To ascertain if a vector field is conservative or not, you need to calculate the curl of the field or integrate over the components of the vector field. If the curl is zero, it's conservative. If the curl isn't zero or an integral doesn't exist, the field is not conservative.
Explanation:To determine if the vector field f(x, y, z) = ye−xi + e−xj + 2zk is conservative, we need to find if there exists a function f such that f is the gradient (denoted by ∇) of f. This can be done by checking if the cross product of the vector field is equal to zero, which signifies that the field is conservative.
First, we calculate the curl (∇ x F) of the vector field, which gives us the derivatives of the field components. If the curl is zero, then the vector field is conservative. If it is not zero, this indicates that the vector field is non-conservative.
Alternatively, we can integrate over the components of the vector field to try and find a potential function. If an integral exists, then we can say that the vector field is conservative.
However, if it fails these conditions, then the vector field is not conservative and the function f does not exist for it (dne). Thus, in the case where the vector field is not conservative, enter 'dne'.
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Surface area of a cylinder with a diameter of 14 and height is 9
The scores of adults on an iq test are approximately normal with mean 100 and standard deviation 15. clara scores 118 on such a test. she scores higher than what percent of all adults
Which function represents a reflection of f(x) = 5(0.8)^x across the x-axis?
g(x) = 5(0.8)^–x
g(x) = –5(0.8)^x
g(x) = (0.8)^x
g(x) = 5(–0.8)^x
Answer: The correct option is second.
Explanation:
The given function is,
[tex]f(x)=5(0.8)^x[/tex]
If we graph a function is f(x), then its coordinates is defined as (x,f(x)).
When the graph of f(x) is reflect across the x-axis, then the the x-coordinate remains the same and the sign of y-coordinate is changed. It means after reflecting across the x-axis,
[tex](x,y)\rightarrow(x,-y)[/tex]
The given given equation can be written as,
[tex]y=5(0.8)^x[/tex]
To find the equation of the graph after reflection across the x-axis multiply both sides by -1.
[tex]-y=-5(0.8)^x[/tex]
Because f(x)=y and g(x)=-y.
[tex]g(x)=-5(0.8)^x[/tex]
Therefore the second option is correct and the graph of both function is given below.
Answer:
B. g(x) = –5(0.8)^x
Step-by-step explanation:
We have the function, [tex]f(x) = 5(0.8)^x[/tex].
It is required to reflect the function about x-axis.
Now, as we know,
Reflection across x-axis will flip the graph of the function and the function [tex]f(x)[/tex] becomes [tex]-f(x)[/tex].
So, the reflection of [tex]f(x) = 5(0.8)^x[/tex] across x-axis will give the function [tex]f(x) = -5(0.8)^x[/tex]
So, we see that,
Option B i.e. [tex]g(x) = -5(0.8)^x[/tex] is correct.
Find the equation of the line perpendicular to x−5y=15 that passes through the point (−2,5).
1. Solve the given equation for y.
x - 5y = 15
-5y = -x + 15
y = (-x + 15)/-5
y = (x/5) - 3
y = (1/5)(x) - 3
The slope is 1/5. See it?
The equation we are looking for has a slope which is the negative inverse of the slope in the equation we just solved for y.
The slope for the equation we want is -5 which is the negative inverse of 1/5. Undetstand?
We have the slope of the new equation and one point is given.
Plot BOTH into the point-slope formula and solve for y. To solve for a variable means to isolate the variable ALONE on one side of the equation.
y - y_1 = m(x - x_1)...This is the point-slope formula. Our given point is (5,-2)
y - 5 = -5(x - (-2))
y - 5 = -5(x + 2)
We now solve for y and that's it.
y - 5 = -5x - 10
y = -5x - 10 + 5
The equation we want is y = -5x - 5.
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what is 6 3/4 - 2 3/12=
Answer:
4.5
Step-by-step explanation:
A car is tracing at a rate of 72 kilometers per hour. What is the car rates in kilometers per min? How many kilometers will the car travel in 5 mins
In 5 minutes, the car will travel 6 kilometers.
To convert the car's speed from kilometers per hour to kilometers per minute, we need to divide the given rate by the number of minutes in an hour, which is 60. So, for a car traveling at 72 kilometers per hour, the rate in kilometers per minute is:
72 km/hr / 60 = 1.2 kilometers per minute.
Now, to calculate how many kilometers the car will travel in 5 minutes, we simply multiply the rate in kilometers per minute by the number of minutes:
1.2 km/min * 5 min = 6 kilometers.
Therefore, the car will travel 6 kilometers in 5 minutes at the rate of 72 kilometers per hour.
Eight times the sum of 4 and some number is -56. What is the number?
Isosceles triangles may be obtuse or acute but never right
The statement, "Isosceles triangle may be obtuse or acute but not right", is a false statement.
Isosceles triangles can be defined as triangles that have two sides (angles) having equal measures.
Obtuse triangles have at least one angle greater than 90°.
Acute triangles have all three angles less than 90°.
Right triangles have one of the angles 90°.
Consider a right triangle ABC.
So, one of the angles, let it be A, will be right.
So, m ∠A = 90°.
By the angle sum property of triangles,
90° + m∠B + m∠C = 180°
m∠B + m∠C = 90°
Let both angles are having equal measures, let it be x.
x + x = 90°
2x = 90°
x = 45°
So, each of the angles has a measure of 45°, and so is an isosceles triangle since the two angles are equal.
So, a right triangle can be isosceles.
Hence the statement is false.
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How do you rename 4 thousands 7 hundreds = 47?
How to do you simplify
1/5(40x^5+13x^3-3x-5)-(3x^5-5x^3+5x)
What us the equivalent ratio for 4:3
Please help me!! How do you solve 4x+8=2x+7+2x-20. Thank you
Colin took out a loan with a principal of $32,800. After five years, the interest and principal totaled $48,872. If Colin made monthly payments of $816 for five years until the loan was paid off, how much did Colin pay in service charges? a. $16,072 b. $88 c. $16,160 d. $163
The service charges would be, $88
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
Colin took out a loan with a principal of $32,800.
And, After five years, the interest and principal totaled $48,872.
Now,
The value of principal amount is,
⇒ 816 × 5 × 12 = 48960
Now, We get;
Amount of Colin pay in service charges is,
48960 - 48872= 88
Hence, The service charges were $88
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Your Bank account balance was $235 and 24. After two checks were cashed (each for the same amount) your balance is now -45.58. What was the amount of each of those checks?
235.24 + 45.58 = 280.82
280.82/2 = 140.41
each check was 140.41
The divison of the whole bumber N by 13 gives a quotient of 15 and a remainder of 12. Find N
Franco's Pizza is selling their pizzas 35% cheaper than usual if a pizza normally cost $12 how much is it now
Answer:
New or current cost = 12 - 4.2 = $7.8
Step-by-step explanation:
Franco's Pizza is selling their pizzas 35% cheaper than usual. This is a discount on the normal cost. To get the amount it costs now, we will find the percentage of the discount on the original cost and subtract what we get from the original cost.
Discount = 35℅
Original cost of pizza is $12 (if a pizza normally cost $12).
So the discount in terms of dollars
= ℅ discount / 100 × normal cost of pizza
= 35 / 100 × 12 =0.35 × 12 = $4.2
New or current cost of pizza would be normal or original cost - the discount in dollars.
New or current cost = 12 - 4.2 = $7.8
The pizza is now $7.80.
Explanation:If Franco's Pizza is selling their pizzas 35% cheaper than usual, we can calculate the new price by multiplying the original price by (1 - 0.35).
So, the new price of the pizza would be $12 * (1 - 0.35) = $7.80.
Therefore, the pizza is now $7.80.
Line ET is a tangent to circle A at point T and the measure of ∠TNG is 25°
What is the measure of ∠NET?
A) 130°
B) 50°
C) 65°
D) 90°
Answer:
C) 65°
Step-by-step explanation:
G ∈ NE, so ∠TNG = ∠TNE. ∠ATE = 90° because a radius (AT) is always perpendicular to a tangent line (ET) at the tangent point (T). A ∈ TN, so ΔTNG is a right triangle, and angles NET and TNE are complementary. Then ...
... ∠NET = 90° - ∠TNG
... = 90° - 25°
... ∠NET = 65°
About 11/12 of a golf course is in the fairways, 1/18 in the greens, the rest in the trees. What part of the golf course is in the trees?
how to write 412.638 using fractions
What is the equation for the linear model in the scatter plot obtained by choosing the two points to the closest line?
y=-1.5 X +6
yEquals 1.5 X +6
The equation for the linear model in a scatter plot can be determined by selecting any two points closer to the line and utilizing them to find its slope and y-intercept. This information is then used to write the equation y = mx + b, where m is the slope and b is the y-intercept.
Explanation:The question pertains to the equation of the linear model in a scatter plot which basically describes the best fit line passing through the points on the plot. In simple terms, in a scatter plot if you choose any two points closer to the line, we can use these to determine the equation of that line.
Suppose you have two points (x1, y1) and (x2, y2), where x represents the independent variable and y is the dependent variable. To find the slope (m) of the line, we use the formula: m = (y2 - y1) / (x2 - x1). Once the slope is determined, we proceed to find the y-intercept (b), which is the y-value where the line crosses the y-axis.
The general form of a linear equation is y = mx + b. Hence, using the values of slope and y-intecept obtained earlier, we can write the equation of our line. For example, in the equations given in the question, -1.5 and 1.5 are the slopes and 6 is the y-intercept.
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Using the following production tally, determine how many total mousetraps were produced during a shift:
Quantity per package: 60
Number of packages you sealed: 41
Starting quantity in first package (from previous shift): 52
Ending quantity in your last unsealed package (leave for next shift): 24
Rejected mousetraps: 34
Which point does NOT lie on the graph of the line -2x + 5y = 20?
A. (-10, 0)
B. (0, 4)
C. (1, 4)
D. (5, 6)
a triangle is reflected across the line x=2. which of the following is true?
A. the image and pre-image have the same orientation.
B. the image and pre-image have different sizes.
C. the image and pre-image are congruent.
D. the image and pre-image are separated by a given angle.
Answer: C
Step-by-step explanation:
Answer:
C. the image and pre-image are congruent.
Step-by-step explanation:
a triangle is reflected across the line x=2
Check with each option
A. the image and pre-image have the same orientation.
The image will not be in same order
B. the image and pre-image have different sizes. the size will not change
C. the image and pre-image are congruent. the reflection will not change the size. so they are congruent
D. the image and pre-image are separated by a given angle.
The angles never change in reflection
the fully shaded grid shows 1. EXPLAIN how these three models are related
Find the value of x (7x) (2x+27)
A. 7
B. 49
C. 61
D. 17
The value of x is 17.
To find the value of x when (7x) and (2x+27) are the two angles made on a straight line, we can use the fact that the sum of the angles on a straight line is 180 degrees.
Let's set up an equation:
(7x) + (2x+27) = 180
First, we simplify the equation by combining like terms:
9x + 27 = 180
Next, we isolate the variable x by subtracting 27 from both sides of the equation:
9x = 180 - 27
9x = 153
Finally, we solve for x by dividing both sides of the equation by 9:
x = 153/9
Simplifying the division gives us:
x = 17
Therefore, the value of x is 17.
Complete question :-
Find the value of x, if (7x) and (2x+27) are the two angles made on a straight line?
A. 7
B. 49
C. 61
D. 17
So, the value of x is not one of the given options A, B, C, or D.
To find the value of x in the expression (7x)(2x+27), we need to simplify the expression and solve for x.
Step 1: Distribute the 7x to both terms inside the parentheses:
(7x)(2x+27) = 14x^2 + 189x
Step 2: Set the expression equal to 0 and factor out common terms, if possible:
14x^2 + 189x = 0
Step 3: Factor out x:
x(14x + 189) = 0
Step 4: Set each factor equal to 0 and solve for x:
x = 0 (from the first factor)
14x + 189 = 0
14x = -189
x = -189/14
So, the value of x is not one of the given options A, B, C, or D.
Subtract using the number line. −4−(8)
Answer:
-12
Step-by-step explanation: I Took K12 TEST
How do I FULLY answer this question. I have 2/4 marks
Evaluate 11x-4 when x=_4
A sample is selected from a population with m = 50 and s = 12. if the sample mean of m = 56 produces a z-score of z = +1.00, then how many scores are in the sample? 2 4 9 16
Final answer:
The number of scores in the sample is 4.
Explanation:
The question provided asks us to determine the number of scores in the sample based on the z-score of +1.00, given a population with a mean (μ) of 50 and a standard deviation (σ) of 12.
The z-score formula for a sample is
z = (M - μ) / (σ / √n),
where
M is the sample mean, μ is the population mean, and σ is the population standard deviation, n representing the sample size.We are given that M = 56, z = 1, μ = 50, and σ = 12.
To find the sample size (n), we use the formula and rearrange to solve for n:
z = (M - μ) / (σ / √n)1 = (56 - 50) / (12 / √n)1 = 6 / (12 / √n)√n = 12 / 6n = (2)^2n = 4Therefore, the number of scores in the sample is 4.
What ratio correctly compares the measurements 10,000 cm to 1000 m? Drag and drop the appropriate numbers into the boxes to show the ratio in the simplest form.