Find the work done by F over the curve in the direction of increasing t. W = 32 + 5 F = 6y i + z j + (2x + 6z) K; C: r(t) = ti+taj + tk, Osts2 1012 W = 32 + 20 V3 W = 56 + 20 V2 O W = 0
Answers
The work done by the force vector F over the curve C in the direction of increasing t is W = 3a^2 i + (1/2) j + 4k, where a is a parameter.
To determine the work done by the force vector F over the curve C in the direction of increasing t, we need to evaluate the line integral of the dot product of F and dr along the curve C.
We have:
F = 6y i + z j + (2x + 6z) k
C: r(t) = ti + taj + tk, where t ranges from 0 to 1
The work done (W) is given by:
W = ∫ F · dr
To evaluate this integral, we need to find the parameterization of the curve C, the limits of integration, and calculate the dot product F · dr.
Parameterization of C:
r(t) = ti + taj + tk
Limits of integration:
t ranges from 0 to 1
Calculating the dot product:
F · dr = (6y i + z j + (2x + 6z) k) · (dx/dt i + dy/dt j + dz/dt k)
= (6y(dx/dt) + z(dy/dt) + (2x + 6z)(dz/dt))
Now, let's calculate dx/dt, dy/dt, and dz/dt:
dx/dt = i
dy/dt = ja
dz/dt = k
Substituting these values into the dot product equation, we get:
F · dr = (6y(i) + z(ja) + (2x + 6z)(k))
Now, we can substitute the values of x, y, and z from the parameterization of C:
F · dr = (6(ta)(i) + (t)(ja) + (2t + 6t)(k))
= (6ta i + t j + (8t)(k))
Now, we can calculate the integral:
W = ∫ F · dr = ∫(6ta i + t j + (8t)(k)) dt
Integrating each component separately, we have:
∫(6ta i) dt = 3ta^2 i
∫(t j) dt = (1/2)t^2 j
∫((8t)(k)) dt = 4t^2 k
Substituting the limits of integration t = 0 to t = 1, we get:
W = 3(1)(a^2) i + (1/2)(1)^2 j + 4(1)^2 k
W = 3a^2 i + (1/2) j + 4k
Therefore, the work done by the force vector F over the curve C in the direction of increasing t is given by W = 3a^2 i + (1/2) j + 4k.
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Related Questions
find the exact length of the third side
Answers
you would have to use pythagorean theorem and do 7 squared plus 3 squared. you would get 58. then you have to square root 58 which would give you 7.62
The student council at Greenwood High School is making T-shirts to sell for a fundraiser, at a price of $19 apiece. The costs, meanwhile, are $8 per shirt, plus a setup fee of $88. Selling a certain number of shirts will allow the student council to cover their costs. What will the costs be? How many shirts must be sold?
Answers
Answer:
19-8=11,11*n>=88,n>=8 ，8*119-8=11,11*n>=88,n>=8 9=152
Step-by-step explanation:
Unit price - cost = unit profit
When unit profit * quantity > = Installation cost, achieve positive profit
someone pls help im struggling if you do tysm ! <333 :)
Answers
Answer:
everything except -1 will be the answer
Step-by-step explanation:
4n + 13 < 9
n < -1
if n is -1, the answer would be 9(INCORRECT)
if n is -2, the answer would be 5(CORRECT)
if n is -3, the answer would be 1(CORRECT)
if n is -4, the answer would be -3(CORRECT)
Can someone please help me solve this. You need to find the missing numbers
Answers
Answer:
4+4 9-3
Step-by-step explanation:
Answer:
3.5 + 4.5 = 8
+ +
9.5 - 3.5 = 6
= =
13 8
Step-by-step explanation:
the product of a number and -7 is 63."
Answers
Answer:
the number is -9
Step-by-step explanation:
represented by the equation 5x + 2y = 10.
How is the slope of the line related to values of
A, B, and C in standard form Ax + By = C?
-Can you please explain how to solve this problem? I wouldnt want only the answer. Thank you so much
Answers
The equation given 5x + 2y = 10 given, represents the slope considering the form Ax + By = C: by slope = - A/B = -5/2
How to find the slope of the lineAx + By = C
rewriting in standard form which is y = mx + c, where m is the slope, is done as follows
By = -Ax + C
y = ( - Ax + C ) / B
y = - Ax/B + C/B
comparing with standard form the slope, m is - A/B
using the other equation 5x + 2y = 10
rewriting gives
y = -5x/2 + 10/2
the slope here is -5/2
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A book normally cost $5.50 is marked up by 40%. What is the selling price of the book?
Answers
Answer:
Selling Price of the Book - $7.70
I believe that this is the answer
Step-by-step explanation:
We need to find what is 40% of 5.50.
40/100 x 5.50
After solving this, we will get 2.20
Now, the question is asking what is the selling price of the book will be after it is marked up. Marked up means an increase in price, and the increase in price is 40% of 5.50 which we have already found. All there is left for us to do is add 5.50 and 2.2. This will give us $7.70.
What is the angle between the vectors − 2i 3j k and i 2j − 4k?
Answers
The angle between the vectors can be found using the dot product. The formula is θ= |A| =√(x12 + y12 + z12) The angle between the vectors -2i + 3j + k and i + 2j - 4k is approximately 137.8 degrees.
v1 • v2 = (-2i + 3j + k) • (i + 2j - 4k)
= -2 - 6 + 1 = -7
|v1| = \(\sqrt{((-2)^2 + 3^2 + 1^2)}\)
=\(\sqrt{(4 + 9 + 1)}\)
=\(\sqrt{14}\)
|v2| = \(\sqrt{((1)^2 + 2^2 + (-4)^2)}\)
= \(\sqrt{(1 + 4 + 16) }\)
= (\(\sqrt{21}\)
θ= |A| (-7/\(\sqrt{14}\)\(\sqrt{21}\))
= |A| (-7/21*14)
= |A|(-7/294)
= 137.8 degrees
The angle between two vectors can be found using the dot product formula. This formula isθ= |A| =√(x12 + y12 + z12). In the case of the vectors -2i + 3j + k and i + 2j - 4k, this formula can be used to find the angle between them. The dot product of the two vectors is -2 - 6 + 1 = -7. The magnitude of the first vector, |v1|, can be found using the Pythagorean theorem, which is
\(\sqrt{((-2)^2 + 3^2 + 1^2)}\)
= \(\sqrt{(4 + 9 + 1)}\)
= \(\sqrt{14}\).
The magnitude of the second vector, |v2|, can be found using the Pythagorean theorem, which is
\(\sqrt{((1)^2 + 2^2 + (-4)^2)}\)
= \(\sqrt{(1 + 4 + 16)}\)
= \(\sqrt{21}\)
Once the dot product and magnitudes are known, the angle between the two vectors can be found using the formula .Therefore, the angle between the two vectors is approximately 137.8 degrees.
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Please help me with this, I need to find the missing angle of both of the triangles. Thank you. :))
Answers
The missing side of FDE = 24
Pythagorean Theorem: a² + b² = c²
Pythagorean Theorem is for right-angled triangle only.
The missing side of ABC is:
12² + 5² = AC²
169 = AC²
AC = √169
AC = 13
The missing side of FDE is:
DE² + 10² = 26²
DE² = 26² - 10²
DE² = 576
DE = √576
DE = 24
Solve the recursion using all three methods in any order you choose. Clearly label each solution as recursion tree, substitution, or Master Theorem. (15pt: 5 for each method): T(n)=2T(n/2)+23n
Answers
The solution of the given recurrence relation `T(n) = 2T(n/2) + 23n` using all three methods are:`T(n) = Θ(nlog2n)`
Given recursive relation is `T(n) = 2T(n/2) + 23n`.
We have to solve the above recursion using all three methods in any order we choose and label each solution as recursion tree, substitution, or Master Theorem.
Now, let's solve the above recursion using all three methods one by one:
1. Recursion Tree method:
To solve the above relation using recursion tree method, we will create a tree and the value of each level will be the sum of the values of all nodes present in that level or the sum of all previous levels + current level.
The tree will look like:
Therefore, the answer of the given recurrence relation `T(n) = 2T(n/2) + 23n` using the recursion tree method is:
`T(n) = Θ(nlog2n)`
2. Substitution method:
To solve the above recurrence relation using the substitution method, we can assume a solution and prove it by the Mathematical induction method.
Let `T(n) = 2T(n/2) + 23n`
Then, `T(n/2) = 2T(n/4) + 23n/2`
Also, `T(n/4) = 2T(n/8) + 23n/4`
Therefore, `T(n) = 2(2T(n/4) + 23n/2) + 23n`Or, `T(n) = 2²T(n/2²) + 23n(1 + 2)`
In general, we have `T(n) = 2kT(n/2k) + 23n(1 + 2 + ... + 2k-1)`
When `n/2k = 1`Or, `k = log2n`
Therefore, `T(n) = 2log2nT(1) + 23n(1 + 2 + ... + 2log2n-1)`Or, `T(n) = 2log2nT(1) + 23n(2log2n - 1)`
As `T(1) = 1`
Therefore, `T(n) = Θ(nlog2n)`
Hence, the answer of the given recurrence relation `T(n) = 2T(n/2) + 23n` using the substitution method is:
`T(n) = Θ(nlog2n)`
3. Master Theorem method:
To solve the above recurrence relation using the Master theorem, we have to compare the function `nlogba` with the function `f(n)`.
Here, `a = 2`, `b = 2`, and `f(n) = 23n`.
As per the Master theorem:
`If f(n) = Θ(nlogba),
then T(n) = Θ(nlogba log2n)` `
= Θ(nlog2n)` if
`f(n) = 23n
= Θ(nlog2n)`
Therefore, the solution of the given recurrence relation `T(n) = 2T(n/2) + 23n` using the Master theorem is:
`T(n) = Θ(nlog2n)`
Hence, the solution of the given recurrence relation `T(n) = 2T(n/2) + 23n` using all three methods are:`T(n) = Θ(nlog2n)`
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m(x) = -2/3x + 8; m(x) = 2
Answers
Answer:
Answer is x = 9
How do you calculate 2 + 3 x 7?
a. 2+3 x 7 = 2+21= 23
b. 2+7x7 = 2 + 21 = 35
C. 2+7x3 = 2 + 21 = 23
Answers
Answer:
A
Step-by-step explanation:
using BODMAS
3×7=21+2=23
For a data set with an odd number of observations that have been sorted from smallest to largest values, where is the median located?
Answers
For a data set with an odd number of observations that have been sorted from smallest to largest values, the median is located at \(\frac{x+1}{2}\)
Given,
The conditions
There are odd number of observationThe observation have been sorted from smallest to largest valuesWe know,
Median is the middle number of ordered data set.
Consider the number of observations as x
Then the median is located at \(\frac{x+1}{2}\)
Hence, for a data set with an odd number of observations that have been sorted from smallest to largest values, the median is located at \(\frac{x+1}{2}\)
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can someone help show my work HAHAHAHA its due today
Answers
Step-by-step explanation:
Since it is a regular pentagon, all five sides are equal and you know one side is x-3. Thus the equation would be: x-3 = 18.8/5
x - 3 = 18.8/5
= 3.76
x = 3.76 + 3
x = 6.76
Total consumption of fruit juice in a particular country in 2006 was about 1.82 billion gallons. The population of that country in 2006 was 300 million. What was the average number of gallons of fruit juice consumed per person in the country in 2006? Use pencil and paper. Using the per person amount from this problem, about how many gallons would your class consume?
Answers
Total consumption of fruit juice in a particular country in 2006 was about 1.82 billion gallons. The population of that country in 2006 was 300 million. What was the average number of gallons of fruit juice consumed per person in the country in 2006? Use pencil and paper. Using the per person amount from this problem, about how many gallons would your class consume?
3 *(x-7)*(x+7)-(x-1)*(3x+2)=13
Answers
The value of x will be 158. The value of x is obtained by simplifying the equation.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
Identity used;
(x+a)(x-a) = x² - a²
Given expression;
3(x-7)(x+7) - (x-1)(3x+2) = 13
Solving the equation step by step;
\(\rm 3(x^2 - 7^2 ) - [x(3x+2)-1(3x+2) ]= 13\\\\ 3x^ 2 -147 -[3x^2 +2x -3x-2] = 13 \\\\ 3x^2 -147 -[3x^2 -x-2] = 13\\\\ 3x^2-147-3x^2 +x+2 = 13 \\\\ x= 13+145 \\\\ x= 158\)
Hence, the value of x will be 158.
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Need help with my math hw
Answers
In Central City, Elm Street and Maple Street are parallel to one another. Oak Street crosses both Elm Street and Maple Street as shown.Tell whether each statement is True or False.
Answers
Answer:
a. True, because they are corresponding angles.
b. False, because angles 1 and 2 are supplementary, meaning that they add up to 180 degrees, but 125 + 65 = 190 degrees.
c. True, because they are corresponding angles.
d. True, becuase they are two angles that add up to 180 degrees.
e. True, because they are both interior angles on opposite sides of the transversal.
Answer:
a. True.
b. False.
c. True.
d. True.
e. True.
Step-by-step explanation:
a. This statement is true because angles 6 and 8 are vertical angles. That means they are congruent.
b. This statement is false because Elm Street is a straight line, which means that angles 1 and 2 are supplementary angles and their measures will add up to be 180 degrees. 65 + 125 = 190, which is not equal to 180.
c. This statement is true because angles 5 and 1 correspond to each other.
d. This statement is true because angles 7 and 8 form a straight line.
e. This statement is true because they are interior angles that are alternate.
Hope this helps!
It's really important, please help
Answers
The question isn't complete. This is just part of the question
So please send the whole question together.
Answer:
98 mins
Step-by-step explanation:
147.5 +x = 245.5
x = 245.5-147.5
x= 98 mins
The perimeter, P, of a rectangle is equal to twice the sum of the length and width of the rectangle. Determine the width of a rectangle with a perimeter of 34 inches and a length of 5 inches. In your final answer, include all necessary calculations.
Answers
Answer:
12 inches
Step-by-step explanation:
5 + 5 = 10
34 - 10 = 24
24 ÷ 2 = 12
Therefore, the answer is 12 inches.
-1.25(z+8)=-6
Please help; find z
Answers
Answer:
z = -3.2
Step-by-step explanation:
-1.25(z + 8) = -6
-1.25z - 10 = -6
+10 +10
-----------------------
-1.25z = 4
÷(-1.25) ÷(-1.25)
--------------------------
z = -3.2
I hope this helps!
Rang of the number 12,9,24,24,37,18,9,6,24
Answers
Answer:
it is 15
Step-by-step explanation:
Answer:
31
Step-by-step explanation:
Range = Largest number ( in terms of value ) - smallest number ( in terms of value )
The largest number of the set is 37 and the smallest number is 6
Range = 37 - 6
37 - 6 = 31
Hence, the range is 31
What is equivalent to 1/5(15+10x-5)
Answers
1/5(15+10x-5) is equivalent to 2(x+1).
What is equivalent equation?
Equivalent equations are algebraic equations with the same roots or solutions.
1/5(15+10x-5) can be simplified as follows:
1/5(15+10x-5) = 1/5(10x + 10)
Factor out 10 from the expression in the parentheses:
1/5(10x + 10) = 1/5 * 10 * (x + 1)
Simplify:
1/5 * 10 * (x + 1) = 2(x + 1)
Therefore, 1/5(15+10x-5) is equivalent to 2(x+1).
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What is 4573 - 3892?
Answers
Answer:
The answer is 681.
681
would be your answer when subtracting 4573 - 3892
suppose that one customer who participated in the study is chosen at random. what is the probability that the customer had a high level of satisfaction and used the company more than five times per month?
Answers
The probability of an event is given by the number of favorable outcomes divided by the total number of possible outcomes.
In this case, the favorable outcome is that the customer had a high level of satisfaction and used the company more than five times per month. The total number of possible outcomes is the total number of customers in the study, which is 700.
Therefore, the desired probability can be calculated as:
P(High satisfaction and more than 5 times per month) = 70 / 700
And the answer is P(High satisfaction and more than 5 times per month) = 70 / 700 = 1/10.
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The circular lid of a jar has a diameter of 3 inches. Which of the following
expressions could be used to find the radius of the jar?
The circular lid of a jar has a diameter of 3 inches. Which of the following
expressions could be used to find the radius of the jar?
1. 2 • 3
2. 3π
3. 3 • 3
4. 3 ÷ 2
Answers
So the answer is:
4. 3 / 2
determine if the set of vectors is orthonormal. if the set is only orthogonal, normalize the vectors to produce an orthonormal set. u= −0.6 −0.8 , v= −0.8 0.6
Answers
The vectors u and v are orthogonal, and their magnitudes are equal to 1. Hence, the set {u, v} is an orthonormal set.
To determine if the set of vectors {u, v} is orthonormal, we need to check if the vectors are orthogonal and if their magnitudes are equal to 1.
First, let's check if the vectors u and v are orthogonal. Two vectors are orthogonal if their dot product is zero.
The dot product of u and v is given by:
u · v = (-0.6)(-0.8) + (-0.8)(0.6) = 0.48 - 0.48 = 0
Since the dot product of u and v is zero, we can conclude that the vectors u and v are orthogonal.
Next, let's check if the magnitude of vector u is equal to 1. The magnitude of a vector u = (u1, u2) is given by:
|u| = √(u1² + u2²)
Substituting the values of u = (-0.6, -0.8):
|u| = √((-0.6)² + (-0.8)²) = √(0.36 + 0.64) = √1 = 1
The magnitude of vector u is equal to 1.
Similarly, let's check the magnitude of vector v. The magnitude of vector v = (-0.8, 0.6) is given by:
|v| = √((-0.8)² + (0.6)²) = √(0.64 + 0.36) = √1 = 1
The magnitude of vector v is also equal to 1.
No further normalization is required since the vectors are already of unit length.
In summary, the set {u, v} is an orthonormal set.
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HELP QUICK! Can someone please explain this and show your work please!
Answers
Answer:
x > -2
Step-by-step explanation:
\(-\frac{x}{2} + \frac{3}{2} < \frac{5}{2} \\-\frac{x}{2} < \frac{2}{2} \\-\frac{x}{2} < 1\\-x < 2\\-\frac{x}{-1} < \frac{2}{-1} \\x > -2\)
See picture of graphed number line below:
A firework rocket consists of a cone stacked on top of a cylinder where the radius of the cone and the cylinder are equal the diameter of the cylindrical base of the rocket is 8 in and the height of the cylinder is 5 in while the height of the cone is 3 in
Answers
Answer:
Surface area of the rocket = 76π
Step-by-step explanation:
Given:
Diameter = 8 in
Radius of cylinder = 4 in
Radius of cone = 4 in
Height of the cylinder = 5 in
Height of the cone = 3 in
Find:
Surface area of the rocket.
Computation:
Slant hight = \(\sqrt{4^2 + 3^2}\)
Slant hight = 5 in
Surface area of the rocket = Surface area of cylinder + Surface area of cone + Area of circle
Surface area of the rocket = 2πrh + πrl + πr²
Surface area of the rocket = 2π(4)(5) + (π)(4)(5) + (π)(4)²
Surface area of the rocket = 40π + 20π + 16π
Surface area of the rocket = 76π
A plot has a concrete path within its borders on all sides having uniform width of 4m. The plot is rectangular with sides 20m and 15m. Charge of removing concrete is Rs. 6 per sq.m. How much is spent
Answers
A total of Rs. 2064 would be spent on removing the concrete path.
To calculate the amount spent on removing the concrete path, we first need to find the area of the path.
The total area of the plot including the concrete path is:
Total Area = (20 + 2 * 4) * (15 + 2 * 4) square meters
= (28) * (23) square meters
= 644 square meters
The area of the plot without the concrete path is:
Plot Area = 20 * 15 square meters
= 300 square meters
Therefore, the area of the concrete path is:
Path Area = Total Area - Plot Area
= 644 - 300 square meters
= 344 square meters
The cost of removing concrete is given as Rs. 6 per square meter.
Hence, the amount spent on removing the concrete path is:
Amount spent = Path Area * Cost per square meter
= 344 * 6 Rs.
= 2064 Rs.
As a result, Rs. 2064 would be needed to remove the concrete path.
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