The curl of the vector field is:
[tex]=z e^x \hat{\imath}-\left(y z e^x-7 x y e^z\right) \hat{\jmath}-7 x e^z \hat{k}[/tex]
What do we mean by multivariable calculus?Multivariable calculus (also known as multivariate calculus) is the extension of one-variable calculus to multivariable calculus: the differentiation and integration of functions involving multiple variables rather than just one.Multivariable calculus is a fundamental component of advanced calculus. Calculus on Euclidean space is an advanced calculus topic.So,
To find the curve:
[Vector Field] Set up [curl F]:
[tex]Curl F=\left|\begin{array}{ccc}\hat{1} & \hat{\jmath} & \hat{k} \\\frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\7 x y e^z & 0 & y z e^x\end{array}\right|[/tex]
Simplify [3x3 Matrix Determinant] with [curl F]:
[tex]Curl F=\left|\begin{array}{cc}\frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\0 & y z e^x\end{array}\right| \hat{i}-\left|\begin{array}{cc}\frac{\partial}{\partial x} & \frac{\partial}{\partial z} \\7 x y e^z & y z e^x\end{array}\right| \hat{j}+\left|\begin{array}{cc}\frac{\partial}{\partial x} & \frac{\partial}{\partial y} \\7 x y e^z & 0\end{array}\right| \hat{k}[/tex]
Simplify [2x2 Matrix Determinant] with [curl F]:
[tex]Curl F=\left[\frac{\partial}{\partial y} y z e^x-\frac{\partial}{\partial z} 0\right] \hat{\mathrm{i}}-\left[\frac{\partial}{\partial x} y z e^x-\frac{\partial}{\partial z} 7 x y e^z\right] \hat{\mathrm{\jmath}}+\left[\frac{\partial}{\partial x} 0-\frac{\partial}{\partial y} 7 x y e^z\right] \hat{\mathrm{k}}[/tex]
The partial derivatives can be differentiated using the basic differentiation techniques listed above under "Calculus":
[tex]\begin{aligned}&\frac{\partial}{\partial y} y z e^x=z e^x \\&\frac{\partial}{\partial z} 0=0 \\&\frac{\partial}{\partial x} y z e^x=y z e^x \\&\frac{\partial}{\partial z} 7 x y e^z=7 x y e^z \\&\frac{\partial}{\partial x} 0=0 \\&\frac{\partial}{\partial y} 7 x y e^z=7 x e^z\end{aligned}[/tex]
When we substitute our partial derivative values, we get:
[tex]\begin{aligned}Curl F&=\left(z e^x-0\right) \hat{1}-\left(y z e^x-7 x y e^z\right) \hat{\jmath}+\left(0-7 x e^z\right) \hat{k} \\&=z e^x \hat{\imath}-\left(y z e^x-7 x y e^z\right) \hat{\jmath}-7 x e^z \hat{k}\end{aligned}[/tex]
So, we've discovered the curl of the given vector field.
Therefore, the curl of the vector field is:
[tex]=z e^x \hat{\imath}-\left(y z e^x-7 x y e^z\right) \hat{\jmath}-7 x e^z \hat{k}[/tex]
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The correct question is given below:
Consider the following vector field. f(x, y, z) = 7xyezi + yzexk (a) find the curl of the vector field.
In the diagram, m∠BDA = 119° . Find m∠BDC
Answer: angle BCD is 77°
Step-by-step explanation:
BDC+CDA=119°
-5x+52°-2x+32°=119°
-7x+84°=119°
-7x=35°
x=-5°
Then substitute x in the equation for BDC
-5(-5)+52°=BDC
25+52°=BDC
BDC=77°
The interior angle measure of a regular polygon is given. Identify the polygon.
108
The regular polygon with an interior angle of measure 108° is a pentagon.
A regular polygon is a polygon that has equal side lengths and equal interior angle measures.
Interior angle of a polygon is the angle inside it that is formed by two adjacent sides. The number of interior angles formed inside a polygon is the same as the number of its sides. Meanwhile, the sum of all the interior angles of any polygon is constant to that polygon and depends on the number of sides.
sum = 180(n - 2)
Using this formula,
sum = 180(n - 2)
where n = number of sides of the polygon = number of interior angles
sum = measure of interior angle x n
108n = 180(n - 2)
108n = 180n - 360
180n - 108n = 360
72n = 360
n = 5
If the polygon has 5 sides and 5 interior angles, then the regular polygon is a pentagon.
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y=-|x|
where does that go on a graph ?
Find the factor pairs for the number.
24
Answer:(1, 24), (2, 12), (3, 8), and (4, 6).
Step-by-step explanation:a pair of numbers when multipled you get 24.
Write an explicit and a recursive formula for each sequence. 27,15,3,-9,-21, . . . . . .
an=a1+d(n−1) is the explicit and a recursive formula for each sequence .
What is sequence?An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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Solve each equation. t-2(3-2 t)=2 t+9
The solution of the given linear equation in one variable t - 2(3 - 2t) = 2t + 9 is at t = 5.
According to the given question.
We have a linear equation in one variable.
t -2(3-2t) = 2t + 9
As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Thereofre, the solution of the linear equation in one variable t -2(3-2t) = 2t + 9 is given by
t - 2(3 - 2t) = 2t + 9
⇒ t - 6 + 4t = 2t + 9 (by distributive rule)
⇒ 5t - 6 = 2t + 9
⇒ 5t - 2t = 9 + 6
⇒ 3t = 15
⇒ t = 15/3
⇒ t = 5
Hece, the solution of the given linear equation in one variable t - 2(3 - 2t) = 2t + 9 is at t = 5.
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2^4x2^-7
Solution_______________
Answer:
1/8
Step-by-step explanation:
a machine operator can program machine #1 to produce 100 parts per hour, but the machine requires 2 hours of service each day when it is not operating. machine #2 can produce only 80 parts per hour, but only requires 30 minutes of service each day. which machine is more productive in an eight hour work day?
If a machine operator can program machine #1 to produce 100 parts per hour, but the machine requires 2 hours of service each day when it is not operating and machine #2 can produce only 80 parts per hour, but only requires 30 minutes of service each day, then both the machines are equal in productivity in an eight hour work day.
To determine which machine is more productive in an eight hour work day, an algebraic expression can be used.
x = y ( 8 hours - s )
Here, x = to the parts produced in an eight hour work day
y = parts produced per hour
s = service hours
Thus, the parts produced by both the machines in an eight hours work day can be calculated using this algebraic expression as follows,
For Machine #1:
y = 100 and s = 2
x = 100 ( 6 )
x = 600
Machine #2:
y = 80 and s = 0.5
x = 80 ( 8 - 0.5 )
x = 80 ( 7.5 )
x = 600
Hence, both machines are equally productive in an eight hour work day.
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If Zb= 85° and Ze = 115°, then Zc is
Answer:
∠ c = 30°
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ e is an exterior angle of the triangle , then
∠ b + ∠ c = ∠ e , that is
85° + ∠ c = 115° ( subtract 85° from both sides )
∠ c = 30°
What is the y -coordinate of the y -intercept of the line?
The y-intercept of the equation of a line in general form is:(0, -c/b) or -c/b
The y-intercept is the point where the graph intersects the y-axis. To graph, any function that is of the form y = f(x) finding the intercepts is really important. There are two types of intercepts that a function can have. They are the x-intercept and the y-intercept. An intercept of a function is a point where the graph of the function cuts the axis.
The y-intercept of a function is a point where its graph would meet the y-axis. The x-coordinate of any point on the y-axis is 0 and we use this fact to derive the formula to find the y-intercept. i.e., the y-intercept of a function is of the form (0, y).
The equation of a straight line in general form is ax+by+c=0. For the y-intercept, we substitute x=0 and solve it for y.
a(0)+ by + c =0
by + c =0
y = - c/b
Thus, the y-intercept of the equation of a line in general form is:(0, -c/b) or -c/b
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A glide reflection includes both a reflection and a (rotation, translation).
Translation, rotations are not involved in a glide reflection.
How is a glide reflection created?
There is a mirror line in every reflection. A glide reflection is a mirror reflection that is followed by a parallel translation to the mirror. Every glide reflection has a translation distance and mirror line.
A glide reflection is made up of what two transformations?
A glide reflection is made up of a translation and a reflection in which the translation and the reflection are parallel to each other or the direction of the translation. A gliding reflection has opposite isometry and is -commutative.The translation of a glide reflection?
The composition of transformations is a glide reflection. In a glide reflection, the figure is first translated before being reflected over a line.
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Use the order of operations to simplify each expression.
5[(2+5) / ]
Simplification of the given expression 5[(2+5) /35 ] using the order of operation PEDMAS is equal to 1.
As given in the question,
Given expression is 5[(2+5) /35 ]
Simplify the given expression using the order of operation PEDMAS,
5[(2+5) /35 ]
= 5[ 7/35]
= 5 [ 1/5]
=1
Therefore, simplification of the given expression 5[(2+5) /35 ] using the order of operation PEDMAS is equal to 1.
The complete question is :
Use the order of operations to simplify each expression.
5[(2+5) /35 ]
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e function.
f(x)= -x²
Find f(-1)
Answer:
f(-1) = -1
Step-by-step explanation:
f(x) = -x^2
Let x = -1
f(-1) = - ( -1) ^2
= -1
Please Help if pQ = 6n QR=3 and PR=27 find n and PQ
Answer:
4
Step-by-step explanation:
PR - QR = PQ
27 - 3 = 24 =PQ
24=6n
n=4
A large western state consists of 4825 million acres of land. approximately 75% of this land is federally owned. find the number of acres that are not federally owned.
Answer:
1206.5 acres
Step-by-step explanation:
tatle acres=4825m
%of not federally owned =100%-75%=25%
[tex]( \frac{25}{100} ) \times 4825[/tex]
=1206.5 acres
What is y = -3x - 19 in Ax+By=C form?
The equation y = -3x - 19 (slope-intercept form) in Ax + By = C form is 3x + y = 19.
What is slope intercept form?The slope-intercept form of a linear equation is a way to express a linear equation in the form y = mx + b, where y represents the dependent variable, x represents the independent variable, m represents the slope of the line, and b represents the y-intercept.
According to the given information:
The given equation, y = -3x - 19, is already in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. However, to write it in the Ax + By = C form, also known as the standard form of a linear equation, we need to rearrange it.
The standard form of a linear equation is Ax + By = C, where A, B, and C are constants, and A is usually required to be a positive integer or zero.
To convert y = -3x - 19 into standard form, we can follow these steps:
Step 1: Move all the terms to one side of the equation.
y + 3x = -19
Step 2: Multiply all the terms by -1 to make the coefficient of x positive.
-1(y + 3x) = -1(-19)
-y - 3x = 19
Step 3: Rewrite the equation with positive coefficients for x and y.
3x + y = 19
So, the equation y = -3x - 19 in Ax + By = C form is 3x + y = 19.
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How are tables of values like pictorial representation? How are they different?
Answer: The difference is that the pictorial representation is usually used to visualize the pattern, whether the tabular form is an organized form of data used to show the relation between inputs and outputs (usually using numerical representation).
Step-by-step explanation:
Find the scale factor used to dilate quadrilateral LOVE, L (0,-7), O (5,-4), V (1,-5), E (3, -1) to L'O'V'E', L' (0, -21), O' (15, -12), V' (3, -15), E' (9,-3).
Answer:
7142213126 LOVE
Step-by-step explanation:
i dont no what i am doing this answer is wrong
If anyone could please answer the following questions!! (photo is below)
Answer:
Natural Numbers:
1 , 17 , 24.0
Whole Numbers:
0 , 1 , 17 , 24.0
Integers:
-775 , -54.3 , -12
Rational Numbers:
0.5 , 24.0 , 3/4 , 2 5/8
An ant carries food at a speed of 1 centimeter/second. How long will it take an ant to carry a cookie crumb a distance of 500 centimeters?
The total time taken by the ant to take cookie crumb from the kitchen table to an anthill is 83.33 minutes.
What is the linear system?
It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.
Given
An ant carries food at a speed of 1 cm/s.
The kitchen table to an anthill, a distance of 50 m.
We know the relation between speed and time.
Time=distance/speed.
Speed = 1 cm per second = 0.6 m per minute
Distance = 50 m
Then total time taken will be
=50/0.6
=83.33
Thus, the total time taken by the ant to take cookie crumb from the kitchen table to an anthill is 83.33 minutes.
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Find following measure.
m WX
When an angle exists encircled by a circle, its measure exists equivalent to the intercepted arc's measure divided by two.
The measure of m WX is 66.
What is meant by inscribed arc?The arc that is inside the inscribed angle and whose endpoints are on the angle is known as the intercepted arc. Anywhere on the circle that the sides of an inscribed angle intersect to produce an intercepted arc can serve as the angle's vertex.
Angles with vertices on a circle and that cross an arc on the circle are said to be inscribed angles. Half of the intercepted arc's length and half of the central angle's length intersecting that same arc make up the measure of an inscribed angle. Congruent inscribed angles are those that intersect the same arc.
According to the Inscribed Angle Theorem, an inscribed angle's measure is equal to half of its intercepted arc's measure. Congruent inscribed angles are those that intersect the same arc.
In the given diagram, XY is a semi-circle. So,
m XWY = 180
m WX + m WY = 180
If an angle is inscribed in a circle, then the measure of the angle equals one half the measure of its intercepted arc.
m WY = 2(m ∠X)
m WY = 2(m ∠X) = 114
Therefore, m WX = 180 - m WY = 66.
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Consider the given right triangle if A=20 and b =20 then
The points (8, 3) and (j, 5) fall on a line with a slope of -1/4. What is the value of j? help me ASAP
==================================================
Work Shown:
m = slope
m = (y2 - y1)/(x2 - x1)
m = (5 - 3)/(j - 8)
m = 2/(j - 8)
Plug in the given slope of -1/4 and solve for j
m = 2/(j - 8)
-1/4 = 2/(j - 8)
-1*(j-8) = 4*2
-j + 8 = 8
-j = 8-8
-j = 0
j = 0
The slope through (8,3) and (0,5) is -1/4
--------------
Check:
m = (y2 - y1)/(x2 - x1)
m = (5-3)/(0-8)
m = 2/(-8)
m = -1/4
The answer is confirmed.
Answer:
j = 0
Step-by-step explanation:
Slope-intercept form of a linear equation:
[tex]\large\boxed{y=mx+b}[/tex]
where:
m is the slope.b is the y-intercept.Given:
Slope = -¹/₄Point = (8, 3)Substitute the given slope and point into the formula and solve for b:
[tex]\begin{aligned}y & = mx+b\\\implies 3 & = -\dfrac{1}{4}(8)+b\\3 & = -2+b\\3+2&=-2+b+2\\5&=b\\\implies b & =5\end{aligned}[/tex]
Substitute the given slope and found value of b into the formula to create an equation for the line:
[tex]\boxed{y=-\dfrac{1}{4}x+5}[/tex]
Substitute the point (j, 5) into the equation and solve for j:
[tex]\begin{aligned}y&=-\dfrac{1}{4}x+5\\\implies 5&=-\dfrac{1}{4}j+5\\5-5&=-\dfrac{1}{4}j+5-5\\0&=-\dfrac{1}{4}j\\\implies j&=0\end{aligned}[/tex]
Solution
Therefore, the value of j is 0.
with what force will a car hit a tree if the car has a mass of 3,000 kg and an acceleration of 2 m/s2
Answer:
6000 Newtons
Step-by-step explanation:
just multiply 3000 by 2
The triangles are similar. Find the value of x.
First triangle:
Width: 3
Length: 17
Second triangle:
Width: x
Length: 102
Answer:
Step-by-step explanation:
I would say the width is 18 because the scale factor is 6
102/17= 6
3*6=18
Is 2 5/8 a rational number??
Answer:
2×5/8 which is 5/4 which is a rational number because denominator is not 0
Step-by-step explanation:
Hope it helps you
Answer:
yes it is
Step-by-step explanation:
rational numbers are numbers that can be expressed in the form of ratio. for example
[tex] \frac{85}{5} [/tex]
=
85:5
Determine whether each sequence is arithmetic, geometric, or neither. Then find the tenth term. -12,-5,2,9,16, . . . .
The sequence -12,-5,2,9,16, . . . .. is an arithmetic sequence and its 10th term is a(10) = 65
To determine whether a sequence is an arithmetic or geometric one, we need to check the relation between two consecutive terms.
In an arithmetic sequence, the nth term is obtained by adding the (n-1)th term with a constant, called a common difference (d).The given sequence is:
-12,-5,2,9,16, . . . .
In this sequence:
a(1) = -12
a(2) = -5
a(3) = 2
a(4) = 9
and so on.
Notice that:
a(2) - a(1) = -5 - (-12) = 7
a(3) - a(2) = 2 - (-5) = 7
a(4) - a(3) = 9 - 2 = 7
Since each consecutive terms have common difference, then, the given sequence is an arithmetic sequence. Furthermore, the common difference, d = 7.
The formula for the nth term in an arithmetic sequence is given by:
a(n) = a(1) + (n - 1) . d
Substitute n = 10, d = 7, and a(1) = -12
a(10) = -12 + (12 - 1) . 7
a(10) = -12 + 77 = 65
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Record remainder.
2.
44) 6,668
Steps
Answer:
24.
Step-by-step explanation:
44)6668(151
44
226
220
68
44
24 <-------- Remainder
The average sale price (online) for a certain brand of professional mountain bike is approximately normally distributed with a mean of $4,200 and a standard deviation of $250.
Find the 30th percentile of this distribution.
According to the question, for the average sale price the given parameters are mean as $4200 and standard deviation as $250.
As per normal distribution, the standard formula is as written below:
[tex]z = \frac{value - mean}{SD}[/tex]
And through normal distribution, the value of z = -0.52 which gives the area of the left bounded.
Now, substitute the values in the given expression, we get:
[tex]-0.52=\frac{x-4200}{250}[/tex]
Now the calculated value of 'x' = $4070.
To calculate the 30 percent of the mountain bike, the sale price will be $4068.90.
Therefore, the 30th percentile of the distribution is $4068.90.
What is normal distribution?
The normal distribution play a vital role in statistics. It measured the data which occurred very frequently and it is close to the mean value of the data. And it is of bell shaped.
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Write an explicit formula for each sequence. Then generate the first five terms. a₁ = 10, r=-1
The explicit formula for the nth term is a(n) = 10 . (-1)ⁿ⁻¹, while the first five terms are 10, -10, 10, -10, 10
In a geometric sequence, the next term is obtained by multiplying the previous term by a common ratio, usually denoted as r.
The general formula of the nth term of a geometric sequence is:
a(n) = a₁ . r^(n-1)
Here a₁ refers to the first term and r to the ratio.
In the problem, the given parameters are:
a₁ = 10, r = -1
Substitute these into the general formula, we get:
a(n) = 10 . (-1)ⁿ⁻¹
Notice that
(-1)ⁿ⁻¹ = -1 if n-1 is an odd number, or if n is an even number
(-1)ⁿ⁻¹ = 1 if n-1 is an even number, or if n is an odd number
Therefore, the first five terms are: 10, -10, 10, -10, 10
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