The integral can be evaluated by substituting everything you know:
[tex]\displaystyle\int_C\mathbf F\cdot\mathrm d\mathbf r=\int_C\mathbf F(x(t),y(t),z(t))\cdot\dfrac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^1(t^3\,\mathbf i+t^5\,\mathbf j+t^4\,\mathbf k)\cdot(\mathbf i+2t\,\mathbf j+3t^2\,\mathbf k)\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^1(t^3+5t^6)\,\mathrm dt[/tex]
[tex]=\dfrac{t^4}4+\dfrac{5t^7}7\bigg|_0^1=\dfrac14+\dfrac57=\boxed{\dfrac{27}{28}}[/tex]
The line integral ∫F · dr along the curve is 9/10.
To evaluate the line integral ∫F · dr along the curve C, where F(x, y, z) = xyi + yzj + zxk and C is the twisted cubic given by x = t, y = t², z = t³ for 0 ≤ t ≤ 1, we need to parameterize the curve C and compute the dot product between F and the tangent vector dr.
The parameterization of C is:
r(t) = ti + t²j + t³k
To compute dr, we take the derivative of r(t) with respect to t:
dr = (dx/dt)i + (dy/dt)j + (dz/dt)k
dr = i + 2tj + 3t²k
Now we can compute the dot product between F and dr:
F · dr = (xy)(dx/dt) + (yz)(dy/dt) + (zx)(dz/dt)
F · dr = (t)(i) + (t²)(2t)(j) + (t)(t³)(3t²)(k)
F · dr = ti + 2t³j + 3t⁴k
To evaluate the line integral, we integrate F · dr with respect to t over the interval [0, 1]:
∫[0,1] F · dr = ∫[0,1] (ti + 2t³j + 3t⁴k) dt
Integrating each component separately:
∫[0,1] ti dt = (1/2)t² ∣[0,1] = (1/2)(1)² - (1/2)(0)² = 1/2
∫[0,1] 2t³j dt = (1/4)t⁴ ∣[0,1] = (1/4)(1)⁴ - (1/4)(0)⁴ = 1/4
∫[0,1] 3t⁴k dt = (1/5)t⁵ ∣[0,1] = (1/5)(1)⁵ - (1/5)(0)⁵ = 1/5
Adding the results together:
∫[0,1] F · dr = (1/2) + (1/4) + (1/5) = 5/10 + 2/10 + 2/10 = 9/10
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ILL MARK BRAINLIST !!
Assume that each circle shown below represents one unit. Express the shaded
amount as a single fraction and as a mixed number.
Answer:
3 1/11 as a mixnumber its 3/33
What is the answer 6•4+2/2-7
Answer:
18 is the answer
Step-by-step explanation: Solve by multiplication/division first and then addition and/subtraction
Will mark brainliest!!! And 20 points!! Select the correct answer.
What is the range of the function shown on the graph?
Answer:
A.
Step-by-step explanation:
10 times as many as 1 ten is
Answer:
not sure sorry
Step-by-step explanation:
11. Michelle purchased a kids table with a
square top. If the area of the square top is
400 square inches, what is the length of one
of the sides?
A = 400 in 2
The null space for the matrix is spanned by the vector:_______
Answer:
True
Step-by-step explanation:
The null space of matrix is set of all solutions to matrix. The linearly independent vectors forms subset which are spanned and forms the null space. The null space of vector can be found by reducing its echelon. The non zero rows formed are the null spaces of matrix.
20 POINTS HELP ASAP Which of the following expressions is equivalent to 18 m - 12? 2(-9 m + 6) -1(18 m + 12) 6(3 m - 2) -3(-6 m - 4)
Hey there! I'm happy to help!
The correct answer is 6(3m-2). This is because if you use the distributive property (multiplying outside number by each term in the parentheses) you end up with 18m-12
6(3m)=18m
6(-2)=-12
18m-12
The other answer options don't yield this result.
Have a wonderful day! :D
How do you write
write -7 2/3
as a decimal?
Answer:
-7.66
Step-by-step explanation:
divide 2 by 3 to get a decimal.
what is the difference of fractions
solve the literal equation for y
3=5x+6y
Answer:
y=1/2-5x/6
Step-by-step explanation:
Answer:
y=1/2-5x/6
if this is helpful than good job
Plssssss help me! What is the area of the shaded portion to the nearest hundredth?
Step-by-step explanation:
A1= area of the rectangle
A1= 4yd • 10yd
A1= 40 square yd
A2= area of the part of the circular section
A2= 180°• pi • 4 square yd/360°
A2= 180° • 16yd • pi/ 360°
A2= 16yd•pi/2
A2= 8yd•pi
A2= 25,12yd
A= areo of rhe shaded portion
A= A1-A2
A= 40yd-25,12yd
A= 14,88yd
Answer:
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Step-by-step explanation:
lllllllll,,,,,,,,,,,,,
3x-2=2x+6 ayuda porfis
Answer:
x = 8
Step-by-step explanation:
3x - 2 = 2x + 6
3x - 2x - 2 = 2x - 2x + 6
x - 2 = 6
x - 2 + 2 = 6 + 2
x = 8
Answer:
x = 8
Step-by-step explanation:
move 2x to 3x and move -2 to 6
since its across the equal sign, it switches (postive to negative, negative to positive)
3x -2x = x
6 + 2 = 8
x = 8
:)
Which of the following is a quadratic equation that has the roots x = 3 and x = −4?
Answer:
x^2 + x = 12
Step-by-step explanation:
(x - 3)(x + 4) = 0
x^2 + 4x - 3x - 12 = 0
x^2 + x - 12 = 0
x^2 + x = 12
The quadratic equation that has the roots x = 3 and x = −4 will be x²+x-12=0.
Any equation using the formula ax² + bx + c = 0 When x is a variable and a, b, and c are any real values; a quadratic equation is one where a≠0.
It is given that the quadratic equation that has the roots x = 3 and x = −4.
We know that one such equation is provided by x²-(a+b)x+ab=0 if a and b are the roots of a quadratic equation.
x²-(a+b)x+ab=0
Substitute the value of an as 3 and b as -4.
x²-(3-4)x+(3)(-4)=0
x²-(-1)x-12=0
x²+x-12=0
Thus, the obtained quadratic equation will be x²+x-12=0.
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What is the sum of 12 – 5i and –3 + 4i?
–16 + 63i
9 – i
9 – 9i
15 – 9i
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{9 - i}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{12 - 5i + ( - 3 + 4i)}[/tex]
When there is a ( + ) in front of an expression in parentheses, there is no need to change the sign of each term. That means, the expression remains the same. Just remove the parentheses
[tex] \longrightarrow{ \sf{12 - 5i - 3 + 4i}}[/tex]
Collect like terms
[tex] \longrightarrow{ \sf{ 12 - 3 - 5i + 4i}}[/tex]
Subtract 3 from 12
[tex] \longrightarrow{ \sf{9 - 5i + 4i}}[/tex]
Collect like terms
[tex] \longrightarrow{ \sf{9 - i}}[/tex]
Hope I helped!
Best regards! :D
The sum of the given complex numbers is (9 - i) and this can be determined by using the arithmetic operations and the given data.
Given :
Complex numbers -- (12 - 5i) and (-3 + 4i)
The following steps can be used in order to determine the sum of the given complex numbers:
Step 1 - The arithmetic operations can be used in order to determine the sum of the given complex numbers.
Step 2 - The mathematical expression of the given situation is:
= (12 - 5i) + (-3 + 4i)
Step 3 - Add 12 and -3 in the above expression.
= 9 - 5i + 4i
Step 4 - Add -5i and 4i in the above expression.
= 9 - i
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What is the remainder of 16 divided by 4,005
Answer:(4005/16) ÷ 2 = 125.15625
Step-by-step explanation:
Write an equation where the left side is your power of 10 times n and the right side is the result of multiplying 0.1515... by that power.
Answer:
(10)n =(9915)n
Step-by-step explanation:
An equation where the left side is your power of 10 times n and the right side is the result of multiplying 0.1515... by that power could be as;
(10)n = 10(0.11515).
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Solving equations generally means finding the values of the variables used in it for which the considered equation is true.
We have to write an equation where the left side is your power of 10 times n and the right side is the result of multiplying 0.1515... by that power.
Therefore, the equation could be as;
(10)n = 10(0.11515)
Hence, An equation where the left side is your power of 10 times n and the right side is the result of multiplying 0.1515... by that power could be as;
(10)n = 10(0.11515).
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Max sprints forward 10 feet and then stops and sprints
back 15 feet. Use subtraction to explain where Max is.
relative to where he started.
Answer:
10-15= -5
Step-by-step explanation:
max is 5 feet behind from where he started
There are 9 marbles in a bag. 4 of those marbles are red,
What is the probability of picking a red marble randomly from the bag?
Answer:
4/9
Step-by-step explanation:
I think because you take the total and the amount of red you have
The probability of picking a red marble randomly from the bag will be equal to 0.44 .
It is given that there are total 9 marbles in a bag out of which 4 are red marbles.
We have to find the probability of picking a red marble randomly from the bag.
What do you mean by probability ?
Probability is the possibility or chance of an event to occur and is given by ratio of no. of favorable outcomes to total no. of outcomes.
As per the question ;
The total no. of outcomes (marbles) = 9
The no. of favorable outcomes (red marbles) = 4
We know that , probability is given by ;
Probability = No. of favorable outcomes / Total no. of outcomes
So ;
The probability of picking a red marble randomly from the bag will be equal to ;
Probability = 4 / 9
P(E) = 0.44
Thus , the probability of picking a red marble randomly from the bag will be equal to 0.44 .
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Is a compound inequality graph combined or separated?
Answer:
.A compound inequality graph is combined!
6th grade math
PLEASE HELP
An object is translated by (x-2, y-6). If one point in the pre-image has the coordinates (-3, 7), what would be the coordinates of its image? (-1,7) O (-5,1) O(-9,5) O (-1, 13)
Answer:(-5,1)
Step-by-step explanation:! X= -3 so -3-4= -7, Y= 7 so 7+2=9, So the coordinates will be (-7,9) I hope that I could help you
Tips for Rounding numbers to the ten thousands
Answer:
Focus on the thousands and the ten thousand
Step-by-step explanation:
Focus on the number before the ten thousand value.
Then check whether it is smaller or bigger than 5 .
if it is bigger add 1 to the ten thousand value. if it is smaller do not add anything to the ten thousands.
HOPE IT HELPED
-1/9 -1/2, 14/9,4/3 midpoints
Answer: (13/18, 1/6)
Step-by-step explanation: (-1/9, -1/2),(14/9, 4/3)
What you want to do is -1/9 + 14/9. Here our answer is 13/9. We then do 13/9 divided by 2 which in equation form is 13/9X1/2 which is 13/18. We want to solve the Y now. In equation form we do: 4/3 - 1/2 which equals 1/6 Therefore, the answer is (13/18, 1/6)
give the perimeter of each figure as a simplified expression
Answer:
5k² - 7k + 6
Step-by-step explanation:
The perimeter of the figure given = the sum of all sides of the figure.
Perimeter = (k² - 9k + 23) + (k² + k) + (k² + k) + (2k² - 17)
Simply the expression as follows:
Perimeter = k² - 9k + 23 + k² + k + k² + k + 2k² - 17
Combine like terms
Perimeter = k² + k² + k² + 2k² - 9k + k + k + 23 - 17 (like terms are terms with the same degree)
Perimeter = 5k² - 7k + 6
Write an expression to represent: Eight more than the product of two and a number xxx.
Answer:
8+2X is the expression of eight more than the product of two and a number
Answer:
2x+8
Step-by-step explanation:
An open-top box is being designed by cutting a corner piece out of a 16" by 14" piece of metal and folding the sides upwards. The designer wants to maximize the volume of this box. Enter the maximum volume of this box (rounded to the nearest cubic inch). in3
Answer:
The strip of 16 by 14 inches.
Let x be the corner of the square cut
Then the box would have height as x, length 16-2x and width 14-2x
Hence volume =
Use derivative to test to find x for maximum volume
V'(x) =
v"(x) =
Equate first derivative to 0
Solutions are
x= 2.483 and x = 7.517
Practically cutting more than 7 inches is not possible from 14 inches dimention
Hence 2.483 is the side of square and maximum volume
= 247.508
Step-by-step explanation:
Hope this helps!
Point B is the midpoint of point C and D. If CB is 14in, what is CD and BD?
Answer:
[tex]BD = 14\ in[/tex]
[tex]CD = 28\ in[/tex]
Step-by-step explanation:
Given
CB = 14in
B as midpoint
Required
Determine CD and BD
Since B is the midpoint, then the two line segments (CB and BD), we have the following relationships:
[tex]CB = BD[/tex]
[tex]CD = CB + BD[/tex]
Reorder the first equation
[tex]BD = CB[/tex]
Substitute 14 for CB
[tex]BD = 14\ in[/tex]
Taking the second equation into consideration
[tex]CD = CB + BD[/tex]
[tex]CD = 14 + 14[/tex]
[tex]CD = 28\ in[/tex]
What value should go in the empty boxes to complete the calculation for finding the product of 0.61 × 0.45? Both numbers are the same; however, only input the number one time in your answer
its 0.106 because I said so
Answer:
.106
Step-by-step explanation:ggrrrr
Solve the given equation for h
B=V/h
Solve the given equation for V
B=V/h
Answer:
Step-by-step explanation:
B = V/h
V/h = B
V = Bh
What is the additive inverse of -17 ?
a) -16
b) -71
c) 17
d) 0
Answer:
c)17
Step-by-step explanation:
additive inverse example:Using the same approach, if x is a negative number, then its additive inverse is equal and opposite in sign to it. This means that the additive inverse of a negative number is positive. For instance, if x equals -12, then its additive inverse is y = 12.
