Let ⃗ =(6x2y+2y3+8x)⃗ +(2y2+216x)⃗
F→=(6x2y+2y3+8ex)i→+(2ey2+216x)j→. Consider the line integral of ⃗
F→ around the circle of radius a, ce
Answers
The line integral of F around the circle is:∮C F · dr = ∫(t=0 to 2π) [(6a^2 cos^2(t) sin(t) + 2a^3 sin^3(t) + 8a cos(t))(-a sin(t)) + (2a^2 sin^2(t) + 216a cos(t))(a cos(t))] dt.
To evaluate the line integral of the vector field F around the circle of radius a centered at the origin, we can use the parameterization of the circle and calculate the corresponding line integral.
The given vector field F is defined as F = (6x^2y + 2y^3 + 8x)i + (2y^2 + 216x)j.
We want to calculate the line integral of F around the circle of radius a centered at the origin. Let's parameterize the circle using polar coordinates as follows:
x = a cos(t)
y = a sin(t)
where t is the parameter that ranges from 0 to 2π.
Using this parameterization, we can express the vector field F in terms of t:
F(x, y) = F(a cos(t), a sin(t)) = (6a^2 cos^2(t) sin(t) + 2a^3 sin^3(t) + 8a cos(t))i + (2a^2 sin^2(t) + 216a cos(t))j.
Now, we can calculate the line integral of F around the circle by integrating F · dr along the parameter t:
∮C F · dr = ∫(a=0 to 2π) [F(a cos(t), a sin(t)) · (dx/dt)i + (dy/dt)j] dt.
Substituting the parameterization and differentiating with respect to t, we get:
dx/dt = -a sin(t)
dy/dt = a cos(t)
The line integral becomes:
∮C F · dr = ∫(t=0 to 2π) [(6a^2 cos^2(t) sin(t) + 2a^3 sin^3(t) + 8a cos(t))(-a sin(t)) + (2a^2 sin^2(t) + 216a cos(t))(a cos(t))] dt.
Simplifying the integrand and evaluating the integral over the given range of t will yield the value of the line integral.
In summary, to evaluate the line integral of the vector field F around the circle of radius a centered at the origin, we parameterize the circle using polar coordinates, express the vector field F in terms of the parameter t, differentiate the parameterization to obtain the differentials dx/dt and dy/dt, and then evaluate the line integral by integrating F · dr along the parameter t.
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Related Questions
Given z varies jointly as x and y, use the given values to find an equation that relates x, y, and z.
x = 3, y = 8, and z = 54
A) Z = 9/4xy
B) Z = 2.25xy
C) Z = 4/9 xy
D) Z = 36xy
Answers
Given that z varies jointly as x and y, we can find an equation that relates x, y, and z using the given values. Plugging in the values x = 3, y = 8, and z = 54 into the equation options, we find that option D) Z = 36xy is the equation that satisfies the given values.
When two variables, z and y, vary jointly with a third variable x, it means that their relationship can be represented by an equation of the form z = kxy, where k is a constant. To find the specific equation that relates x, y, and z, we can substitute the given values x = 3, y = 8, and z = 54 into the equation options.
Plugging these values into option A) Z = 9/4xy yields 9/4 * 3 * 8 = 54, which does not match the given value of z.
Plugging the values into option B) Z = 2.25xy gives 2.25 * 3 * 8 = 54, which matches the given value of z.
Plugging the values into option C) Z = 4/9xy results in 4/9 * 3 * 8 = 32/3, which does not match the given value of z.
Finally, plugging the values into option D) Z = 36xy gives 36 * 3 * 8 = 864, which does not match the given value of z.
Therefore, the equation that relates x, y, and z based on the given values is option B) Z = 2.25xy.
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Find the 21st term.
an=12+(n-1)6
Answers
The 21st term of the arithmetic formula aₙ = 12 + (n - 1) 6 is 132.
How to solve arithmetic progression?The arithmetic formula for arithmetic progression, can be calculated as follows;
aₙ = a + (n - 1)d
where
a = first termn = number of termsd = common differenceHence, let's find the 21 st term of the Arithmetic formula,
aₙ = 12 + (n - 1) 6
where
n = 21a₂₁ = 12 + (21 - 1) 6
a₂₁ = 12 + (20)6
a₂₁ = 12 + 120
a₂₁ = 132
Therefore, the 21st term is 132.
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A ball is thrown into the air at an initial velocity of 18 meters per second from an initial height of 10 meters. The equation that models the path of the ball is given by h=-4.9t^2+18t+10h When does the ball hit the ground?
Group of answer choices
4.9 seconds
4.15 seconds
1.8 seconds
10 seconds
Answers
Answer:
Step-by-step explanation:
This is your position equation:
There's a whole lot of information in that equation, but what we are concerned about right now is the height of the ball after t = 3 seconds. If this is the position of the ball at any time t, we will sub in 3 for t to find out where the ball is at 3 seconds.
which simplifies to
s(3) = -44.1 + 54 + 10 which is
s(3) = 19.9 meters
That's how high the ball is in the air at 3 seconds.
Write in point-slope form an equation of the line through the pair of points (4,0) and (8,7).
Answers
Answer:
y - 0 = -7/4(x - 4)
Step-by-step explanation:
Slope Formula: (y2 - y1) / (x2 - x1)
Point-Slope form Formula: y - y1 = slope(x -x1)
The slope of the points (4,0) and (8,7) is -7/4 plug in the numbers in the the point slope equation it will be y - 0 = -7/4(x - 4)
Answer: In point slope form, the equation would be:
(y-0) = 7/4 (x-4)
hope this helps :)
Step-by-step explanation:
Each student at college has a student ID number consisting for four digits (the first digit is non zero and digits can repeat) followed by four letters A, B, C, D, E, and F (letters cannot repeat). How many different student numbers are possible?
Answers
First, we count the number of ways we can arrange the digits. The first number has 9 possibilities:
\(1\text{ to 9,}\)the other digits have 10 possibilities each:
\(0\text{ to 10.}\)Therefore, the number of ways we can arrange the digits is:
\(9*10*10*10=9*10^3=9000.\)Now, for the letters, the order matters, therefore, we can use the permutation formula:
\(P(6,4)=\frac{6!}{(6-4)!}=360.\)Finally, the total possible number of IDs is:
\(9000*360=3240000.\)Answer: \(\begin{equation*} 3240000. \end{equation*}\)Directions: Find the complemen
ANGLE
EXAMPLE: 54°
1. 63°
2. 87°
3. 45°
4. 72°
5. 5°
Answers
Given:
The angles are:
Example \(54^\circ\)
1. \(63^\circ\)
2. \(87^\circ\)
3. \(45^\circ\)
4. \(72^\circ\)
5. \(5^\circ\)
To find:
The complimentary angle of the given angles.
Solution:
If two angles are complimentary, then their sum is 90 degrees.
Example: Let x be the complimentary angle of \(54^\circ\), then
\(x+54^\circ=90^\circ\)
\(x=90^\circ -54^\circ\)
\(x=36^\circ\)
Similarly,
1. The complimentary angle of \(63^\circ\) is:
\(90^\circ -63^\circ=27^\circ\)
2. The complimentary angle of \(87^\circ\) is:
\(90^\circ -87^\circ=3^\circ\)
3. The complimentary angle of \(45^\circ\) is:
\(90^\circ -45^\circ=45^\circ\)
4. The complimentary angle of \(72^\circ\) is:
\(90^\circ -72^\circ=18^\circ\)
5. The complimentary angle of \(5^\circ\) is:
\(90^\circ -5^\circ=85^\circ\)
Therefore, the complimentary angles of \(54^\circ, 63^\circ, 87^\circ, 45^\circ, 72^\circ, 5^\circ\) are \(36^\circ, 27^\circ, 3^\circ, 45^\circ, 18^\circ, 85^\circ\) respectively.
Which one of the following represents exponential growth?
A: y = (48000)(.05)^x
B: y = (48000)(.95)^x
C: y = 2400(.05)^x
D: y = (48000)(1.05)^x
Answers
describe how to solve any equation in the form a x plus b equals c for the variable x
Answers
To solve any equation in the form ax + b = c for the variable x, the following steps are used:
Isolate the term containing the variable x to one side of the equation. Do so by subtracting b from both sides of the equation to obtain:ax = c - b
Divide both sides of the equation by a. Doing so will leave x alone on one side of the equation, and the value of x on the other. To get this done, divide both sides by a.ax/a = (c - b)/a
Simplify by dividing out the coefficient. The equation can now be written as x = (c - b)/aThis is the method used to solve any equation in the form ax + b = c for the variable x.
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What is the solution to 4x-5(2x-1) <= 7(2x+3)
Answers
To raise funds, students chose to sell 300 t-shirts and 600 pens. To this end, they decided to make two types of batches:
Type A: 1 t-shirt and 1 ballpoint pen;
Type B: 2 t-shirts and 5 ballpoint pens
a) Formulate the LP problem that allows you to determine how many lots should be formed to obtain the maximum income from their sale, knowing that type A lot is sold at $8 and type B lot at $18.
b) Present the canonical form in a simplex table and interpret the basis presented in that table.
c) Given the previous paragraph, what type of batch will start to be formed? In what amount?
d) Determine the solution that responds to the objective of the problem, interpreting the bases that you build.
e) With this optimal solution, do you have t-shirts and ballpoint pens left over?
f) The Treasurer argued that the prices of the lots could be changed, with the type A lot sold at $4 and the type B lot at $20. All previous restrictions remain. What will now be the optimal solution?
Answers
The LP problem that allows us to determine how many lots should be formed to obtain the maximum income from their sale is Maximize the income Z = 8x + 18ySubject to the constraints:x + 2y ≤ 300 (number of t-shirts) y + 5y ≤ 600 (number of pens) where x and y denote the number of type A and type B batches sold, respectively.
The basis presented in this table are:x = 0y = 0c) The first batches that will be formed will be Type A batches. Since the amount of t-shirts is a limiting factor, we have to first use up the entire stock of t-shirts by selling Type A batches. The amount of t-shirts that can be sold in total using Type A batches is 300. Thus, we will form 300 Type A batches in the beginning.d) The solution that responds to the objective of the problem is as follows:From the simplex table above, we can interpret the bases as follows:
x = 0, y = 0x = 300,
y = 0Z = 8(300) + 18(0) = 2400
Hence, the maximum income obtained is $2400. The interpretation of the bases is that at the optimal solution, 300 Type A batches and 0 Type B batches will be sold.e) Since all the t-shirts are used up in the formation of Type A batches, there will be no t-shirts left over.
Also, the number of ballpoint pens used in forming the Type A batches is 300. Thus, there will be 300 ballpoint pens left over which will be used in the formation of the Type B batches.f) If we change the prices of the lots such that Type A lots are sold at $4 and Type B lots are sold at $20, then the new LP problem is as follows:Maximize the income
Z = 4x + 20y
x + 2y ≤ 300 (number of t-shirts) y + 5y ≤ 600 (number of pens)Using the simplex method, we get the following tableau: The optimal solution is at x = 150 and y = 75, and the maximum income obtained is $2250.
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Which is the following functions is graphed below?
Answers
Answer:
A.y=|x|+7
Step-by-step explanation:
The national executive of M.A.N is made up of 10 men and 4 women what is the ratio in its simplest form of men to women in the executive
Answers
Answer:
10 to 4
Step-by-step explanation:
If there are 10 men and 4 women and you want to go from men to women then yes the answer is 10 to 4
Answer: 5 to 2
Step-by-step explanation: divieven both by two
An easy way to simplify fractions
Answers
Determine the largest factor that is common between the two
Divide the numerator and denominator by the greatest common factor
Write down the reduced fraction
Example:
Reduce the fraction
Step 1:
Factors for 8 = 1, 2, 4, 8
Factors for 24 = 1, 2, 3, 4, 6, 8, 12, 24
Step 2:
The greatest common factor is 8
Step 3:
Divide both the numerator and denominator by 8
8 divided by 8 = 1
24 divided by 8 = 3
Step 4:
The answer is
More examples:
Find the value of x.
Answers
Answer:
x = 78
Step-by-step explanation:
180 - 60 - 42 = 78
Pardon me if i'm wrong :/
Question 10(Multiple Choice Worth 5 points)
(Identifying Functions LC)
The graph represents a relation where x represents the independent variable and y represents the dependent variable.
a graph with points plotted at negative 5 comma 1, at negative 2 comma 0, at negative 1 comma 3, at negative 1 comma negative 2, at 0 comma 2, and at 5 comma 1
Is the relation a function? Explain.
No, because for each input there is not exactly one output.
No, because for each output there is not exactly one input.
Yes, because for each input there is exactly one output.
Yes, because for each output there is exactly one input.
Answers
Is the relation a function:
No, because for each input there is not exactly one output.How to know if the relation is a functionTo determine if the relation is a function, we need to check if there is exactly one output for each input.
Looking at the given set of points, we see that there are two points with an x-coordinate of -1: (-1, 3) and (-1, -2).
This means that there are two outputs for the same input, so the relation is not a function.
Therefore, the correct answer is: "No, because for each input there is not exactly one output."
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which of the following will cause a movement along the demand curve for chicken, a normal good, resulting in an increase in the quantity demanded?
Answers
A change in the price of chicken, the good's own price, will cause a movement along the demand curve for chicken, a normal good, resulting in an increase in the quantity demanded.
The demand curve for chicken represents the relationship between the price of chicken and the quantity of chicken demanded by consumers. The law of demand states that there is an inverse relationship between the price of a good and the quantity demanded, holding all other factors constant. In other words, as the price of chicken decreases, the quantity demanded of chicken increases, and vice versa.
A movement along the demand curve for chicken occurs when there is a change in the price of chicken. When the price of chicken decreases, ceteris paribus, consumers are willing to purchase more chicken at the lower price, resulting in an increase in the quantity demanded along the demand curve. Conversely, when the price of chicken increases, consumers are willing to purchase less chicken at the higher price, resulting in a decrease in the quantity demanded along the demand curve.
Other factors that can shift the demand curve for chicken include changes in consumer income, the prices of substitute or complementary goods, and changes in consumer preferences. However, these factors cause a shift in the entire demand curve, rather than a movement along the curve.
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1 punto
4. Los miembros de una
asociación de productores
decidieron donar $5,000.00
cada uno para mejorar la
producción. Que
procedimiento permite
conocer la aportación total?
A) Dividir $5,000.00 entre la
cantidad de productores
B) Multiplicar la cantidad de
productores por $5,000.00
C) Sumar la cantidad de
productores más $5,000.00
О
D) Restar $5,000.00 a la cantidad de
productores
Answers
Answer:
Multiply the number of producers by $ 5,000.00
Question:
Members of a producer association
decided to donate $ 5,000.00 each to improve the production. Than
procedure allows know the total contribution?
A) Divide $ 5,000.00 between the
number of producers
B) Multiply the amount of producers for $ 5,000.00
C) Add the amount of producers plus $ 5,000.00
О
D) Subtract $ 5,000.00 from the amount of producers
Step-by-step explanation:
We are asked to find the total contribution
Each manufacture will contribute $5,000.00
We were not told the number of manufacturers that would be contributing the amount.
Total contribution = number of manufactures × $5000
The procedure that allows one to know the total contribution:
Multiply the number of producers by $ 5,000.00
Option has B stated 'amount' instead of 'number'. It may be a mistake
B) Multiply the amount of producers for $ 5,000.00
how many ways can you make a 5 digit password that can be any number (including zero) or letter (not case sensitive)? 916132832
Answers
These work out to 60,466,176 case insensitive combinations of letters.
There are 10 digits 0–9.
The are 26 letters in the modern alphabets.
However, you didn’t specify whether capital and lowercase letters count as the same letter or separate. In the former case, there are 26 letters, in the latter, there are 52.
There is also such a thing as lowercase numbers, but since they aren’t in common standard usage, I won’t count those.
You also didn’t specify that characters couldn’t be repeated, so I am going to assume that the same character can appear multiple times in a 5 character combination.
Also, since the combinations are an alphanumeric string of characters rather than a number, I will assume that leading zeroes are allowed.
So, there are either 36 (10 digits and 26 letters).
To find the number of combinations you multiply the number of possibilities for each character;
36 x 36 x 36 x 36 x 36
These work out to 60,466,176 case insensitive combinations of letters.
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We have two rational expressions: The first rational expression has (y² - 13y +36) in the numerator and (y² + 2y - 3) in the denominator. The second rational expression has (y²-y-12) in the numerator and(y²-2y+1) in the denominator .Simplify them
Answers
We are given two rational expressions: one with (y² - 13y + 36) in the numerator and (y² + 2y – 3) in the denominator, and the other with (y² - y – 12) in the numerator and (y² - 2y + 1) in the denominator. We need to simplify these rational expressions.
Simplifying the first rational expression:
The numerator of the first expression, y² - 13y + 36, can be factored as (y – 4)(y – 9).
The denominator, y² + 2y – 3, can be factored as (y + 3)(y – 1).
Therefore, the first rational expression simplifies to (y – 4)(y – 9) / (y + 3)(y – 1).
Simplifying the second rational expression:
The numerator of the second expression, y² - y – 12, can be factored as (y – 4)(y + 3).
The denominator, y² - 2y + 1, can be factored as (y – 1)(y – 1) or (y – 1)².
Therefore, the second rational expression simplifies to (y – 4)(y + 3) / (y – 1)².
By factoring the numerator and denominator of each rational expression, we obtain the simplified forms:
First rational expression: (y – 4)(y – 9) / (y + 3)(y – 1)
Second rational expression: (y – 4)(y + 3) / (y – 1)²
These simplified expressions are in their simplest form, with no common factors in the numerator and denominator that can be further canceled.
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Zeke ran 4 1/2 miles around the track. Each lap is 1/2 of a mile. How many laps did Zeke
run?
Answers
Answer:
Zeke ran 9 laps.
Step-by-step explanation:
Find the lateral surface area of the cylinder. Round your answer to the nearest tenth
Answers
Answer:
Step-by-step explanation:
\(A_L=2\pi rh\)
The slope between the points (4,2) and (1. p) is 4. Find p and write the
equation of the line that has these points in point slope form.
Hint
P-2
D-10
equation of the line: \y - y1) = m(- X1)
Y1
m-
X1
Answers
Answer:
\(slope = \frac{y_2 - y_1}{x_2-x_1}\\\\4 = \frac{p-2}{1-4} \\\\4 \times -3 = p -2\\\\-12 + 2 = p \\\\p = -10 \\\\Equation \ of \ line : \\\\(y -y_1) = m(x - x_1)\\\\y - 2= 4(x-4)\\\\y - 2 = 4x -16\\\\y = 4x -14\)
Hi there! The slope formula is:
\( \large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }\)
We know that the slope is 4 but we are missing the value of p. (Define m = slope)
What we have now are:
two ordered pairs (4,2) and (1,p)value of slope = 4We are going to substitute these values and solve the equation for p-term.
\( \large{4 = \frac{2 - p}{4 - 1} } \\ \large{4 = \frac{2 - p}{3} } \\ \large{4(3) = \frac{2 - p}{3} (3)} \\ \large{12 = 2 - p} \\ \large{p = 2 - 12 \longrightarrow \boxed{p = - 10}}\)
Hence, the value of p is -10.
Next, we have to write the equation of a line in point-slope form. The point-slope form is:
\( \large \boxed{y - y_1 = m(x - x_1)}\)
Define that (x1, y1) = ordered pairs
Since we have two given points, we can either use the first point or second point. Both work.
First Point
For our first ordered pairs (4,2), substitute x1 = 4 and y1 = 2 in the equation.
\( \large{y - 2 = 4(x - 4)}\)
Hence, the equation of a line in point-slope form as in (4,2) is y-2=4(x-4)
Second Point
For our second ordered pairs (1,p), we know that p = -10 from the equation that we solved. Therefore (1,p) = (1,-10). Substitute x1 = 1 and y1 = -10 in the equation.
\( \large{y - ( - 10) = 4(x - 1)} \\ \large{y + 10 = 4(x - 1)}\)
Hence, the equation of a line in point-slope form as in (1,-10) is y+10 = 4(x-1)
Answer
The value of p is -10 (p = -10)y - 2 = 4(x-4) —> use (4,2) to form an equation. y + 10 = 4(x-1) —> use (1,-10) to form an an equation.Both equations work for point-slope form.
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during a one-month promotional campaign, tiger films gave either a free dvd rental or a 12-serving box of microwave popcorn to new members. it cost the store $1 for each free rental and $2 for each box of popcorn. a total of 89 new members were signed up and the store's cost for the incentives was $135. how many of each incentive were given away?
Answers
By using system of equations, there are 43 free DVD rentals and 46 boxes of microwave popcorn were given away during the promotional campaign.
Let's use the following variables
x: the number of free DVD rentals given away
y: the number of boxes of microwave popcorn given away
We can set up a system of equations to represent the given information:
x + y = 89 (total number of new members signed up)
1x + 2y = 135 (total cost of the incentives)
We can solve for x or y in the first equation and substitute into the second equation
x = 89 - y
1(89 - y) + 2y = 135
89 - y + 2y = 135
y = 46
Substituting y = 46 into the first equation:
x + 46 = 89
x = 43
Therefore, 43 free DVD rentals and 46 boxes of microwave popcorn.
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What is the quotient of 6÷2/3
Answers
Answer:
Im pretty sure it's 9
Step-by-step explanation:
6 : (2/3) = 91 = 9
The distance to your cousin's house is 666 miles, and the distance to Chicago is 37 miles. If it took 18 hours to drive to your cousin's house. howlong would you estimate the drive to Chicago to take?
Answers
We know that it took 18 hours to drive 666 miles. If we divide the distance by the hours (666 miles)/(18 hours)
We find that 666/18= 37 miles per hour . which means we travel 37 miles each hour.
So, we can estimate that driving 37 miles it will take 1 hour (the distance to Chicago).
Answer:
666/18=37miles/hour
it would take 1 hour to drive 37 miles
If the roots of the equation x2-bx+c=0are two consecutive integers, then b2 - 4ac = O a 2 Ob none of the answers is correct Oc. 1 Od not enough information
Answers
We can conclude that b^2 - 4ac is a perfect square. Hence, the correct answer is (a) 2.
We can solve this problem by using the quadratic formula to find the roots of the equation x^2 - bx + c = 0.
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the roots are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, the roots are two consecutive integers, so we can write them as n and n+1, where n is an integer.
Substituting these values into the quadratic formula, we have:
n = (-b ± √(b^2 - 4ac)) / (2a)
n+1 = (-b ± √(b^2 - 4ac)) / (2a)
From these equations, we can see that the only way for the roots to be consecutive integers is if the discriminant (b^2 - 4ac) is a perfect square. This is because the discriminant must be non-negative for real roots, and if it is a perfect square, then taking its square root will give an integer value.
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2. Convert the complex numbers below to Trigonometric form, with the angle 8. Clearly write down what are the values of r and 0 (in radians)? (6 marks: 3 marks each) (a) √3+j (b) √-1/4+j^4 √3/2
Answers
We need to express them in the form r(cosθ + isinθ), where r is the magnitude or modulus of the complex number, and θ is the argument or angle in radians. Therefore, in trigonometric form, √(-1/4) + j^4 √3/2 = √7/2(cos(-π/3) + isin(-π/3)).
(a) √3 + j:
To find r, we calculate the magnitude using the formula: r = |√3 + j| = √(√3² + 1²) = √4 = 2.
To find θ, we calculate the angle using the formula: θ = arctan(b/a) = arctan(1/√3) ≈ π/6 radians.
Therefore, in trigonometric form, √3 + j = 2(cos(π/6) + isin(π/6)).
(b) √(-1/4) + j^4 √3/2:
To find r, we calculate the magnitude using the formula: r = |√(-1/4) + j^4 √3/2| = √((-1/4)² + (√3/2)²) = √(1/16 + 3/4) = √7/4 = √7/2.
To find θ, we calculate the angle using the formula: θ = arctan(b/a) = arctan((√3/2) / (√(-1/4))) = arctan(-√3/2) ≈ -π/3 radians.
Therefore, in trigonometric form, √(-1/4) + j^4 √3/2 = √7/2(cos(-π/3) + isin(-π/3)).
In the trigonometric form, the angle is given in radians.
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Help need in 29 minutes
Answers
Answer:
d)
c)
Step-by-step explanation:
any more help just ask :)
out of 500 people , 200 likes summer season only , 150 like winter only , if the number of people who donot like both , the seasons is twice the people who like both the season , find summer season winter season , at most one season with venn diagram
Answers
Answer:
250 people like the summer season, 200 people like the winter season, and 50 people like both seasons.
Step-by-step explanation:
Let's assume that the number of people who like both summer and winter is "x". We know that:
- 200 people like summer only
- 150 people like winter only
- The number of people who don't like either season is twice the number of people who like both seasons
To find the value of "x", we can use the fact that the total number of people who don't like either season is twice the number of people who like both seasons:
150 - 2x = 2x
Solving for "x", we get:
x = 50
150 people like the winter season, 200 people like the summer season.
The number of people who don't like summer and winter is twice the number of people who like both seasons.
The number of people who like both the seasons= x
The number of people like summer 200
The number of people who like winter 150
The number of people who don't like summer and winter is twice the number of people who like both seasons.
To find the value of x, we can use the equation:
150-x= 2x
150= 3x
x= 50
The number of people who like both seasons is 50
The number of people who don't like both seasons is 100
For more information:
brainly.com/question/31893545
Assume that A + T/G + C equals 0.5 in one strand of DNA. What is the ratio of these bases in the complementary strand?
Answers
The overall ratio of A + T/G + C in the complementary strand is 0.5.
This is because the bases A and T, and G and C, always pair together in DNA. Therefore, if one strand of DNA has a ratio of 0.5 for A + T/G + C, the complementary strand will also have the same ratio.
To further explain, let's look at the individual bases. If A + T = 0.5, this means that the ratio of A to T is 1:1. Similarly, if G + C = 0.5, this means that the ratio of G to C is also 1:1. Since A always pairs with T, and G always pairs with C, the complementary strand will also have a 1:1 ratio for these bases. Therefore, the overall ratio of A + T/G + C in the complementary strand will also be 0.5.
You can learn more about complementary DNA strands at: brainly.com/question/29776082
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