Evaluate the line integral ſvø• dr for the following function and oriented curve C (a) using a parametric description of C and evaluating the integral directly, and (b) с using the Fundamental Theorem for line integrals. x² + y² + z² Q(x,y,z) = C: r(t) = cost, sint, 2 1111 for sts 6 Sve•dr=[. Using either method, с (Type an exact answer.)
Answers
The line integral ſvø• dr for the function \(Q(x, y, z) = x^2 + y^2 + z^2\) along the oriented curve C can be evaluated using both a parametric description of C and by applying the Fundamental Theorem for line integrals.
(a) To evaluate the line integral using a parametric description, we substitute the parametric equations of the curve C, r(t) = (cost, sint, 2t), into the function Q(x, y, z). We have \(Q(r(t)) = (cost)^2 + (sint)^2 + (2t)^2 = 1 + 4t^2\). Next, we calculate the derivative of r(t) with respect to t, which gives dr/dt = (-sint, cost, 2). Taking the dot product of Q(r(t)) and dr/dt, we get \((-sint)(-sint) + (cost)(cost) + (2t)(2) = 1 + 4t^2\). Finally, we integrate this expression over the interval [s, t] of curve C to obtain the value of the line integral.
(b) Using the Fundamental Theorem for line integrals, we find the potential function F(x, y, z) by taking the gradient of Q(x, y, z), which is ∇Q = (2x, 2y, 2z). We then substitute the initial and terminal points of the curve C, r(s), and r(t), into F(x, y, z) and subtract the results to obtain the line integral ∫[r(s), r(t)] ∇Q • dr = F(r(t)) - F(r(s)).
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Related Questions
Give the NEGATION and TRUTH VALUE of the NEGATION, of the following statement: All Rational numbers are Integers There Exists Integers that are not Rationals (True) There Exists Integers that are not
Answers
The given statement is: All Rational numbers are Integers. The negation of the above statement is: All Rational numbers are not Integers. The truth value of the negation is False.
The statement: There Exist Integers that are not Rationals is True as well. So, the answer is NEGATION: All Rational numbers are not Integers. TRUTH VALUE: False.The statement: There Exist Integers that are not Rationals is True.
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Find the circumference and area of the circle. Use 3.14 for π. Round to the nearest hundredth if necessary.
Answers
Answer:
2 x 3.14 x 13 = 81.64 m is your circumference
13^2 x 3.14
169 x 3.14 = 530.66 m^2 is your area
Solve the quadratic equation below by factoring: *2 + 9x = -20 O A. x = 4,5 O B. x = 1,9 O C. x = -2,-10 O D. x= -4,-5
Answers
x^2 + 9x = -20
Rearrange:
x^2 + 9x - (-20) = 0
x^2 + 9x + 20 = 0
the Equation has the form:
ax^2 + bx +c = 0
Where:
a=1
b= 9
c= 20
Find the sum of 2 numbers that equal b, and multiplied equal c.
4+5= 9 (b)
4x5 =20 (c)
Factor:
(x+ 4) (x+5) = 0
Equal each equation to zero and solve for x
x+4= 0
x= -4
x+5=0
x=-5
Solution:
x=-4 , x =-5
Express this number in scientific notation: 0.0002077
Answers
Given the number:
0.0002077
Let's express in scientific notation.
To express the number in scientific notation, move the decimal point so that there is only one non-zero number to the left of the decimal point.
Then, the number of decimal places you move will be the exponent on 10.
If the decimal point is moved to the right, the exponent will be negative.
If the decimal pointt is moved to the left, the exponent will be positive.
In this case the decimal point will be moved to the right.
Using this description, we have the scientific notation below:
\(undefined\)Answer:
2.077 x \(10^{-4}\)
Step-by-step explanation:
First, move the decimal place until we have a single digit between 1 and 10 to the left of the decimal point. In this problem, if we keep moving the decimal point to the right in 0.0002077 we will get 2.077.
Next, count how many places we moved the decimal point. If we have to move the decimal place to the right, the exponent will be negative. If we had moved the decimal place to the left, the exponent would be positive. In this case we had to move it 4 places to the right to change 0002077 to 2.077. We show that we moved it 4 places to the right by noting that the number should be multiplied by \(10^{-4}\).
a bicycle company needs to ship 328 bicycles across the country. if they can fit 50 bicycles in each truck about how many trucks will the company use?
Answers
The company will use approximately 7 trucks.
to separate into two or more parts or pieces. : to separate into classes or categories. : cleave entry 2, part.
To calculate the number of trucks needed, divide the total number of bicycles by the number of bicycles that can fit in each truck:
328 bicycles / 50 bicycles per truck = 6.56 trucks.
Since you can't have a fraction of a truck, the company will need to round up to the nearest whole number. Therefore, the company will use 7 trucks to ship the 328 bicycles across the country.
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Graph the linear function f(x)=3−6x
Answers
Answer:
(-1,9) (0,3), (1,-3), (2,-9)
Step-by-step explanation:
y intercept is -3
slope is -6, so you would go down by 6 and right by 1.
Answer:
The coordinates to graph this would be (-1,9) (0,3) (1,-3) (2,-9)
Please help!! I need to get this! Brainliest For Right Anwser!
Answers
Answer:
Data set A best fit by the regression line.
Answer:
Data Set C.
Step-by-step explanation:
Well just even by common sense, the line for "data set A" is not good for the points on the graph
What is the solution
Answers
Answer:
B: (x-6)^2=0
Step-by-step explanation:
which equation represents the function y= 1/x-3 after a reflection in y-axis
Answers
Answer:
y=-1/x-3
Step-by-step explanation:
Equations have a negative slope once they're reflected over the y-axis.
Each person who applies for an assembly job at Robert's Electronics is given a mechanical aptitude test. One part of the test involves assembling a plug-in unit based on numbered instructions. A sample of the length of time it took 42 persons to assemble the unit was organized into the following frequency distribution. Length of Time (in minutes) Number 1 up to 4 4 4 up to 7 8 7 up to 10 14 10 up to 13 9 13 up to 16 5 16 up to 19 2 What is the mean (in minutes)
Answers
The mean in minutes of the length of time given= 9.1
Calculation of mean when frequency table is givenThe formula used for the determination of mean when a frequency table is given is
= total/n
Where total = frequency×midpoint
n = 42
To calculate the total, the mid point of each length of time is determined as follows;
1+4/2 = 2.5 × 4 = 10
4+7/2= 5.5 × 8 = 44
7+10/2 = 8.5 × 14= 119
10+13/2 = 11.5× 9 = 103.5
13+16/2= 14.5×5 = 72.5
16+19/2= 17.5× 2= 35
Total= 10+44+119+103.5+72.5+35 = 384
Therefore mean = 384/42= 9.1
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A helicopter pilot flying at an altitude of 500 meters finds that the angle of depression to a bouy on the ocean is 52? Find the distance along the line of sight from the helicopter to the bouy.
Answers
The distance along the line of sight from the helicopter to the buoy is 634.51 meters.
How to determine the distance along the line of sightFrom the question, we have the following parameters that can be used in our computation:
Angle of depression, x = 52 degrees
Altitude = 500 meters
The distance (d) along the line of sight is calculated as:
sin(x) = Altitude/d
So, we have
d = Altitude/sin(x)
Substitute the known values in the above equation, so, we have the following representation
d = 500/sin(52 degrees)
So, we have
d = 634.51
Hence, the distance is 634.51 meters.
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Solve for x on [0, 2pi]
secx-cscx=0
I know what the answer is but can someone help me with the process of finding it?
Answers
The required solution to the trigonometry equation is x = π/4 + π n.
The equation of trigonometry functions is given in the question as
secx - cscx = 0
We have to determine the solution to the given equation
As per the question, we have
⇒ secx - cscx = 0
⇒ 1/cosx - 1/sinx = 0
⇒ (-cosx + sinx)/cosxsinx = 0
Using property : f(x)/g(x) = 0 ⇒ f(x) = 0
⇒ -cosx + sinx = 0
Divided by cosx into the equation,
⇒ -1 + tanx = 0
⇒ tanx = 1
The general solution for tan tanx = 1 is
⇒ x = π/4 + π n
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What is the solution to the system of equations?
y = 0x + 3
x=-2
---
아돌
12 1
뷔
Answers
The solution to the system of equations is x = -2 and y = 3
What is the solution to the system of equations?From the question, we have the following parameters that can be used in our computation:
y = 0x + 3
x=-2
Evaluate the product of 0 and x
So, we have
y = 3
x = -2
This means that the solution is x = -2 and y = 3
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find two numbers whose difference is 88 and whose product is a minimum. (smaller number) (larger number)
Answers
Two two numbers whose difference is 88 and whose product is a minimum are -44 and 44.
How to solve?Let the numbers be x and y where x is larger value and y is smaller number.
According to ques,
x - y =88
and we need to make product of numbers i.e 'xy' minimum.
So we can take x = 88 + y ------(2)
substituting value of x in xy, we get
(88 + y) (y) = y² + 88y ------(1) to make it minimum we need to equate its derivative equal to zero.
derivative of (1) is 2y + 88
Equating it to zero, we get
2y + 88 = 0
subtracting 88 from both sides, we get
2y = -88
Dividing 2 from both sides, we get
y = -44 ------(3)
Substituting value of y from (3) in (2), we get
x = 88 - 44
x = 44
So, we get value of x as 44 and y as -44 to get their product as minimum.
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Mr. Ramirez is always trying to clean up his garage. He has 1/5 liter of oil in one can and 2 5 liter of oil in another can. How much will he have if he pours them both into one can URGENT PLEASE ANSWER
Answers
The total amount of oil he would have if he pours them both in a can is 2.7 liters.
How much oil would he have?In order to determine the amount of oil he would have, add both numbers together. In order to add the numbers, both numbers have to be in the same form. One of the numbers is a decimal and the other is a fraction.
In order to convert the fraction to a decimal, divide the numerator by the denominator.
1/5 = 0.2
Total number of oil = 0.2 + 2.5 = 2.7 liters
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Decide whether there is enough information to prove m ∥ n . If so, state the theorem you would use
Answers
The correct option regarding whether the lines m and n are parallel is given as follows:
B. Yes. Alternate Interior Angles Converse.
Alternate Interior Angles Converse TheoremThe Alternate Interior Angles Converse Theorem states that when a transversal line crosses two parallel lines, the alternate interior angles are congruent.
The alternate interior angles are the angles that are between the two parallel lines, and on opposite sides of the parallel lines.
In the context of this problem, we have that:
Line n is the transversal line.The two marked angles are congruent.These two angles are alternate interior, and since they are congruent, we can prove that lines m and n are parallel, and the correct option is given by option B.
Missing informationThe options are given as follows:
A. No, there is not enough information.
B. Yes. Alternate Interior Angles Converse
C. Yes. Alternate Exterior Angles Converse
D. Yes.Consecutive Interior Angles Converse
E. Yes. Corresponding Angles Converse
The image with the lines is given at the end of the answer.
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Divide.
0.45 18 i need help ;\
Answers
Answer:
Step-by-step explanation:
hey buddy all you do is divide 0.45 by the number 18 so that aswer will be 0.025
Answer:
1/40
Step-by-step explanation:
0.45 divided by 18
rewrite 0.45 as 45/100 divided by 18:
\(\frac{\frac{45}{100}}{\frac{18}{1}}\)
\(\frac{45}{100} / 18 \\\\\frac{45}{100} * \frac{1}{18} \\\)
= 45/1800
1800 can be divided by 45 and gives 40.
so
1/40
80% of 90 is the same as 8/9 of 90. true or false
20% of 90 is the same as 1/5 of 90. true or false
Answers
Answer:
Both true
Step-by-step explanation: 80%*90=72. 72/90=8/9.
20%*90=18. 18/90=1/5
80% of 90 is the same as 8/9 of 90 is false.
20% of 90 is the same as 1/5 of 90 is true.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, 80% of 90 is the same as 8/9 of 90.
80% of 90 is,
= (80/100)×90.
= 8×9.
= 72.
And,
(8/9)×90.
= 8×10.
= 80.
So, 80% of 90 and 8/9 of 90 is not the same.
20% of 90 is the same as 1/5 of 90.
(20/100)×90.
= 2×9.
= 18.
And,
(1/5)×90.
= 18.
So, 20% of 90 is the same as 1/5 of 90.
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What is the surface area of this cone round to the nearest hundreth
Answers
Given:
Diameter of cone = 4 mm
Slant height (l) = 7 mm
Find-: Surface area of the cone.
Sol:
The surface area of a cone is:
\(A=\pi r(r+\sqrt{r^2+h^2})\)Where,
\(\begin{gathered} r(\text{ radius\rparen}=\frac{\text{ Diameter}}{2} \\ \\ h=\text{ Height} \end{gathered}\)Height of cone:
\(\begin{gathered} l^2=r^2+h^2 \\ \\ h^2=l^2-r^2 \\ \\ h^2=7^2-2^2 \\ \\ h^2=49-4 \\ \\ h=\sqrt{45} \end{gathered}\)So, the surface area of a cone is:
\(\begin{gathered} A=\pi r(r+\sqrt{r^2+h^2}) \\ \\ A=\pi(2)(2+\sqrt{2^2+45}) \\ \\ A=2\pi(2+\sqrt{49}) \\ \\ A=2\pi(9) \\ \\ A=18\pi \\ \\ A=18\times3.14 \\ \\ A=56.52 \end{gathered}\)So, the surface area of a cone is 56.52
is it true that s >_ 4.5 has a closed circle and the arrow points to the left
Answers
Answer:no
Step-by-step explanation:
it has a closed circle because it's "-or equal to"
if s is more than 4.5 then the arrow would point to anything 4.5 or higher which is to the right
Stacey wishes to make a hamburger which is lower in fat without having to give up the great taste. She purchases 5 pounds of ground beef which is 15% fat and combines it with 7 pounds of ground turkey which is only 3% fat. What is the percentage of fat in the mixture?
Answers
Answer:
%P = 8%
the percentage of fat in the mixture is 8%
Step-by-step explanation:
Given;
The percentage of fat in the mixture is;
%P = total mass of fat in mixture/total mass of mixture × 100%
%P = F/T × 100% ….....1
Mass of fat in mixture is;
She purchases 5 pounds of ground beef which is 15% fat
F1 = 15% of 5 pounds = 0.15×5 pounds
F1 = 0.75 pound
and combines it with 7 pounds of ground turkey which is only 3% fat
F2 = 3% of 7 pounds = 0.03 × 7
F2 = 0.21 pound
Total mass F = F1 + F2
F = 0.75+0.21
F = 0.96 pound
Total mass of mixture T = 5 + 7 pounds
T = 12 pounds.
From equation 1,
%P = F/T × 100%
%P = 0.96/12 × 100%
%P = 0.08×100%
%P = 8%
the percentage of fat in the mixture is 8%
What is the equation of a line parallel to y = 2x + 3 and passes through the point (4, 1)?
Answers
Answer:
What is the value of k used to find the coordinates of a point that partitions a segment into a ratio of 5:3?
Step-by-step explanation:
Marcus borrows $16,500 to pay for his tuition. The annual interest rate of the loan is 4.8%. How much interest does Marcus owe at the end of one year? need help due tomorrow
Answers
Answer:
$792 in interest
Step-by-step explanation:
16500(0.048) = 792
Answer:
792 is the answer
Step-by-step explanation:
Well, what I did was I figured out 4.8% as a decimal = (0.048) and then I timed that with $16,500. Like this --> (0.048×16,500). Which gave me the total of (792)!
Hope this helps! ^^Three same-sized cubes are attached to the top of a rectangular prism as shown below.
If a=10 cm, b = 26 cm, and c = 6 cm, what is the surface area of the figure?
ANSWER ASAP PLEASE!!! IT WOULD MEAN ALOT
Answers
Answer:
Surface area of the figure = 1672 \(cm^{2}\)
Step-by-step explanation:
Surface area of the figure = surface area of the prism + surface area of the 3 cubes
The surface area of the rectangular prism = sum of the area of its individual sides
= 2(26 x 10) + 2(10 x 10) + 2(26 x 10)
= 520 + 200 + 520
The surface area of the rectangular prism = 1240 \(cm^{2}\)
Surface area of one of the cubes = 5(6 x 6)
= 180 \(cm^{2}\)
The surface area of the 3 cubes = 3 x 180
= 540 \(cm^{2}\)
Thus, the surfaces of the cubes on the prism covers a total area of 108 \(cm^{2}\).
So that;
The surface area of the figure = (1240 - 108) + 540
= 1132 + 540
= 1672 \(cm^{2}\)
En la clase de carpintería, la profesora explica que se usan tarugos cilíndricos de madera para unir las piezas de un escritorio. Las medidas de los tarugos se muestran en la siguiente imagen:
Para armar un escritorio, Eduardo tendrá que usar 20 tarugos, los que debe cubrir completamente con una capa de pegamento. Él calcula que debe tener pegamento suficiente para cubrir 52 000 mm2 de la superficie de los tarugos usados. Sin embargo, su compañera Francisca le dice que esa cantidad de pegamento no alcanzará para cubrir todos los tarugos.
Quién tiene la razón? Marca tu respuesta.
Marco
Francisca
Justifica tu respuesta calculando la superficie total de los tarugos que se debe cubrir con pegamento. Usa una aproximación adecuada.
es urgente,, lo necesito ahora):
Answers
The total surface area of the cylindrical dowels that must be covered with glue 8020 mm2 this is less than the 52,000 mm2 of glue that Eduardo calculated so the correct answer is Francisca.
To find out who is correct, we need to calculate the total surface area of the 20 dowels that Eduardo will use. Each dowel has a diameter of 8 mm and a length of 40 mm, so its surface area can be approximated as the sum of the area of two circles (one for each end) and the area of a cylinder (the lateral surface). Using an approximation of π ≈ 3.14, the surface area of one dowel can be calculated as:
2 × (π × (8/2)2) + π × 8 × 40 ≈ 401 mm2
The total surface area of the 20 dowels is therefore:
20 × 401 ≈ 8020 mm2
This is less than the 52,000 mm2 of glue that Eduardo calculated he would need, so it seems that Francisca is correct and Eduardo will not have enough glue to cover all the dowels. Therefore, the answer is:
Francisca.
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_____The given question is incorrect, the correct question is given below:
"In carpentry class, the teacher explains that cylindrical wooden dowels are used to join the pieces of a desk. The measurements of the dowels are shown in the following image:
To assemble a desk, Eduardo will have to use 20 dowels, which he must completely cover with a layer of glue. He calculates that he must have enough glue to cover 52,000 mm2 of the surface of the dowels used. However, his classmate Francisca tells him that that amount of glue will not be enough to cover all the dowels.
Who is correct? Mark your answer.
Eduardo
Francisca
Justify your answer by calculating the total surface area of the dowels that must be covered with glue. Use an appropriate approximation."
If three farmers share some bags of fertilizers in the ratio 3:4:5.if the smallest share is 18 bags.what is the largest share
Answers
Answer:
30
Step-by-step explanation:
Sum of the ratios = 3 + 4 + 5 = 12
Smallest share = 18 bags
Ratio of the smallest share = 3
Let the largest share = x
From the question
18 ------------ 3
x --------------5
Cross multiply
3x = 18 × 5
Dividing bothsides by 3
X = 18 × 5/ 3
X = 90 / 3
X = 30
Therefore.
The largest share = 30
Find the length of the third side of the right triangle
The length of the third side is?
Answers
Answer:
12
Step-by-step explanation:
by pythagoras’ theorem:
a^2 + b^2 = c^2
5^2 + b^2 = 13^2
b^2 = 144
b = 12
Answer:
blurry
Step-by-step explanation:
noob
PLEASE HELP!!! Find the slope of each side of the triangle.
Answers
9514 1404 393
Answer:
AB: -3BC: 2/3AC: -1/4Step-by-step explanation:
The slope of a given segment is the ratio rise/run. The "rise" is the number of vertical divisions between the points. The "run" is the number of horizontal divisions between the points. The "run" is positive left-to-right. The corresponding "rise" is positive up.
Here are the segment slopes (rise/run).
AB = -3/1 = -3
BC = 2/3
AC = -1/4
Find the generating function of the sequence {an}n≥0 determined by an = an−1 + 6an−1 with initial conditions a0 = 1, a1 = 3. You need to find the closed form of the generating function, but you don’t need find the closed form of the coefficients.
Answers
The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.
To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.
The given recurrence relation is: an = an-1 + 6an-2
We are also given the initial conditions: a0 = 1 and a1 = 3.
To find the generating function, we define the generating function A(x) as:
a(x) = a0 + a1x + a2x² + a3x³ + ...
Multiplying the recurrence relation by x^n and summing over all values of n, we get:
∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)
Now, let's express each summation in terms of the generating function a(x):
a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾
Simplifying and rearranging the terms, we have:
a(x)(1 - x - 6x²) = a0 + (a1 - a0)x
Using the given initial conditions, we have:
a(x)(1 - x - 6x²) = 1 + 2x
Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):
a(x) = (1 + 2x) / (1 - x - 6x²)
Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).
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Helpppppppppp pleaseeee
