What is calculas of variations?
Answer:
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Step-by-step explanation:
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The calculus of variations is a field of mathematics about solving optimization problems. This is done by minimizing and maximizing functionals. The methods of calculus of variations to solve optimization problems are very useful in mathematics, physics and engineering.
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Sum of 3x + 2 and 8x
Given m∠1≅m∠2
Proof m∠3≅m∠4
Complete the flow chart to proof m∠3≅m∠4
The flow chart to prove m∠3≅m∠4 is given below.
What is the vertical angle theorem?
The Vertical Angle Theorem states that when two straight lines cross, they create two linear pairs. Due to the fact that their angles add up to 180 degrees, the adjacent angles created when two lines intersect are known as supplementary angles.
Given, m∠1≅m∠2
Then, m∠1≅m∠3 ( vertical angles theorem)
m∠2≅m∠3 (Given)
Then, m∠2≅m∠4 (vertical angle theorem)
Hence, m∠3≅m∠4 (transitive property of congruence) proved
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Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 4 liters of natural oil for every 7 liters of synthetic oil. In order to make 825 liters of Petrolyn oil, how many liters of natural oil are needed?
The natural oil that will be needed to make make 825 liters of Petrolyn oil is 300 liters.
How to illustrate the ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
In this situation, Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 4 liters of natural oil for every 7 liters of synthetic oil. In order to make 825 liters of Petrolyn oil, the natural oil will be:
= 4 / (4+7) × 825
= 4 / 11 × 825
= 300
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Triangle congruence
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To allow last minute christmas shopping silverburn shopping centre is opening from 8am till midnight on Monday to Saturdays and 8am till 10pm on sundays. How many hours is it open in one week
Name the three types of triangles that deal with the measure of the sides
At what values of x does the graph of y=e−x+2xe−x+x2e−x have a point of inflection?
Where the voice rises and falls. But inflection also describes a departure from a normal or straight course.
What is inflection point and how to find an inflection point?
Inflection points for the given equation x^2e^{-2x} are
f'(x) =[tex]2x2xe^{(-2x)}-2{(x2)} e^{(-2x)}[/tex]
f'(x) =[tex]-2(x-1)xe {(^-2x)}[/tex]
The point of inflection, also known as the inflection point, is when the function's concavity changes. Changing the function from concave down to concave up, or vice versa, signifies that. In other words, an inflection point is the location at which the rate of slope shift from a growing to a decreasing way, or vice versa, occurs. There is no doubt that those positions are neither local maxima nor minima. They are fixed points.On a curve, an inflection point is when the concavity changes, according to definition. (i.e., a shift in the sign of curvature). We are aware that the function is concave up if f " > 0, and that it is concave down if f " 0. The point of inflection on a graph is where the function switches from positive to negative, or from negative to positive, at a particular value of x = c.x= -b±√(b^2 - 4ac)/2a
x=4±√(16+16)4
x=4±4√2/4
x=[tex]\sqrt{2+2/2}[/tex]
x=[tex]\sqrt{2-2/2}[/tex]
We get,
x=[tex]\sqrt{(2+2)/2^{2}*\sqrt{2+2}[/tex]
so, inflection points are,
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7.1.1 use the results of section 3.7 to show that each member of isom (r2) is either a translation or a rotation. 7.1.2 why does an isometry map any circle to a circle? we took care to write the inverse of the isometry r1r2r3 as r3r2r1 because only this ordering of terms will always give the correct result. 7.1.3 give an example of two reflections r1 and r2 such that r1r2
Every isometry can be expressed as composition of reflection and translation only. Also the composition of isometries is isometry. each member of ISOM+R² is either a translation or rotation.
Given that,
Show that each component of isom (r²) is either a translation or a rotation using the findings from section 3.7.
An isometry of R² is a mapping T:R²⇒R² which preserves distance.
The formula for the distance between x and y is
d(x,y)=|y-x|=√(y₂-x₂)²+(y₁-x₁)²
The preservice means,
d(x,y)=d(T(x),T(y))
A translation is an isometry.
Since,
d(Tv(x),Tv(y))=|(xv)-(y-v)|=d(x,y)
The rotation matrix, for rotating by an angle Θ, is defined as,
cosΘ -sinΘ
sinΘ cosΘ
Therefore, every isometry can be expressed as composition of reflection and translation only. Also the composition of isometries is isometry. each member of ISOM+R² is either a translation or rotation.
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Cameron invests money in a bank account
which gathers compound interest each year.
After 4 years there is $736.80 in the account.
After 7 years there is $788.82 in the account.
Work out the annual interest rate of the bank
account.
Give your answer as a percentage to 1 d.p.
The annual interest rate of the bank account is 2.3%
Let's check the equation for each year.
Compound Interest earned amount
A = P( 1 + r/n)ⁿˣ
A = accumulated amount
P = original amount deposited
r = interest rate
n = times it compounds per year
x = years
when Amount = $736.80, x = 4 years and r% → r/100
736.80 = P(1 +[(r/100)/1] ¹×⁴
736.80 = P(1 + r/100)⁴
when Amount =$788.82 , x = 7 years and r% → r/100
788.82 = P(1 +[(r/100)/1] ¹×⁷
788.82 = P(1 + r/100)⁷
using the 1st equation:
736.80 = P(1 + r/100)⁴
P = 736.80 /[(1 + r/100)⁴]
Substitute on the Using 2nd equation
788.82 = P(1 + r/100)⁷
788.82 = 736.80 /[(1 + r/100)⁴] * (1 + r/100)⁷
788.82 = 736.80 * [(1 + r/100)⁷/(1 + r/100)⁴]
788.82 = 736.80 * (1 + r/100)³
788.82/736.80 = (1 + r/100)³
∛788.82/736.80 = ∛ (1 + r/100)³
∛788.82/736.80 = (100 + r)/100
100 ∛788.82/736.80 = 100 + r
100 ∛788.82/736.80 - 100 = r
r ≈ 2.3%
Hence, the annual interest rate of the bank account is 2.3%
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25% of 24 is what number
Answer: 6
Step-by-step explanation: you can ask siri
if c is (5x-7) degrees and b is (8x-55) degrees what is the value of x
The value of x is 18 if ∠C and ∠D are vertical angles. m∠C = 5x - 7 and m∠D = 8x – 55.
What are vertically opposite angles?
It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.
It is given that:
∠C and ∠D are vertical angles.
From the definition of the vertically opposite angles:
5x-7 = 8x-55
After solving we get:
-7 = 3x -55
3x = 48
x = 16
Thus, the value of x is 18 if ∠C and ∠D are vertical angles. m∠C = 5x - 7 and m∠D = 8x – 55.
The complete question is:
∠C and ∠D are vertical angles. m∠C = 5x - 7 and m∠D = 8x – 55. What is m∠D ?
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A cable company offers its customers two plans.
- Plan A costs $135 per month plus $15 for each premium channel.
- Plan B uses the equation C=5 p+180 to determine the cost, where C represents the total cost and p represents the number of premium channels.
If a customer wants 5 premium channels, which statement comparing the cost of Plan A and Plan B is true?
A. Plan A will cost $5 less than Plan B.
B. Plan A will cost $10 less than Plan B.
C. Plan A will cost $5 more than Plan B.
D. Plan A will cost $10 more than Plan B.
After solving the equation we can say that Plan A will cost $10 more than Plan B. So, D is the Correct answer
What is an Equation?
A statement that affirms the equality of two expressions connected by the equals sign "=" is known as an equation.
For illustration, 2x - 5 = 13.
The two most well-known groups of equations in algebra are the linear
equations and the polynomial equations.
P(x) = 0 can be used to represent polynomial equations with a single variable. P is a polynomial, and axe + b = 0 is the standard form for linear equations.
Here, the parameters a and b. To solve these equations, we can use geometric or computational techniques from linear algebra or mathematical analysis. There are several sorts of equations
as well, including:
linear algebra quadratic formulas cube-based equations linear equations Equations that differ Statistical equations
Plan A:- $135 + $15(no. of premium channel)
Plan A for 5 premium channels will be
=$135 + $15(5)
= $135 + $75
=$210
Plan B:-
equation
C=$(5p+180)
p = no. of premium channel
Plan B for 5 premium channels will be equation
C = $25 + $180
= $205
Thus,
Plan A will cost $5 more than Plan B
As Plan A cost $210 and Plan B cost $205
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A force of 400 newtons stretches a spring 2 meters. A mass of 50 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 10 m/s. Find the equation of motion.
The equation of motion for the mass attached to the spring
x = x_0 + 10 m/s t + (1/2)(-4 m/s^2)t^2
What is the equation of motion?Generally, The equation of motion for a mass on a spring is given by Hooke's law, which states that the force exerted by a spring is proportional to its displacement from equilibrium. The proportionality constant is known as the spring constant, which is denoted by the letter k.
In this case, the force exerted by the spring is 400 newtons, and the displacement from equilibrium is 2 meters. Therefore, the spring constant is given by:
k = F/x = 400 N/2 m = 200 N/m
The equation of motion for a mass on a spring is given by:
F = ma = -kx
where F is the force exerted by the spring, m is the mass of the object, a is the acceleration of the object, and x is the displacement of the object from equilibrium.
Substituting the values for the spring constant and the mass, we get:
-kx = -(200 N/m)(50 kg)(x'')
Solving for the acceleration, we get:
x'' = -k/m = -200 N/m / 50 kg = -4 m/s^2
This is the equation of motion for the mass attached to the spring. The negative sign indicates that the acceleration is in the opposite direction of the displacement, as is expected for a mass on a spring.
Finally, to find the equation of motion, we need to take into account the initial velocity of the mass. The equation of motion for an object with initial velocity is given by:
x = x_0 + v_0t + (1/2)at^2
where x is the displacement of the object, x_0 is the initial displacement (in this case, the equilibrium position of the spring), v_0 is the initial velocity, t is time, and a is the acceleration.
Substituting the values for the acceleration and the initial velocity, we get:
x = x_0 + 10 m/s t + (1/2)(-4 m/s^2)t^2
This is the equation of motion for the mass attached to the spring. The initial displacement, x_0, is the equilibrium position of the spring, which is assumed to be at x=0 in this case.
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which ordered pair is the solution y=(1/3)x-4
To find the ordered pair that is the solution to the equation y = (1/3)x - 4, we need to solve the equation for x.
To do this, we can first add 4 to both sides of the equation to get y + 4 = (1/3)x. Then, we can multiply both sides of the equation by 3 to get 3y + 12 = x.
Therefore, the ordered pair that is the solution to the equation y = (1/3)x - 4 is (12, 3y).
Note that the value of y is unknown in this solution. In order to find the exact solution, we would need to know the value of y. For example, if y = 2, then the ordered pair that is the solution to the equation y = (1/3)x - 4 is (12, 6).
hi if someone wouldn’t mind doing this that would be great!!! 100 points im just desperate i need a whole bunch of stuff done tomorrow, thank you! :)
Answer:
1. y=2x−5
2. y=-x-4
3. y=-1/2x+1
Step-by-step explanation:
First Question:
We are given (3, 1) and (1, -3)
The slope is the difference of y-values over x-values. From this we get:
(1−−3)/(3−1)=4/2=2
Now, we want to find the y-intercept. To do this, we plug our slope and one of our points into the slope intercept equation: y=mx+b
Plugging in (3, 1) gives us 1=3∗2+b ⇒ b=1−6 = −5
We have our slope and y-intercept now, so the equation is y=2x−5.
Second Question:
We are given (-4, 0) and (1, -5)
The slope is
(-5-0)/(1--4)=-5/5=-1
Now, we want to find the y-intercept. To do this, we plug our slope and one of our points into the slope intercept equation: y=mx+b
Plugging in (-4, 0) gives us 0 = -1∗-4+b ⇒ b = -4
We have our slope and y-intercept now, so the equation is y=-x-4.
Third Question:
We are given (-6, 4) and (-2, 2)
The slope is
(4-2)/(-6--2)=2/48=-1/2
Now, we want to find the y-intercept. To do this, we plug our slope and one of our points into the slope intercept equation: y=mx+b
Plugging in (-2, 2) gives us 2 = -1/2∗-2+b ⇒ b = 2-1 = 1
We have our slope and y-intercept now, so the equation is y=-1/2x+1
Write a
system of equations with the solution (4, -3).
Answer:
A (0, -3) translated to the right 4 units.
Step-by-step explanation:
If you go right 4, you get (4, -3)
(-4)³·7⁰
_____ this a fraction!
(-1³)
Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
Based on the information in the fragment, it can be inferred that Josiah's mistake is that he did not multiply the numerator and denominator by the correct number to equal 1,500 (option B). So, the correct statements are A, C, and D.
How to find the ratio?To find the proportion in this problem we have to do the following procedure:
The first step is multiply both sides by 1500.The second step is to evaluate the expression on the right-hand side.The third step is multiply 10 by 1500 on the left-hand side.The fourth step is divide 15000 by 20 on the left-hand side.Once we have carried out the previous steps we must continue the procedure rewriting the equation with the data obtained previously. With this information we can conclude that Josian had the necessary information to discover how many songs of each genre were played during an hour on his MP3, however he performed the wrong procedure so his result was wrong.
According to the above, we can infer that the products are not well carried out. So, Josiah's mistake is no multiplying the numerator and denominator by the correct number to equal 1,500 (option B).
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23. For the data in the table, does y vary directly with x? If it does, write an equation for the direct (1 point) variation.
yes; y=2 x
yes; y=5 x
yes; y=7 x
no; y does not vary directly with x.
The ratio y/x is not constant (k) for all the data points, then y does not vary directly with x.
What is the constant of variation?
The constant of variation is the number that relates two variables that are directly proportional or inversely proportional to one another.
We have,
x y
2 10
4 24
6 36
To determine whether y varies directly with x, you need to see if the ratio of y to x is constant for all the data points.
If y varies directly with x, then the ratio y/x will be constant for all the data points. In this case, you can write an equation for the direct variation in the form y = kx, where k is the constant of variation, which is equal to the ratio y/x.
If the ratio y/x is not constant for all the data points, then y does not vary directly with x.
so, let's see the k constant of variation,
k = y/x
k = 2/10 =1/5
k = 4/24 = 1/6
k = 6/36 = 1/6
so, k = 1/5, k=1/6, k=1/6.
Hence, the ratio y/x is not constant (k) for all the data points, then y does not vary directly with x.
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Write a linear function f with f (0)
7 and f(3) = 1.
f(x) =
Answer:
f(x) = -2x +7
Step-by-step explanation:
The 2-point form of the equation for a line is suitable for this. For points (x1, y1) and (x2, y2), the equation is ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
For the given points (0, 7) and (3, 1), the equation is ...
y = (1 -7)/(3 -0)(x -0) +7
y = -6/3x +7 . . . . . . . . simplify.
We can use f(x) for y to get ...
f(x) = -2x +7
Anybody good at statistics that’s can help outside of here?
I'm here trying to help my 12 yr old
an exploring ship is pulling up a diver at the rate of 25 feet per minute. The diver is currently 100 feet below the sea level. How deep was the diver 15 minutes ago?
Solve one eighth times quantity x plus 32 end quantity equals negative 7.
HURRY 100 PTS
x = 56
x = 7
x = −88
x = −24
The solution of the expression will be;
⇒ x = - 88
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
'' one eighth times quantity x plus 32 end quantity equals negative 7.''
Now,
Since, The algebraic expression is,
'' one eighth times quantity x plus 32 end quantity equals negative 7.''
Hence, We can formulate;
⇒ 1/8 (x + 32) = - 7
⇒ x + 32 = - 56
⇒ x = - 56 - 32
⇒ x = - 88
Thus, The solution of the expression will be;
⇒ x = - 88
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the perimeters of the square and the rectangle below are the same. Write and solve an equation to find the value of x area= 121inches squared the rectangle is 3x and x-2
the area of the square is 121 in. Squared.
The equation is written as 3x + x - 2 = 11(2). Then the value of the variable 'x' is 6.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The borders of the square and the square shape underneath are something similar.
Perimeter of the square = Perimeter of the rectangle
4a = 2(L + W)
2a = L + W
If the area of the square is 121 square inches. Then the side length of the square is given as,
a² = 121
a = 11 inches
And the dimension of the rectangle is 3x and x - 2. Then the equation is given as,
3x + x - 2 = 11 (2)
4x - 2 = 22
4x = 24
x = 6
The equation is written as 3x + x - 2 = 11(2). Then the value of the variable 'x' is 6.
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If g'(x) = (2-x)x² So how many extreme points does the function g(x) has?
There are 3 extreme points does the function g(x) = (2 - x) x².
What is Function?A relation between a set of inputs having one output each is called a function.
Given that;
The function is,
⇒ g ' (x) = (2 - x) x²
Now,
Since, The function is,
⇒ g ' (x) = (2 - x) x²
We know that;
The extreme points are find as;
⇒ g ' (x) = 0
So, We get;
⇒ g ' (x) = 0
⇒ (x - 2) x² = 0
This gives two values as;
⇒ (x - 2) = 0
⇒ x = 2
And, x² = 0
⇒ x = 0, 0
Thus, The extremes values are;
⇒ x = 2 , 0, 0
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[tex]-16x^{\frac{-3}{2}[/tex]
The expression -16x^(-3/2) represents a term that has a coefficient of -16 and a variable x raised to the power of -3/2.
What is an expression?Generally, The expression -16x^(-3/2) represents a term that consists of a coefficient of -16 and the variable x raised to the power of -3/2.
In general, the exponentiation operator (^) represents the idea of raising a number (called the base) to a certain power (called the exponent). For example, x^2 means "x raised to the power of 2" and can be calculated as x * x = x^2.
Similarly, x^3 means "x raised to the power of 3" and can be calculated as x * x * x = x^3.
The exponent -3/2 means that the base (in this case, x) is raised to the power of -3/2. This can be simplified as follows:
x^(-3/2) = 1 / x^(3/2) = 1 / (x^(3/2))
The expression -16x^(-3/2) can then be simplified as follows:
-16x^(-3/2) = -16 * 1 / x^(3/2) = -16 / x^(3/2)
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The complete Question was not found
Find the amount that results from the given investment.
$600 invested at 6% compounded quarterly after a period of 4 years
After 4 years, the investment results in $.
(Round to the nearest cent as needed.)
We can tell that the investment results after 4 years will be $761 with the help of compound interest.
What is compounding?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it so that interest is generated the next period on the principal amount plus any accumulated interest.
In finance and economics, compound interest is common.
So, we have an initial investment of %600.
And the interest is 6% which will be compounded quarterly for 4 years.
Then the amount we will receive after 4 years is:
(Refer to the table attached below)
So, the amount we will get after 4 years is $761.39.
Rounding off: $761
Therefore, we can tell that the investment results after 4 years will be $761 with the help of compound interest.
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Organize the angles from largest to smallest.
GIVING BRAINLIEST!!!
What fraction is shown on the number line?
A. 2 over 3
B. 1 over 3
C. 2 over 4
D. 3 over 4
Answer:
a
Step-by-step explanation:
Answer:a
Step-by-step explanation: