when x = 10
Step-by-step explanation:
8=k*20
divide both sides by 20 to solve for k
2/5=k
y=2/5 *10
y= 4 when x = 10
Trigonometry I need help please
Answers
Answer:
10.7°
Step-by-step explanation:
SOH CAH TOA
Tan(BCA) = x/y
= 4/21
BCA= Tan`¹(4/21)
= 10.7856
to 3SF = 10.7°
At Buffalo Wild Wings, you order a meal that costs $15.86. You leave an 18% tip (on the pre-tax amount).
The sales tax is 8%. What is the total cost of the meal?
Answers
Answer:
round to cent 20.59
Step-by-step explanation:
The counting number ABAB is a multiple of 36. If different letters represent different digits, what is the greatest value ABAB can have? PLS HELP ONLY 10 minutes
Answers
The greatest value ABAB can have is 7272.
The given parameters:
Counting number ABAB = multiple of 36The counting number can be expanded as follows;
ABAB = 100 x AB + AB
= AB00 + AB
= AB(100 + 1)
= AB(101)
101 is a prime factor of AB and has only two factors.
The prime factor of 101 = 1 x 2
Since 101 is prime, the counting number AB must 2-digits multiples of 36.
The greatest value ABAB can have is calculated as follows;
ABAB = (36 x 2)(36 x 2)
ABAB = 7272
Thus, the greatest value ABAB can have is 7272.
Learn more about prime factors here: https://brainly.com/question/24612438
need help with this problem
Answers
Answer:
x = 6
Step-by-step explanation:
Answer:
Step-by-step explanation:
tan30 = x/12
x = 12tan30
x = 12(sin30/cos30)
x = 12(½ / ½√3)
x = 12/√3
x = (12/3)√3
x = 4√3
The temperature was -1°F at noon and dropped to -14°F by the evening.
What was the change in temperature?
13°F
-13°F
-15°F
15°F
Answers
Answer:
-13°F is the change in temperature.
Step-by-step explanation:
The change in temperature is,
→ -1 + x = -14
→ x = -14 + 1
→ [ x = -13 ]
Hence, -13°F is the change.
3. What is the exact area of triangle ABC? Use special right triangles to help find the base of the triangle. Show your work.
Answers
The exact area of triangle ABC is 93.51 cm².
The given parameters;
Height of the triangle, h = 18 cmThe base of the triangle is calculated by using trigonometry ratio as follows;
[tex]tan (30) = \frac{b}{18} \\\\[/tex]
where;
b is the base of the triangle ABC[tex]b = 18 \times tan(30)\\\\b = 10.39 \ cm[/tex]
The area of the triangle ABC with the calculated base and given height is calculated as follows;
[tex]A = \frac{1}{2} \times base \times height\\\\A = \frac{1}{2} \times 10.39 \times 18\\\\A = 93.51 \ cm^2[/tex]
Thus, the exact area of triangle ABC is 93.51 cm².
Learn more about area of a triangle here: https://brainly.com/question/23945265
I want a way to solve such a problem
Answers
Answer:
none of these is the answer
hope it helps you
Step-by-step explanation:
Hope it will help you...
Convert 62% into a fraction
Answers
Answer:
62% = 31 / 50
Step-by-step explanation:
62/100
if you need to simplify then it would be 31/50
Geoff works at a warehouse , earning $17.50 per hour plus a $200 what’s the equation?
Answers
Answer:
P = 17.50x + 200
Step-by-step explanation:
x is the number of hours worked
P is how much money Geoff earns
can you help me solve 4x - 15 = 17 - 4x
Answers
[tex]4x-15 = 17-4x\\\\\implies 4x +4x = 17 +15\\\\\implies 8x = 32\\\\\implies x = \dfrac{32} 8\\\\\implies x = 4[/tex]
PLEASE ANSWER!!!
Boris Drove to the mountains last week. There was heavy traffic on the way there, and the trip took 10 hours. When Boris drove home, there was no traffic and the trip only took seven hours. If his average rate was 18 mph faster on the trip home, how far away does Boris live from the mountains?
Answers
Answer:
Step-by-step explanation:
Answer:
Let +d+ = the one-way distance to the mountains in miles
Let +s+ = his speed going to the mountains in mi/hr
+s+%2B+27+ = his speed on the trip home in mi/hr
equation for going to the mountains:
(1) +d+=+s%2A7+
Step-by-step explanation:
I hope this helps mark as brainliest if correct
HELP PLEASE TAKING A TEST RIGHT NOW
the graph shows a system of equations
what is the solution to the system of equations?
a. -3, 2
b. 3, -2
c. 3, 2
d. -3, -2
Answers
The answer is where the lines internet which are the coordinates 3, 2. So it’s C.
can someone help plz I need help ASAP!
Answers
Answer:
[tex]y= \frac{1}{3}x -9[/tex]
Step-by-step explanation:
First you must substract -5 to both sides
-5-4= -9
[tex]y= \frac{1}{3}x -9[/tex]
if 10 people share 5 cookies , how much cookie does each person get
Answers
Answer:
1/2
Step-by-step explanation:
5 / 10 = 1/2
Amanda went to the Farmer’s market with her family. She had $5.00 to spend and decided she wanted to spend it on peaches. Each peach cost 68 cents. How many peaches could she buy ?
Answers
Sin(180-A)/tan(180-A) × cot(90-A)/tan(90+A) × cos(-A)/ cos(270-A) Please solve
Answers
so tan = me sun bathing for 2.5 second
QUESTION 16 PLEASE HELP ME ASAPP
Answers
Answer: changes over time
Step-by-step explanation: it is always decreasing
An open-top box is to be constructed from a sheet of tin that measures 36 inches by 20 inches by cutting out squares from each corner as shown and then folding up the sides. Let V(x) denote the volume of the resulting box.
Answers
Answer:
[tex]V(x)=4x^3-112x^2+720x[/tex]
Step-by-step explanation:
[tex](36-2x)(20-2x)x[/tex]
[tex](720-72x-40x+4x^2)x[/tex]
[tex](4x^2-112x+720)x[/tex]
[tex]4x^3-112x^2+720x[/tex]
Therefore, the resulting volume would be [tex]V(x)=4x^3-112x^2+720x[/tex]
A box contains four bags of sugar. The total mass of all four bags is 6 kg. What is the mass of each bag in grams?
Answers
PLEASE HELP WILL MARK BRAINIEST!!!!!
Answers
Answer:
c. copy an angle.
there's no angle in this as far as I can see.
The length of a pool is twice its width. What is the ratio of the length to the width of the pool?
Answers
Answer:
2:1 OR as a fraction, 2/1
Step-by-step explanation:
We don't know the actual length or width of this pool, like we don't know a number, as in exactly how many feet or meters long or wide this pool is. For this question, we don't need to know. "Twice" means 2 times. So if we consider the width (which we don't know) and call it w, then the length, (which we also don't know) which is two times as long, would be 2w
Width = w
Length = 2w
Ratio of Length to Width is
2w:w or as a fraction 2w/w
This can be simplified to
2:1 or as a fraction 2/1
Solve for x:
4x-3Divided by 2 =5/3
Answers
Answer:
x=19/12
Step-by-step explanation:
(4x-3)/2 = 5/3
4x-3 = 10/3
3 = 9/3
4x = 10/3 + 9/3 = 19/3
x = 19/12
Hey there!
4x - 3/2 = 5/3
ADD 3/2 to BOTH SIDES
4x - 3/2 + 3/2 = 5/3 + 3/2
CANCEL out: -3/2 + 3/2 because it gives you 1
KEEP: 5/3 + 3/2 because it helps solve for the x-value.
NEW EQUATION: 4x = 5/3 + 3/2
SIMPLIFY IT!
4x = 19/6
DIVIDE 4 to BOTH SIDES
4x ÷ 4 = 19/6 ÷ 4
CANCEL out: 4 ÷ 4 because it gives you 1
KEEP: 19/6 ÷ 4 because it helps solve for the x-value
NEW EQUATION: x = 19/6 ÷ 4
SIMPLIFY IT!
x = 19/24
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)