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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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The value of x is 18 if ∠C and ​ ∠D ​ are vertical angles. m∠C = 5x - 7 and m∠D = 8x – 55.

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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Where the voice rises and falls. But inflection also describes a departure from a normal or straight course.

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]

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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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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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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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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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).

The equation is written as 3x + x - 2 = 11(2). Then the value of the variable 'x' is 6.

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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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

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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We can tell that the investment results after 4 years will be $761 with the help of compound interest.

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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The natural oil that will be needed to make make 825 liters of Petrolyn oil is 300 liters.

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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The smallest to largest test values of the inequality (x-4)(x-5)<0 are  

(-infinity,4) , (4,5) & (5,+infinity)

What is a inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.

A difference between two values indicates whether one is smaller, larger, or simply not equal to the other.

"A connection is termed an inequality if two real numbers or algebraic expressions are connected by the symbols ">," "," "," or "."

(x-4)(x-5)<0

x-4<0             or             x-5<0

x<4                or              x<5

1)

for False the test values of the inequality (x-4)(x-5)<0  from smallest to largest Lies in between (-infinity,4)

2)

for True the  test values  of the inequality (x-4)(x-5)<0 from smallest to largest Lies in between (4,5)

3)

for True the  test values of the inequality (x-4)(x-5)<0  from smallest to largest Lies in between (5,+infinity)

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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.

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

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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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

Answer:

A (0, -3) translated to the right 4 units.

Step-by-step explanation:

If you go right 4, you get (4, -3)

Answer: 6

Step-by-step explanation: you can ask siri

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There are 3 extreme points does the function g(x) = (2 - x) x².

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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I'm here trying to help my 12 yr old

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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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

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.

To find the proportion in this problem we have to do the following procedure:

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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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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Answer:

a

Step-by-step explanation:

Answer:a

Step-by-step explanation: