The line integral of the vector field f→ = xi→ + yj→ along the line between the points (2,2) and (6,6) is 24.
Parameterize the line between the two points.
We can parameterize the line between (2,2) and (6,6) using the following vector-valued function:
r(t) = (2 + 4t)i→ + (2 + 4t)j→, where 0 ≤ t ≤ 1
This function starts at (2,2) when t=0 and ends at (6,6) when t=1.
Evaluate the line integral.
The line integral of a vector field f→ along a curve C parameterized by r(t) is given by:
∫C f→ · dr→ = ∫[a,b] f(r(t)) · r'(t) dt
where a and b are the values of t that correspond to the endpoints of the curve C.
In this case, we have:
f(r(t)) = r(t) = (2 + 4t)i→ + (2 + 4t)j→
r'(t) = 4i→ + 4j→
Therefore, the line integral becomes:
∫C f→ · dr→ = ∫[0,1] (2 + 4t)i→ + (2 + 4t)j→ · (4i→ + 4j→) dt
= ∫[0,1] (8 + 16t) dt + ∫[0,1] (8 + 16t) dt
= [4t^2 + 8t]0^1 + [4t^2 + 8t]0^1
= (4 + 8) + (4 + 8)
= 24
Therefore, the line integral of the vector field f→ = xi→ + yj→ along the line between the points (2,2) and (6,6) is 24.
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Question
Assuming that you meant to write "f→ = xi→ + yj→" as the vector field, we can calculate the line integral along the line between the points (2,2) and (6,6)
We need to parametrize the line segment from (2,2) to (6,6). Let's take t as the parameter and parametrize the line as follows:
r(t) = (2+4t)i + (2+4t)j, 0 ≤ t ≤ 1
Then, we can calculate dr/dt as follows:
∫f→ · dr→ = ∫(x i→ + y j→) · (dr/dt dt)
= ∫(2 + 4t)i · (4i dt) + (2 + 4t)j · (4j dt)
= ∫8 dt + ∫8 dt
= 16t + C
Evaluating the integral from t = 0 to t = 1, we get:
∫f→ · dr→ = 16(1) + C - 16(0) - C = 16
Therefore, the line integral of the vector field f→ along the line between the points (2,2) and (6,6) is 16.
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-2 + b < 3
.............
Answer:
I believe we are solving for b. b<5
Step-by-step explanation:
will give brainliest at the right answer
Answer:
1.) 40.0 2.) 75.00 3.) 140.00 4.) 200.00 5.) 500.00 6.) 1300.00 7.) 70.0000
8.) 10.00 9.) 245.00 10.) 900.00
Write an equation for the following line.
10
-10
10
-101
Pleasee help wit this
Answer:
Step-by-step explanation:
f(-9)=2(-9)²+5(-9)+20
= 162-45+20
= 137
Answer:
137
Step-by-step explanation:
f(-9) = 2(-9)^2 + 5(-9) + 20
= 162 - 45 + 20
= 137
The sum of two numbers is 12. The product of those same two numbers is -64. Find the numbers.
Answer: The answer for the 2 numbers are 16 and -4.
Step-by-step explanation: 16 + (-4) is 12, and 16 x (-4) is -64.
Which shows the distributive property?
1. 5x + 2 = 2 + 5x
2. 5(x + 2) = 5x + 10
3. 5(x + 2) = 5(2 + x)
Find the missing side length
Answer:
b
Step-by-step explanation:
4(x - 9) plz answer quickly
Answer:
4x - 36
Step-by-step explanation:
(07.02)
How many solutions can be found for the equation 4x+5=10?
A. Zero
B.One
C. Two
D.Infinitely Many
Order the following from LEAST to GREATEST: 3/5, -1/2, 0.50, -7/10, -0.75 *
Answer:
-0.75, -7/10, -1/2, 0.50, 3/5
Answer:
-0.75, -7/10, -1/2, 0.50, 3/5
Step-by-step explanation:
put all of them as a decimal first
3/5 = 0.6 (5)
-1/2 = -0.50 (3)
0.50 = 0.50 (4)
-7/10 = -0.70 (2)
-0.75 = -0.75 (1)
this is just for fun ong sooo yeaaa **delete spaces**
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Answer:
im fanna join
Step-by-step explanation:
Solve 3(x - 2) < 18.
What is x?
Answer:
x < 8
Step-by-step explanation:
First you divide 18 by 3, which gives you 6.
x − 2 < 6
Then, you add 2 to 6, which gives you 8, which leaves you with :
x < 8
:)
Answer:
X<8
Step-by-step explanation:
Distribute the 3 to get 3x-6<18. Then add the 6 to 18 leaving 3x<24. Then divide 24 by 3 to leave x by itself. x<8
I hope this helped! :)
Which of the following expressions are equivalent to 5(m + 3)? hurryy
Answer:
B 5m + 15
Step-by-step explanation:
Use the distributive property and multiply 5 by both terms inside the parentheses.
5(m + 3) = 5 * m + 5 * 3 = 5m + 15
Answer: B 5m + 15
Which story shows 1/3 divided by 5?
3÷1 1/4
i need to know ASAP and i need to know how to do it
Answer:
2.4 or 2[tex]\frac{2}{5}[/tex]
Step-by-step explanation:
Let's set this up:
We have 3/1[tex]\frac{1}{4}[/tex]
That's also 3/1.25
For division, we don't divide if there is a fraction, so we move the decimal place over to the right for both the numbers
300/125
Then you long divide as normal:
And it's really hard to show how to long divide on a computer so I'm just going to go ahead and assume you know how to.
But the answer to that would be 2.4 or 2[tex]\frac{2}{5}[/tex]
Thank you, let me know if you have any questions.
Evaluate the following expression when x = 5. -4x^2 + 3x + 12
Answer:
-73
Step-by-step explanation:
-4(5)^2+3(5)+12
5^2=25
25*-4=-100
-100+15+12=-73
solve each equation by substituting. y=-3x+5
5x-4y=-3
not different problems they are in the same problem
Answer:
(1, 2 )
Step-by-step explanation:
Given the 2 equations
y = - 3x + 5 → (1)
5x - 4y = - 3 → (2)
Substitute y = - 3x + 5 into (2)
5x - 4(- 3x + 5) = - 3 ← distribute and simplify left side
5x + 12x - 20 = - 3
17x - 20 = - 3 ( add 20 to both sides )
17x = 17 ( divide both sides by 17 )
x = 1
Substitute x = 1 into (1) for corresponding value of y
y = - 3(1) + 5 = - 3 + 5 = 2
solution is (1, 2 )
Answer:
x = 1 and y = 2
Step-by-step explanation:
y + 3x = 5 -------------> (1)
-4y + 5x = -3 -------------> (2)
(1) * 4
=> 4y + 12x = 20 --------> (3)
(3) + (2)
=> 0y + 17x = 17
=> 17x = 17
by dividing both sides by 17
=> x = 1
by putting x = 1 into (1)
=> y + 3*1 = 5
=> y + 3 = 5
=> y = 5 - 3
=> y = 2
B. Draw any pictures showing the ratios of:
1. 2 to 5
2.6 to 8
3.4 to 7
4.3 to 9
the supplement of a 65° angle has a measure of
Answer:
115 degrees
Step-by-step explanation:
supplementary angles add up to 180 degrees, so if x is the angle you're trying to have you get:
[tex]x + 65 = 180\\x = 115[/tex]
what is the value of x in the triangle??
Answer:
x=40°
Step-by-step explanation:
Every triangles area equals 180
75+65=140
180-140=40
Answer:
40
Step-by-step explanation:
All angles in a triangle add up to 180°.
65° + 75° + x° = 180
140° + x° = 180°
-140 -140
x° = 40°
the output is double the input
A. Linear
B. Exponential
C. Neither
Select the correct answer.
Identify the expression equivalent to 4(x + x + 7) - 2x+8 - 4 by substituting x = 1 and x = 2.
ОА.
6x +11
OB. 3(x + 7)
OC. 2(3x + 16)
OD.
3x + 16
Reset
Next
Answer:
c
Step-by-step explanation:
The expression equivalent to this expression is 2(3x+16)
Data;
x = 1x = 2Equivalent ExpressionThe given expression is 4(x+x+7) -2x + 8 -4
Let's simplify this
[tex]4(x+x+7) -2x +8 - 4\\4(2x+7) -2x +4 = 8x + 28 - 2x + 4 = 6x + 32[/tex]
This can be simplified as
[tex]6x+ 32 = 2(3x + 16)[/tex]
The expression equivalent to this expression is 2(3x+16)
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Triangle V P M. Angle V is 52 degrees, angle P is 78 degrees, angle M is x degrees.
Answer:
[tex]x = 50[/tex]
Step-by-step explanation:
[tex]52 + 78 + x = 180[/tex]
[tex]130 + x = 180[/tex]
[tex]x = 180 - 130[/tex]
[tex]x = 50[/tex]
what is the equation?
Answer:
y=22x
Step-by-step explanation:
If x=1 and y=22 then y=22x
7/8m^3 +3-1/2m^3. can u please help me solve this
Answer:
3m^3/8 + 3
Step-by-step explanation:
It can't be solved but that's the most simplified version.
Answer:
15/8m^3
Step-by-step explanation:
7/8m^3+2/2m^3
7/8m^3+1/m^3
=15/8m^3
A package weighs 32 ounces. What is the weight of the package in pounds
Answer:
2 pounds
Step-by-step explanation:
1 pound=16 ounces
Given g(x) = -5x+ 2, find g(4).
Answer:
Answer:
-18
Step-by-step explanation:
g(x)=-5x+2
g(4)=-5(4)+2=-20+2=-18
Answer:
-18
Step-by-step explanation:
what is 146 / pi as a fraction
Answer:
Step-by-step explanation:
[tex]\frac{146}{\pi}\\ \\ \text{Pi is irrational and cannot be expressed as a ratio of two integers.}\\ \\ \frac{146}{\pi}\approx 46.47[/tex]
Safeway has ginger ale on sale at 12 cans for $4.00 and Giant has the same brand
of ginger ale on sale for 20 cans for $6.00. Which store has the better deal?
Answer:
Giant
Step-by-step explanation:
Giant: .30c a can
Safeway: .33c a can