The line integral along the boundary of the triangle C is 32/15.
To apply Green's , we need to find the curl of the vector field F:
∂F₂/∂x - ∂F₁/∂y = (2xy³) - (y)
The boundary of the triangle C, which consists of three-line segments:
C₁: From (0,0) to (1,0)
C₂: From (1,0) to (1,2)
C₃: From (1,2) to (0,0)
Using the parametric equations for each line segment, we can express the line integral as:
∫C F · dr = ∫∫R (∂F₂/∂x - ∂F₁/∂y) dA
R is the region enclosed by C.
Since R is a triangle with vertices (0,0), (1,0), and (1,2), we can use a double integral to compute the area of R:
∫∫R dA = [tex]\int_0^1 \int_0^{y_2} dx dy[/tex] = 1/2
Now we can apply Green's Theorem:
∫C F · dr = ∫∫R (∂F₂/∂x - ∂F₁/∂y) dA
= ∫∫R (2xy³ - y) dA
= [tex]\int_0^1 \int_0^{y_2} (2xy^3 - y) dx dy[/tex]
= [tex]\int_0^2 (4/5)y^5 - (1/2)y^2 dy[/tex]
= 32/15
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Determine whether the triangles are similar. If so, write a similarity statement and name the postulate or theorem you used
Answer:
I can't comment, but we can't see what we are supposwd to bw doing
a/a+b is the same as
a/a+b is the same as a/(a+b). This is because the division of two numbers is represented by the symbol '/', and when a and b are being divided, it is written as a/b.
In this case, a and b are being divided by a+b, so it is written as a/(a+b). This is known as a fraction, which represents a ratio of two numbers. This fraction represents the proportion of a to the total of a+b. The numerator (a) represents the part of the total that you are interested in, and the denominator (a+b) represents the entire quantity.
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find the measures of thr angles of a right triangle where one of the two acute angles measurres 8 times the other
The two angle of the right triangle are found as 30 degrees and 60 degrees.
Define the term acute angles?Less than 90 degrees is considered an acute angle. Right angles have a 90 degree angle. More than 90 degrees is found in obtuse angles.
Let one acute angle be 'x'.Then, the other actue angle will be '2x'One of the angle of right angles triangle is 90 degress.By using angle sum property of right angle triangle:
x + 2x + 90 = 180
3x = 90
x = 30 (one angle)
2x = 60 (Other angle)
Thus, the two acute angle of the right triangle are found as 30 degrees and 60 degrees.
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Hello! I need help solving this problem #2
Solving the provided questions, we can say that the exponential growth for the provided data will be 11.
What is exponential growth?The process of quantity growth over time is called exponential growth. occurs when the rate at which a quantity changes instantaneously with time is proportionate to the quantity itself. A data pattern that shows bigger increases with time is known as exponential growth. Compound interest yields exponential rewards in the world of finance. Savings accounts with compound interest sometimes see exponential growth. characterized by an extremely fast exponential growth rate rise (in size or extent). exponentially. The exponential function has the formula f(x)=abx where a and b are positive real values. Sketch exponential functions using the app below for different values of a and b. Describe verbally how modifying a and b changes the graph's form.
the growth rate will be
n(3) = [tex]85e^{0.l8(3)}[/tex]
n(3) = 145.86
[tex]85e^{0.l8(t)} = 600\\e^{0.l8(t)} = 7.059\\ln[e^{0.l8(t)}] = ln[7.059]\\0.18(t) = ln[7.059]\\\\t = 10.86 = 11[/tex]
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4. Find the equation of opened downward parabola which contains the points (0,5), (2,5), and (-2,-5).
Equation of opened downward parabola is (x - 1) ²= - 4/5 (y - 25/4)
What is parabola?Parabola is a curve created by the intersection of a cone and a plane. Generally, parabola is U shaped and either open in downward or opened in upward direction.
What will be the equation of opened downward parabola contains the points given in question?
The formula for opened downward parabola is given by (x - h) ² = - 4p (y - k)
as the parabola contains the points (0, 5) (2, 5) and (- 2, -5)
so, the equation can be (0 -h) ² = - 4p(5 - k) [ put the value (0, 5)]
h² = - 20p+4pk ..... equation 1
while putting the value (2, 5) we have the equation of parabola.
(2 - h) ² = - 4p(5 - k)
4 - 4h + h ² = - 20p + 4pk .... equation 2
from the equation 1 and 2, the right-hand side is similar.
hence, 4 - 4h +h² = h²
4 = 4h
h = 1
put h =1 in the equation 1 we get, 1 = - 20p + 4pk .... equation 3
when we put the value ( -2, -5) in the formula.
(- 2- h) ² = - 4p ( -5 -k)
( -2 -1) ² = 20p +4pk
9 = 20p +4pk ....... equation 4
from equation 4 and equation 3
we get, 9 = 20p +4pk
1 = - 20p+ 4pk
- + -
solve by addition method and we get, 8 = 40p
p = 1/5
from h = 1 and p = 1/5 we get the value of k from equation 3
1 = - 20/5 + 4/5k
k = 25/4
now the equation of opened downward parabola will be.
(x - 1) ² = - 4/5 (y - 25/4)
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The equations equivalent to 2.3p – 10.1 = 6.5p – 4 – 0.01p are;
2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – pThe correct answer is option B and C
How to determine equivalent equation?2.3p – 10.1 = 6.5p – 4 – 0.01p
collect like terms
2.3p - 6.5p + 0.01p = -4 + 10.1
-4.19p = 6.1
p = 6.1/-4.19
p = -1.46
2.3p – 10.1 = 6.5p – 4 – 0.01p
= 2.3p – 10.1 = 6.49p – 4
Given options:
2.3p – 10.1 = 6.4p – 4
False
2.3p – 10.1 = 6.49p – 4
True
230p – 1010 = 650p – 400 – p
divide through by 100
= 2.3p – 10.1 = 6.5p – 4 – 0.01p
True
23p – 101 = 65p – 40 – p
False
2.3p – 14.1 = 6.4p – 4
False
Therefore, 2.3p – 10.1 = 6.49p – 4; 230p – 1010 = 650p – 400 – p are equivalent to 2.3p – 10.1 = 6.5p – 4 – 0.01p.
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What is the area of 8 cm triangle?
The area of a (equilateral) triangle with side 8cm is 16√3cm^2.
What is a triangle and its types?
A figure which has a three-sided closed figure is called a triangle.
Types
Equilateral Triangle
A triangle where all the sides are the same is called an equilateral triangle.
Isosceles Triangle
When two of the sides of a triangle are the same it’s called an isosceles triangle. It’s a hard one to spell, but an easy one to recognize!
Scalene Triangle
In our last triangle, none of the sides have the same length, so this is called a scalene triangle.
Acute Triangle
when the largest angle in the triangle is less than 90, that is an acute triangle. Just remember that acute angles are less than 90 degrees.
Right Triangle
When the largest angle is exactly 90 degrees. You might remember that a 90-degree angle is a right angle, so this triangle is a right triangle.
Obtuse Triangle
When largest angle is more than 90 degrees, this is an obtuse angle, so we call this triangle an obtuse triangle.
Area of an equilateral triangle whose side is 8 cm is √3/4*a^2 where
a=8
= √3/4*8^2
= √3/4*64
= √3*16
Area=16√3
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Is this proportional or nonproportional please tell me asap with right answer please
Answer:
Its proportional
Step-by-step explanation:
Answer:
Proportional
Step-by-step explanation:
36/3 = 12
60/5 = 12
96/8 = 12
Who first used geometry?
Because he invented geometry, Euclid, a renowned mathematician, is frequently referred to as the father of geometry.
Constructions using a compass and a straightedge were a focus of classical geometry. Euclid, who brought mathematical rigour and the axiomatic technique still in use today, transformed geometry. Up until the middle of the 20th century, all educated people in the West were familiar with his book, The Elements, which is usually regarded as the most important textbook of all time.
Current geometric notions have undergone a high level of abstraction and complexity as well as calculus and abstract algebra techniques, resulting in several modern sections of the science that are hardly recognizably descended from early geometry.
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exact solution:
y =?
m=?
n =?
W=?
Approximate Solution
y =?
m =?
n?
W=?
Exact solution are - 1.2, -1, -0.1, 0.75 and approximate solution are -0.012, -0.01, -0.001, 0.0075.
What is exact and approximate solution?
The solution that has no uncertainly is known as exact solution. On the other hand, the solution that has some confusion is termed as approximate solution.
What are the exact and approximate solution of the given problem?
exact solution, y = - 1.2
m = - 1
n= - 0.1
w = 0.75
approximate solution in nearest hundredth,
y = - 0.012
m = -0.01
n = - 0.001
w = 0.0075
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Create two different explicit equations that describe the values in the table. Use a different point in the table for each of the equations you create. Choose one of the equations you created to produce an equivalent form that reveals the y intercept of the function within the equation.
Answer:
Step-by-step explanation:
if x were starting at 0, we would have
y = (x - 7)×7 = 7x - 49
but we start at x = 57. We need adjust for these extra 57 to get the above equation.
so, it
y = (x - 57 - 7)×7 = (x - 64)×7 = 7x - 448
so, for
y = (x - 64)×7
I choose x = 57
y = (57 - 64)×6 = -7×7 = -49
for
y = 7x - 448
I choose x = 58
y = 7×58 - 448 = 406 - 448 = -42
from this form we get the y-intercept (the y- value when x = 0) : -448
6(2+4)negative 1 dived by 2•3+1
Answer:
First you do what is in the parentheses.
2+4= 6
The equation is now:
6(6) -1 / 2 *3 + 1 =
Then you do the division:
-1 / 2 = -0.5
6(6) (-0.5) * 3 + 1 =
3 + 1 = 4
-0.5 * 4 = -2
The equation is now:
6 * 6 * -2
6 * 6 = 36
36 * -2 = -72
How do you find C?? Thank you!
The value of c would be 4.
What are similar triangles?
Similar triangles are triangles that have the same shape, but not necessarily the same size. In other words, the angles of similar triangles are congruent (congruent means the angles are equal in measure) and the corresponding sides are in proportion.
In the given figure, ΔGHF and ΔGDE,
∠G ≅ ∠G ---- Common angle
Side GH ≅ Side GH ---- Corresponding side
∠F ≅ ∠E -----Each 90°
so ΔGHF ~ ΔGDE-----ASA Test
sides of similar triangles are in proportion
GH/HF = GD/DE
5/c=10/8
c=5*8/10
c = 4
Hence, the value of c would be 4.
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Is 1 a polynomial or not?
Yes, 1 is a monomial, a unique type of polynomial.
You must first understand what a word is. A term is a real number multiplied by one or more variables, each of which has been raised to a power. Remember that a constant might appear in a phrase when a variable is multiplied by itself to the power of 0. (which is 1). A polynomial is just the sum of one or more terms that meet the criteria listed below:
1] There are no variables to split the words into.
The variables' exponents are whole numbers, e.g. 0, 1, 2, 3, etc.
Thus, 1 is just 1*(x0).
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Circumference question #1 if you are good at this I’ll be posting each question! 10 points per question
Convert 100 in. to yards, feet, and inches.
?1 yd. 1 ft. 4 in.
?4 yd. 2 ft. 2 in.
?4 yd. 0 ft. 4 in.
?2 yd. 2 ft. 4 in.
The measure of 100 inches is given by the equations ,
100 inches = 2.77778 yards
100 inches = 8.33334 feet
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = 100 inches be equation (1)
Now , the measure of 1 inch = 0.08333 feet
So , the measure of 100 inches = 100 x measure of 1 inch
Substituting the values in the equation , we get
The measure of 100 inches = 8.33334 feet
And , 1 inch = 0.0277778 yard
So , the measure of 100 inches = 2.77778 yards
Hence , the measure of 100 inches is 8.33334 feet
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Travis, Devon, and Ramon have 17, 20, and 26 trading cards, respectively. Every minute, one of the three boys gives away two of his trading cards such that the other two boys get one trading card each. What is the shortest amount of time, in minutes, that it could take for the three boys to each have an equal number of trading cards?
We can start solving this problem by using the concept of greatest common divisor (GCD). The GCD of 17, 20, and 26 is 1, which means that the three numbers are relatively prime to each other. This means that there is no common divisor of the three numbers other than 1.
Since the trading cards are given away in pairs, we need to divide the GCD by 2, which gives us 0.5. This means that it would take half a minute for the three boys to each have an equal number of trading cards.
However, half a minute is not possible as time cannot be measured in fractions of a minute. Therefore, it is not possible for the three boys to have an equal number of trading cards in the shortest amount of time, because the numbers are relatively prime.
Answer: 5 minutes. ✅
PLEASEEEE GIVE BRANLIEST
NEED HELP WITH BOTH. I WILL GIVE BRAINLIST
Find the missing length
Answer
2 =1
3=1.4
Step-by-step explanation:
hb=2A
b=2·5
10=1
hb=2A
b=2·14
20=1.4
Step-by-step explanation:
2 .) Using Pythagorean Theorem,
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex]5^{2}+ 10^{2} = c^{2}[/tex]
[tex]25 + 100 = c^{2}[/tex]
[tex]125 = c^{2}[/tex]
[tex]\sqrt{125}= c[/tex]
[tex]11 . 18 = c[/tex]
3.) Using Pythagorean Theorem,
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex]a^{2} + 14^{2} = 20^{2}[/tex]
[tex]a^{2}= 20^{2}- 14^{2}[/tex]
[tex]a^{2} = 400 - 196\\a^{2} = 204[/tex]
[tex]a = \sqrt{204}[/tex]
[tex]a = 14.28[/tex]
In art class students are mixing black and white paint to make gray paint. Julian mixes 9 cups of black paint and 8 cups of white paint. Harper mixes 7 cups of black paint and 5 cups of white paint. Use Julian and Harper's percent of black paint to determine whose gray paint will be darker.
We calculate the percentage of black paint in each mix by dividing the amount of black paint by the total amount of paint and multiplying by 100. Julian's mix has a black paint percentage of 52.94% while Harper's mix has a black paint percentage of 58.33%. Therefore, Harper's gray paint will be darker.
Explanation:The first step to determine whose gray paint will be darker is to calculate the percentage of black paint each student has in their mix. To find this, one must know that the percentage is calculated by dividing the part (the quantity of black paint) by the whole (the total amount of paint) and then multiplying by 100.
Julian's percentage of black paint: (9 cups black / 17 total cups) * 100 = 52.94%
Harper's percentage of black paint: (7 cups black / 12 total cups) * 100 = 58.33%
Since the percentage of black paint correlates with the darkness of the gray paint, Harper's gray paint will be darker because it contains a higher percentage of black paint.
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What is the additive inverse of 2 /- 7?
The additive inverse of 2 /- 7 is -2 /+ 7.
An additive inverse is a number that when added to the number in question, the sum is equal to zero. This can be expressed by the formula x + (-x) = 0, where x is the number in question. In this case, x is 2 /- 7. So, when 2 /- 7 is added to its additive inverse, -2 /+ 7, the sum is 0. This can be expressed mathematically as 2 /- 7 + (-2 /+ 7) = 0. Calculating this equation, we get 2 /- 7 + (-2 /+ 7) = -2 /+ 7 + (-2 /+ 7) = -4 /+ 14 = 0. Therefore, the additive inverse of 2 /- 7 is -2 /+ 7.
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Without using a calculator, determine between which two integers the following surds lie (1)√5 (2) √1 (3)√107 (4)√3
Answer:
Step-by-step explanation:
The following data points represent the number of points scored in the last basketball game by each player on the Dragons basketball team.
7, 5,8,11,7,5,?
If the mean of the data set is 8 points, find the missing number of points
The missing number of points scored in the last basketball game is 13.
What is the meaning of the data set?
A data set is a grouping of data. A data set refers to one or more database tables in the case of tabular data, where each column of a table represents a specific variable and each row corresponds to a specific record of the data set in question.
Given that,
the number of points scored in the last basketball game by each player on the Dragons basketball team are 7, 5,8,11,7,5,?.
Assume that the missing point is x.
The sum of points is 7+5+8+11+7+5+x = 43 + x.
The number of points is 7.
The mean is the sum of points/number of points
= (43+x)/7
Given that the mean of the data set is 8 points.
Therefore,
(43+x)/7 = 8
Multiply both sides by 7:
43+x = 8×7
43 + x = 56
x = 56 - 43
x = 13
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48 decreased by Craig’s savings is 16. Use the variable c to represent Craig’s savings.
Craig's savings is c-48=16
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given:
Let craig's savings be c then we have c-48=16
c=64
Hence, craig's savings is 64
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Match each function formula with the corresponding transformation of the parent function y= - (x+ 2)^2
Answer:
Step-by-step explanation:
1-6
3-2
4-1
please help Im not sure what I'm doing
The function rules for each table are given as follows:
7. y = 5x - 2.
8. y = x³.
9. y = x³ + 1.
How to obtain the function rules?For item 7, when x increases by one, y is increased by 5, hence the function is a linear function with slope 5, as follows:
y = 5x + b
When x = 6, y = 28, hence the intercept b is given as follows:
28 = 5(6) + b
b = 28 - 30
b = -2.
Hence the function is:
y = 5x - 2.
For item 8, the each term is cubed, hence the function is given as follows:
y = x³.
For item 9, the function is one added to the function in the previous problem, hence:
y = x³ + 1.
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which angles are vertical angles ?
Answer:
<UVS and <WVX
Step-by-step explanation:
They are both supplementary to the same angle. (<SVW)
Otherwise, you could just see if they are across from each other.
natalia orders 5 chocolate chip cookies for every 2 sugar cookies.She needs 42 cookies in all. Chocolate chip cookies cost $1.50 each and sugar cookies cost $0.75 each. How much will natalie spend in all on her cookies?
Therefore , the solution of the given problem of unitary method comes out to be $54.
A unitary method is defined.A single or distinct unit variable is referred to as being "unitary". Therefore, the goal of this technique is to define values in favor of a finite unit. For instance, the unitary method can be used to calculate how many kilometers a car will travel on one litre of gas if it goes 44 on two.
Here,
Given :
In place of every two sugar cookies, Natalie orders five chocolate chip cookies.
In total, she needs 42 cookies. Each sugar cookie costs $0.75, while each chocolate chip cookie costs $1.50.
thus ,
total cost is : 30 * 1.50 + 0.75*12
=> 54
Therefore , the solution of the given problem of unitary method comes out to be $54.
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crying for help on this
For 16-19, graph each equation or inequality.
16. 2y – 4x < 8
17. -4y > -x + 12
18. | x + 3 |= y
19. |2x – 6| + 2 = y
The solution is the set of all points (x,y) that satisfy the inequalities:
y < 2x + 4, y < x/4 - 3, x + 3 = y, and 2x - 6 + 2 = y.
What is the graph of a function?
The graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of the function. In other words, it is a visual representation of the function's rule.
The graph of a function can take many different forms, depending on the function's rule. Linear functions, for example, will produce a straight line on the graph.
i) 2y - 4x < 8 can be solved by adding 4x to both sides and then dividing by 2, giving:
y < 2x + 4.
ii) -4y > -x + 12 can be solved by adding x to both sides and then dividing by -4, giving: y < x/4 - 3.
iii) | x + 3 | = y, you can split this into two cases:
i. x + 3 = y
ii. -(x + 3) = y
iv) |2x – 6| + 2 = y, you can split this into two cases:
i. 2x - 6 + 2 = y
ii. -(2x - 6) + 2 = y
We can use these equations to plot the graph on a coordinate plane.
Hence, the solution is the set of all points (x,y) that satisfy the inequalities:
y < 2x + 4, y < x/4 - 3, x + 3 = y, and 2x - 6 + 2 = y.
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-74f = -6,142 solve for f
Determining the cause of the problem, characterizing the problem, identifying, prioritizing, and choosing potential solutions, as well as putting the solution into action, all have values of 83 for f.
What is the value of f ?-74 f = -6,142 ⇒ f = -6,142 / -74 ⇒f = 83 .
One-step equations can be solved using any one of the following four methods: adding, subtracting, multiplying, or dividing. Both sides of an equation will stay equal if the same integer is added to both sides. A mathematical expression should be evaluated according to a rule known as the order of operations.
The PEMDAS acronym can help us recall the following in that order: parentheses, exponents, multiplication and division (left to right), addition and subtraction (from left to right). A balance scale is like an equation. The scale (or equation) will become out of balance if we add or subtract from one side. Mathematical equations must ALWAYS be balanced such that both sides are equal when the equation is completed.
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Identify a claim made by Sae and explain the reaoning underlying thi claim. Lit at leat two piece of upporting evidence from the paage, and briefly explain how they upport the claim you have identified in tak 1
As consumerism is wiping out American society, Sasse claims that young people have based their achievements and achievements on material goods.
He said parents influenced this by creating a population of young people who are empty in spirit and who will lead American society to grow without direction and positioning.
To support this claim, he provides details on how the country did not encouraged the children to have experiences, conquer and walk their paths, thereby resisting consumerism and presenting the rewards of hard work.
What is the central idea of the Vanishing American Adult?
Sasse tried to explore the causes of a generation that can't grow up in "The Vanishing American Adult" and offers a path for raising children to be active and engaged citizens.
He identifies core formative experiences that all young people should pursue: hard work to appreciate the benefits of labor, travel to understand deprivation and want, the power of reading, the importance of nurturing your body, and how parents can encourage them, and explains how they can be encouraged.
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