The relation between curl vector and rotations is v = wdj
What is curl vector?A vector field is a vector field's curl. The tendency of particles at point P to spin about the axis that faces the direction of the curl at P is measured by the curl of a vector field at P. If and only if its curl is zero, a vector field with a simply linked domain is considered conservative.
Let v represent the particle's velocity as a vector.
vector v=ui+vj+wk
curl v =
curl v = [tex]\left[\begin{array}{ccc}i&j&k\\d/dx&d/dy&d/dz\\u&v&w\end{array}\right][/tex]
= (dw/dy - dv/dz )i - (dw/dx - du/dz)j + (dv/dx - du/dy )k
Now by comparing with rotational matrix ,
We know that w = rotational matrix
[tex]w_{x}[/tex] = 1/2 (dw/dy - dv/dz )
[tex]w_{y}[/tex] = 1/2 (dw/dx - du/dz)
[tex]w_{z}[/tex] = 1/2 (dv/dx - du/dy )
w = [tex]w_{x} i +w_{y} j + w_{z} k[/tex]
w = 1/2[ (dw/dy - dv/dz )i + (dw/dx - du/dz)j + (dv/dx - du/dy )k]
w = 1/2 curl v , rotation = 1/2 curl v
let B be a rigid rotating about z axis
w = w.k
tangential speed =wk *di
v = wdj
curl of v= [tex]\left[\begin{array}{ccc}i&j&k\\d/dx&d/dy&d/dz\\0&w_{x} &0\end{array}\right][/tex]
v = wdj ,
The relation between curl vector and rotations is v = wdj
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100 points and will mark brainliest
Answer:
The x-intercept is 40, which represents the number of monthly payments needed to repay the loan.
Step-by-step explanation:
The x-axis can be represented as y = $0, and in this graph y represents remaining balance. So, the x-intercept represents when no more money needs to be paid back on the loan.
Suppose that sin(a) = 4/6 and cos(b) =1/5 define in the first quadrant, determine cos(a-b). (round to 4 decimal places)
The value of the cosine of the angle of (a - b) will be 0.80.
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
It is a function that repeats itself in a particular time interval.
Suppose that sin(a) = 4/6 and cos(b) = 1/5.
Then the value of 'a' is given as,
sin(a) = 4/6
sin(a) = 2/3
a = 41.81°
Then the value of 'b' is given as,
cos(b) = 1/5
b = 78.46°
Then the value of the cosine of the angle of (a - b) will be given as,
⇒ cos(41.81° - 78.46°)
⇒ cos(-36.65°)
⇒ cos 36.65°
⇒ 0.80
The value of the cosine of the angle of (a - b) will be 0.80.
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a coach took his team out for pizza after their last game. there were 14 players so they had to sit in smaller groups at different tables. six players sat at one table and got 4 small pizzas to share equally. the other 8 players sat at a different table and got 6 small pizzas to share equally. afterwards one of the players said it wasnt fair because some kids got more pizza do u agree?
Yes, it wasn't fair because some kids got more pizza.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
A coach took his team out for pizza after their last game.
There were 14 players, so they had to sit in smaller groups at different tables.
Six players sat at one table and got 4 small pizzas to share equally.
Each of them got = 4/6 = 0.67
The other 8 players sat at a different table and got 6 small pizzas to share equally.
Each of them got = 6/8 = 0.75
0.75 > 0.67
Therefore, some kids got more pizza.
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A line passes through the points (4, -1) and (2, 3). What is the slope of the line?
Answer:
-2
Step-by-step explanation:
We can find slope by using change in y over change in x, as shown:
3-(-1) = 4, and 2-4=-2, and 4/-2 = -2, so our answer is -2.
Please answer soon!!
Which angles are coterminal with 3л/2?
Select each correct answer.
A. 11л/2
B. -л/-2
C. -7л/-2
D. л/2
Answer:
A, C
Step-by-step explanation:
You want to know which answer choices are angles that are coterminal with 3π/2.
CoterminalAngles are coterminal when their terminal rays lie in the same position. In general, any angle will be coterminal with angles that are an integer multiple of 2π added to the original.
That is, an angle is coterminal with all angles that have the same value modulo 2π.
For the given angle and each of the answer choices, the attachment calculates the coefficient of π modulo 2. The ones that match the given angle are ...
A. 11π/2 mod 2π = 3π/2
C. -7π/-2 mod 2π = 3π/2
__
Additional comment
Both -π/-2 and π/2 match the angle π/2, which is not the same as 3π/2.
Of course, the minus signs in numerator and denominator cancel, so -7π/-2 is the same as 7π/2.
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2y+x=-15 and x=3y substitution method
Answer:x = -9, y = -3
Step-by-step explanation:
n baseball, each time a player attempts to hit the ball, it is recorded. The ratio of hits compared to total attempts is their batting average. Each player on the team wants to have the highest batting average to help their team the most. For the season so far, Jana has hit the ball 12 times out of 15 attempts. Tasha has hit the ball 9 times out of 10 attempts. Which player has a ratio that means they have a better batting average?
a. Tasha, because she has the lowest ratio since 0.9 > 0.8
b. Tasha, because she has the highest ratio since 27 over 30 is greater than 24 over 30
c. Jana, because she has the lowest ratio since 0.9 > 0.8
d. Jana, because she has the highest ratio since 27 over 30 is greater than 24 over 30
The player that has a ratio that means they have a better batting average is B. Tasha, because she has the highest ratio since 27 over 30 is greater than 24 over 30
How to illustrate the ratio?From the information Illustrated, the ratio of hits compared to total attempts is their batting average. Each player on the team wants to have the highest batting average to help their team the most.
For the season so far, Jana has hit the ball 12 times out of 15 attempts. This will be:
= 12/15
= 0.8
Tasha has hit the ball 9 times out of 10 attempts. This will be:
= 9/10
= 0.9
The player that has a ratio that means they have a better batting average is Tasha.
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Please help me on this.
Lines h and j are parallel and cut by transversal k. What is the measure of angle x ?
A. 109°
B. 119°
C. 161°
D. 171°
The value of angle x is 161 degree. So the option B is correct.
In the given question, lines h and j are parallel and cut by transversal k.
We have to find the measure of angle x and choose the correct option.
The diagram of the given question is given below:
From the given diagram using the corresponding angle theorem
x = y
As we know that the angle of straight line is 180 degree.
So x+19 = 180
Subtract 19 on both side, we get;
x = 161 degree
Hence, the value of angle x is 161 degree. So the option B is correct.
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I think of a number,take away 4 and multiply the result by 2.
The number that is thought in the form of expression will be 2x - 4.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Let the number be 'x'. Then the expression is given as,
⇒ (x - 4) × 2
Simplify the expression, then we have
⇒ (x - 4) × 2
⇒ 2x - 4
The number that is thought in the form of expression will be 2x - 4.
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0.0000000536 in scientific notation
Answer: 5.36 × [tex]10^{-8}[/tex]
Step-by-step explanation:
5.36 × [tex]10^{-8}[/tex]
In the following lever system, what is the clockwise torque? 40 N. 9m. 3m. 80 N.
Answer:
Counter Clockwise Torque = 360 Nm
Clockwise Torque = 240 Nm
Step-by-step explanation:
Write down the equation in slope intercept form if slope m=4 and y intercept is (0,-5). Do not leave spaces.
Answer:
y=4x-5
Step-by-step explanation:
y=mx+c
m=4
c = y-intercept = -5
y=4x-5
Solve equation:
0=2n+6n
Answer: 0=8n
Step-by-step explanation: Add 2n+6n = 8n, so 0=8n
Answer:
0
Step-by-step explanation:
0=2n+6n
add 2n + 6n =8n
0=8n
divide both sides by 8 and you get 0
I'm not sure though unless it's 0=8n
Tom wants to know whether a new chest of drawers will fit next to his bed. The chest of drawers would like to buy is 70 centimeters wide.He knows that the room is 86 inches wide. The bed is 67
inches wide. Will the chest fit next to bed?
Answer:
no
Step-by-step explanation:
Tom wants to know if a 70 cm chest will fit in the space left by a 67 in bed in a room 86 in wide.
Available spaceThe space available is 86 in -67 in = 19 in.
Space neededAn approximate conversion between cm and inches is that 10 cm corresponds to about 4 in. Then 70 cm will correspond to 7×4 = 28 inches, much too wide for a 19-inch space.
The chest will not fit next to the bed.
PLEASE I REALLY NEED HELP!!! 100 points if answer right
y=1/3x+4 is perpendicular to y=-3x-4,
y=2/5x-7 is perpendicular to y=-5/2x+7,
y=-5/2x+8 is perpendicular to y=2/5x+6,
y=-2x+6 is perpendicular to y=1/2x+3 and
y=7/5x-9 is perpendicular to y=-5/7x-11.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
We know that the product of slopes of perpendicular lines is -1.
mM=-1
m is slope of one line and M is the slope of perpendicular line.
M=-1/m
y=1/3x+4
The perpendicular line is y=-3x-4
y=2/5x-7
The perpendicular line is y=-5/2x+7
y=-5/2x+8
The perpendicular line is y=2/5x+6
y=-2x+6
The perpendicular line is y=1/2x+3
y=7/5x-9
The perpendicular line is y=-5/7x-11.
Hence, the lines with corresponding perpendicular lines are
y=1/3x+4---> y=-3x-4
y=2/5x-7-----> y=-5/2x+7
y=-5/2x+8----->y=2/5x+6
y=-2x+6---->y=1/2x+3
y=7/5x-9-----> y=-5/7x-11.
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Elena makes her favorite shade of purple paint by mixing 3 cups of blue paint, 1 1/2 cups of red paint, and 1/2 cup of white paint. Elena has 2/3 cup of white paint. How much purple paint can she make?
Elena can make 20/3 cups of purple paint
What is the unitary method?
The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
WE are given that Elena makes her favorite shade of purple paint by mixing 3 cups of blue paint, 1 1/2 cups of red paint, and 1/2 cup of white paint.
Since Elena has 2/3 cup of white paint. then;
1 1/2 cups of red paint (1 1/2=1.5)
1/2 cup of white paint (1/2=0.5)
Then the ratio is 3:1.5:0.5
Means every 0.5 cups of white paint Elena makes 5 cups of purple paint (3+1.5+0.5)
Let x the number of cups of purple paint
5/ 0.5 = x / (2/5)
x = 20/3 cups of purple paint
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What is the remainder when 7x^4+6x^3−9x^2−32x+95 is divided by x+1?
Only enter a number
The required quotient is given as [tex]7x^3-x^2-8x-24[/tex] and the remainder term is 119
In the question, it is asked to determine the quotient of the expression, [tex]\frac{\left[7x^4+6x^3-9x^2-32x+95\right]}{x+1}[/tex] .
What is synthetic division?It is a method for performing the division of polynomials, with little writing and lesser calculations than complex division.
Here,
When performing synthetic division of polynomials, the terms in the product that remain as fractions are referred to as the division's remainder, whereas the polynomial is referred to as the division's quotient.
[tex]= \frac{\left[7x^4+6x^3-9x^2-32x+95\right]}{x+1}\\=7x^3-x^2-8x-24+\frac{119}{x+1}[/tex]
Thus, the required quotient is given as [tex]7x^3-x^2-8x-24[/tex] and the remainder term is 119
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Shelby is walking through her favorite store and sees a shirt she likes being sold for $80.00. She then notices the store is having a 45% off sale on all items. Excited to purchase the shirt, she grabs it and goes to the cash register. As she’s taking out her wallet, she finds a coupon for 25% off (that is applied after the store’s sale). What is the final price of the shirt that Shelby pays after the two discounts?
a. $9.00
b. $33.00
c. $28.00
d. $52.00
first we go 45+25=70 so now 80-70=$10.00
Did you mess up one of the answer because I did it two ways and got 10.00?
PLS HELP!!!
Radical functions
Answer:
B
Step-by-step explanation:
Reverse the first and second elements of each ordered pair.
A TPN solution contains 8.25 % amino acids it. If the patient needs 75 grams of protein per day, how much of the TPN solution should the patient receive per day?
The patient should receive 909 mL of the TPN solution per day.
To determine the amount of the TPN solution the patient should receive per day, we need to use the following formula:
amount of TPN solution = (grams of protein needed / percentage of amino acids in TPN solution) × 100
In this case, we are given that the TPN solution contains 8.25% amino acids and that the patient needs 75 grams of protein per day. Substituting these values into the formula, we get:
amount of TPN solution = (75 / 8.25) × 100
amount of TPN solution = 9.09 × 100
amount of TPN solution = 909 mL
Therefore, the patient should receive 909 mL of the TPN solution per day.
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Khalid has 2 bags of cornmeal that each contain 25 servings. One serving is 3/4 cup. Khalid is making muffins that require 2.5 cups of cornmeal per batch. What is the maximum number of batches of muffins that Khalid can make using cornmeal?
Using ratios and proportions, he can make 15 batch of muffins from 2 bags of cornmeal
What are Ratios and ProportionsRatio is used for comparing two quantities of the same kind. The ratio formula for two numbers, a and b is expressed as a : b or a/b. When two or more ratios are equal, they are said to be in proportion. The concept of ratio and proportion is based on fractions.
Proportion refers to the equality of two ratios. Two equivalent ratios are always in proportion. Proportions are denoted by the symbol (: :) and they help us to solve for unknown quantities. In other words, proportion is an equation or statement that is used to depict that the two ratios or fractions are equivalent.
In this problem, we know that he has 2 bags of cornmeal
1 bag of cornmeal = 25 serving
2 bags = x
x = 2 * 25 = 50 servings
When making muffins, he needs 2.5 cups in a batch
But 3/4 cup = 1 serving
x cups = 50 serving
x = 50 * 3/4
x = 37.5 cups
1 batch = 2.5 cups
x batch = 37.5 cups
x = 37.5 / 2.5
x = 15 batch
He can make a 15 batches
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1. Shelby had $33.00. Then,
Now, she wants to spend all of her
money on some ice cream cones
that cost $3.00. How many ice
cream cones can she buy?
Answer:11 cones
Step-by-step explanation: She can by 11 since $3x 11 =$33
IMAGE ATTACHED PLEASE HELP PLEASE
Answer: first one
Step-by-step explanation: when u divide the equation to (x+2) and (x-1)
please help!!!!!!!!!!!!!!!!!!
Answer:
1x2=2 3x3x1=3
Step-by-step explanation:
PLEASE HELP 15 POINTS I'M GIVING BRAINLIEST!!!
Answer:
sec^2(a) - sin(a)
Step-by-step explanation:
Hope it helps!
Answer:
Step-by-step explanation:the answer is (sin2 A+cos2)/cos A
tan A+cot A =? =sin A/cos A + cosA/sinA. = (sin^2 A+cos^2 A)/cos A.
If n represents a power of 10, what is the value of n when 0.006 is rounded to the nearest power of 10?
Enter your answer in the box.
Answer:
The value of n is [tex]10^{-3}[/tex]
What is log function?
The logarithm (log) function is a mathematical function used to determine the logarithm of a number. The logarithm of a number is the exponent to which a particular base must be raised in order to produce that number. For example, the logarithm of 8 with base 2 is equal to 3 because 2 to the third power is 8. In mathematics, the logarithm of a number can be expressed as logbX, where b is the base and X is the number.
Step-by-step explanation:
We can write -
0.006 = 6 x 10^-3
10ⁿ = 6 x 10^-3
[tex]10^{n+3}[/tex] = 6
log([tex]10^{n+3}[/tex]) = log(6)
(n + 3) log 10 = log (6)
n +3 = log(6)/log(10)
n + 3 = 0.78
n = -3 + 0.78
n = -3 (approx.)
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Find −0.5D. with options [9 8] [-7 -4], [9 8] [14 8], [-18 -16] [7 4], [9 8] [7 4]
The evaluation of −0.5D of the matrix gives
[9 8]
[-7 -4]
How to determine -0.5D of the matrix?
A matrix (plural matrices) is a set of numbers arranged in rows and columns so as to form a rectangular array.
Given: the matrix
D = [-18 -16]
[14 8]
To find −0.5D, multiply every number in the matrix D by -−0.5. Thus:
−0.5D = −0.5 × [-18 -16]
[14 8]
−0.5D = [9 8]
[-7 -4]
Therefore, the 1st option is the answer
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My Truck Takes 50 Gallons of gas. I used 20⅔ gallons on Monday. 9¼ on Tuesday. And 2½ on Wednesday. How many Gallons of gas do i still have in my truck?
Answer:
17 7/12 gallons of gas.
Step-by-step explanation:
Set the fractions to like denominators. It'll make it a hell of a lot easier to add.
20 2/3rds = 20 8/12
9 1/4ths = 9 3/12
2 1/2 = 2 6/12
Adding those together gets you 31 17/12 which is 32 5/12 simplified.
Take that fraction and subtract it from your 50 gallons and it'll get you 17 7/12
COMMON IDENTITIES IN VECTOR ANALYSIS
How do i prove that .......... if F, G, and H are scalar fields?
The cross product or the curl of F, G, and H are zero so they are scaler fields.
What are dot products and cross products?The cosine of the angle between the vectors and their magnitude are combined to form the dot product.
The dot product is represented by A.B = ABCos θ.
The sine of the angle between the vectors and their magnitude are combined to form the cross-product.
The cross product is represented by A×B = ABSin θ.
Given, F × (G × H) = (F . H)G - H(F .G).
∴ F × (G × H) = (FHcosФG) - H(FGcosФ).
F × (G × H) = FGHcosФ - FGHcosФ.
F × (G × H) = 0.
We know that cross-product is the curl of a vector field and if the curl is zero it is a scalar field.
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