Find the work done by the force field f(x, y, z) = x − y2, y − z2, z − x2 on a particle that moves along the line segment from (0, 0, 1) to (3, 1, 0).
The work done by force field on a particle moving from one point to another in space is calculated using the concept of dot-product. The force field is represented as a function and the movement of the particle is treated as a path. By integrating the dot product of the force field and the derivative of path over the interval, we get the work done.
Explanation:To calculate the work done by force field on a particle, you need to apply the concept of dot product in vector calculus. The force field is defined as f(x, y, z) = x − y², y - z², z - x² and the movement of the particle is from (0, 0, 1) to (3, 1, 0). We treat this movement as a line segment in the 3-dimensional space.
The work done by the force field on the particle is calculated as W = F . dr = ∫ F(r(t)) . r'(t) dt from t1 to t2. In this case, the force field F is f(x, y, z) and the line segment can be treated as a path r(t) = t * (3, 1, 0) + (1 - t) * (0, 0, 1) and t varies from 0 to 1. Hence, r'(t) = (3, 1, 0) - (0, 0, 1).
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Expression for the following phrase,"an hourly wageof $13.50 plus $75 bounes
Which expression has a positive value A.(-5)(-9) B.2-4 C.12/(-4) D. -3+(-7)
Out of given expressions, only expression A results in a positive value. Expression B, C, and D all result in a negative value.
Explanation:To determine which expression results in a positive value, evaluate each:
A. (-5)(-9): Here, a negative times a negative results in a positive value, so this equals 45.B. 2-4: This equals -2, which is not a positive value.C. 12/(-4): This equals -3, which is also not a positive value.D. -3+(-7): This equals -10, which is not a positive value.
So, "only expression A results in a positive value".
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A multivitamin tablet contains 0.16g of vitamin C. How much vitamin C does a bottle of 60 tablets contain?
Find the fractional notation for the ratio 5 to 9
What is the trigonometric derivative of Y=2sinx-tanx
help quick. first person with the right answer gets brainiest
Jose rented a truck for one day. There was a base fee of $14.99 , and there was an additional charge of 83 cents for each mile driven. Jose had to pay $238.26 when he returned the truck. For how many miles did he drive the truck?
Bertie is x years old now. Four years ago, Chloe was twice as old as Bertie. Write an expression for Chloe's age now.
The present Age of Chloe is 2x - 4 years old.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Bertie is x years old now.
Four years Ago,
Chloe was twice as old as Bertie.
Bertie Age four years ago = x - 4
So, Chloe Age four years ago = 2(x- 4) = 2x- 8
Now, Chloe is 4 years older than she was 4 years ago,
Then, Chloe present age is (2x - 8) + 4 = 2x - 4 years old.
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Differentiate: x√(x+4)
Sample of 3 items is selected at random from a box containing 20 items of which 4 aredefective. find the expected number of defective items in the sample.
divide 28 cans of soda into two groups so the ratio is 3 to 4
Can someone help me with these two questions?
Is the converse of the following conditional true?
If b≤2, then b≥2.
yes
or
no
1 2 3 4 5 6 7 8 9 10
TIME REMAINING
48:54
What number should be added to both sides of the equation to complete the square?
x2 + 3x = 6
3
62
2.25
Explanation:Consider the square ...
... (x+a)² = x² +2ax +a²
The constant term (a²) is the square of half the x-coefficient: a² = (2a/2)².
The x-coefficient in your expression is 3. The square of half that is ...
... (3/2)² = 9/4 = 2.25
Adding 2.25 to both sides gives ...
... x² +3x + 2.25 = 6 + 2.25
... (x +1.5)² = 8.25 . . . . completed square
(3/2)^2
I believe it is (3/2)^2 because I tried working it out and got something like it. I did get an answer of x = ±[tex]\sqrt{33}[/tex] over 2.
Most sources appear to give 2.25, which is equal to 3/2 squared.
Attached some work.
What is the equation of the horizontal line through (-7,-3)
a rectangle is 4 centimeters longer than it is wide. the area is 117 square centimeters. find the dimensions of the rectangle
Answer:
width: 9 cmlength: 13 cmStep-by-step explanation:
Integer factors of 117 include ...
... 117 = 1×117 = 3×39 ≈ 9×13
The last factor pair is two factors that differ by 4. We can take these to be the dimensions of the rectangle.
_____
If you want to write an equation for width (w), it might be ...
... w(w+4) = 117
... w² +4w -117 = 0
The factorization problem for this quadratic is the problem of finding two factors of 117 that differ by 4. That is what we have done, above.
If you want to solve this by completing the square, you can to this:
... w² +4w = 117
... w² +4w +4 = 121 . . . . . add 4 = (4/2)² to complete the square
... (w+2)² = 121
... w + 2 = ±√121 = ±11 . . . . take the square root
... w = -2 ± 11 . . . . . we're only interested in the positive solution
... w = 9, then w+4 = 13 and the dimensions are 9 cm by 13 cm.
7,080,267 written in expanded form
The number 7,080,267 in expanded form is written as the sum of each digit multiplied by its place value: 7,000,000 + 80,000 + 800 + 200 + 60 + 7.
Explanation:To write the number 7,080,267 in expanded form, we break it down into each digit's place value and represent it as the sum of each digit multiplied by its place value.
The expanded form of 7,080,267 is:
7,000,000 + 80,000 + 800 + 200 + 60 + 7
This shows that there are seven millions, eighty thousands, eight hundreds, two hundreds, six tens, and seven ones.
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The clown Also bought 5 bags of heart shaped Balloons with 14 Balloons in each Bag
The clown bought a total of 70 heart-shaped balloons. This is found by multiplying the number of bags (5) by the number of balloons in each bag (14).
Explanation:
The question involves a basic multiplication operation in mathematics. The clown bought 5 bags of heart-shaped balloons and each bag contains 14 balloons. To find the total number of balloons, you multiply the number of bags (5) by the number of balloons in each bag (14). This is done as follows:
Identify the numbers in the question: 5 bags, 14 balloons in each. Perform the multiplication: 5 (bags) x 14 (balloons in each bag) = 70 balloons.So, the clown bought a total of 70 heart-shaped balloons.
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Tabitha found the side length of a cube with a volume of 512 cubic centimeters using the following steps. Cube V = s3
Answer:
the answer is 3cm
HOPE THIS WORKED
Step-by-step explanation:
I JUST ANSWERED THIS ON EDG
The volume of a cube is given as 512 cubic cm then the side length of the cube is 8 mm.
What is the volume of a cube?The volume of a cube can be calculated as the cube of the sides of a given figure.
The volume of a cube = [tex]sides^3[/tex]
We have been given that the volume of a cube is 512 cubic cm. We need to find the side length of the cube.
The volume of a cube = [tex]sides^3[/tex]
64 = [tex]sides^3[/tex]
Now we will take cube-root on both sides of the equation;
∛ 512 = ∛ s^3
∛ 8^3 = ∛ s^3
8 = s
Therefore, the side length of the cube is 8 cm.
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In a certain town, the wind speed, x, in km/h on a certain day is described by two statements: If 2 times the wind speed is increased by 2, the wind speed is still less than 46 km/h. Twice the wind speed minus 27 is greater than 11 km/h. Part A: Create a compound inequality to represent the wind speed range. (3 points) Part B: Can the wind speed in this town be 20 km/h? Justify your answer by solving the inequalities in Part A. (3 points) Part C: The average wind speed in another town is 23 km/h, but the actual wind speed is within 4 km/h of the average. Write and solve an inequality to find the range of wind speed in this town.
What is 49.2532 to 1 decimal place
the second number to the right of the decimal point is 5 so you need to round the 2 up to 3
so the number becomes 49.3
The top of a 15-foot ladder leans against a wall, and the bottom of the ladder slides away from the wall at a rate of 4 ft/sec. find the velocity of the top of the ladder at time t = 1 sec if the bottom of the ladder is 5 feet away from the wall at time t = 0.
Final answer:
The velocity of the top of the ladder at time t = 1 sec is -4 ft/sec.
Explanation:
To find the velocity of the top of the ladder at time t = 1 sec, we can use the concept of similar triangles. Let x be the distance between the bottom of the ladder and the wall at time t = 1 sec. Since the bottom of the ladder slides away from the wall at a rate of 4 ft/sec, we have x = 5 + 4t.
The height of the ladder remains constant at 15 ft, so if we consider the triangle formed by the ladder, the wall, and the ground, we have the ratio of the height to the base is always 15 / x. Therefore, the velocity of the top of the ladder can be found by taking the derivative of the height with respect to time.
Let h be the height of the ladder at time t. Since h = 15, we have 15 / x = 15 / (5 + 4t). Taking the derivative of both sides, we get d/dt (15 / x) = d/dt (15 / (5 + 4t)). Using the quotient rule, we have d/dt (15 / x) = (0 - 15)(0 - (5 + 4t)-2)(4) = -60 / (5 + 4t)². This gives us the velocity of the top of the ladder at time t = 1 sec: v = -60 / (5 + 4(1))² = -4 ft/sec.
An equation that represents the set of points that are 2 units from (-2,-6)
The equation representing the set of points that are 2 units from the point (-2,-6) is a circle with equation (x + 2)^2 + (y + 6)^2 = 4
The question asks for an equation that represents the set of points that are exactly 2 units from the point (-2,-6) in a coordinate system. This set of points forms a circle with a radius of 2 units centered at (-2,-6). The equation for a circle with radius r and center (h, k) is (x - h)² + (y - k)² = r². Thus, the equation of the circle is (x + 2)² + (y + 6)² = 2² or (x + 2)² + (y + 6)² = 4
Is 124 a prime number or not explain why (u can do division to)
Need help with problem, been stuck on it for a while
The nurse develops a plan to prevent atelectasis in a postsurgical client. which intervention will be effective?
Using incentive spirometry is an effective intervention to prevent atelectasis in a postsurgical client.
Explanation:To prevent atelectasis in a postsurgical client, the nurse can implement the following intervention:
Incentive spirometry: This technique involves deep breathing exercises using a device called an incentive spirometer. It helps to expand the lungs, improve lung volumes, and prevent atelectasis.Using the incentive spirometer, the client is instructed to exhale normally, place their lips around the mouthpiece, and take a slow, deep breath. They should hold the breath for a few seconds before exhaling and repeating the process multiple times throughout the day.
This intervention is effective because it encourages deep breathing and lung expansion, preventing the collapse of alveoli in the lungs and promoting better gas exchange.
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To prevent atelectasis in a postsurgical client, the nurse can implement interventions such as deep breathing exercises, mobilization and ambulation, and pain medication.
Explanation:To prevent atelectasis in a postsurgical client, the nurse can implement several interventions:
Encouraging deep breathing exercises to expand the lungs.Assisting with mobilization and ambulation to improve lung expansion.Administering pain medication to ensure the client can take deep breaths without discomfort.These interventions help prevent the collapse of alveoli and promote proper lung function after surgery.
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A model for my number has 2 hundreds blocks no tens blocks and 3 ones blocks
Josie has $47 left on her checking account. If she writes a check for $55, what ill josie's balance be?
Answer:
Step-by-step explanation:
Josie's balance would be -8 dollars.
47-55=-8
Find all local extrema and saddle points of the function ,