Trade in the Vedic Age led to

the rise of kingdoms because of the importance of controlling land and long-distance travel routes
the building of an extensive system of roads because of the difficult terrain
the creation of a large banking class because of the need to exchange different currencies
the development of a centralized government that controlled the economic decisions of its people

The solid with a semicircular base of radius "r" and cross sections perpendicular to the base and parallel to the diameter are squares is called a "right circular cylinder with a half-circle base".

The height of the cylinder is equal to the side length of the square cross sections, and the radius of the semicircular base is equal to "r". The volume of this solid can be calculated as follows:

V = (Pi * r^2 * h) / 2

where Pi is the mathematical constant pi (approx. equal to 3.14), r is the radius of the semicircular base, h is the height of the cylinder, and "/ 2" represents that the volume is half of a full cylinder with a complete circular base.

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The correct answer is C. 0.25 foot.

To find the depth of the mulch, we need to determine the volume of the circular mulch bed and divide it by the area. The volume of a cylinder can be calculated as:

V = πr^2h

where r is the radius and h is the height (or depth) of the cylinder.

For the circular mulch bed, the radius is 1.6 feet and we want to find the height (or depth), so we can set the volume equal to the volume of the mulch:

V = π * 1.6^2 * h

V = 2 cubic feet

Solving for h:

h = V / (π * r^2)

h = 2 / (π * 1.6^2)

Using the value of π = 3.14, we get:

h = 2 / (3.14 * 1.6^2)

h = 0.24 inches

Therefore, the depth of the mulch is approximately 0.24 inches to the nearest hundredth of an inch, which is the appropriate number of significant digits.

To convert inches to feet, divide the number of inches by 12:

0.24 inches / 12 inches/foot = 0.02 feet

Rounding to the nearest hundredth of a foot, we get 0.25 feet as the answer.

The value of the given radical expression [tex]\sqrt[5]{32,768}[/tex] will be 8.

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.

The radical expression is given below.

[tex]\rightarrow \sqrt[5]{32,768}[/tex]

The number 32,768 can be written as,

32,768 = 8 x 8 x 8 x 8 x 8

32,768 = 8⁵

Then the value of the expression is given as,

[tex]\rightarrow \sqrt[5]{32,768}\\\\\rightarrow \sqrt[5]{(8)^5}[/tex]

→ 8

The value of the given radical expression [tex]\sqrt[5]{32,768}[/tex] will be 8.

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The money after 8 quarters is $4,324,500.

The formula for an exponential function is f (x) = aˣ, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

Given the amount invested in the company = $5,000,000

interest loss in each quarter = 7%

the formula for exponential decay

y = a[tex](1 - r)^{t}[/tex]

here t = time in years

1 year = 4 quarter

8quater = 2 years

t = 2

r = rate = 7% = 0.07

a = $5,000,000

y = 5,000,000(1 - 0.07)²

y = $4,324,500

Hence the amount after 8 quarters is $4,324,500.

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Answer:

275.5

Step-by-step explanation:

In order to convert.

It is fairly simple, follow my directions and next time when you have a question similar to this you’ll know what to do!

1 kg = 2.2 lb. It is as simple as that!

So your question,

“ Convert 125 kilograms to pounds “

125x2.2 = 275 .

Our answer is very close to the verified one, so now you know how to convert kilograms to pounds!.

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56.69904625 kg in 125 lbs. Likewise the question how many pound in 125 kilogram has the answer of 275.577827731 lbs in 125 kg.

125 kg*2.2046226218 lbs/1kg = 275.577827731 lbs

The weight of 125 kilograms is equivalent to 275.577827731 pounds (125kg = 275.577827731lbs). It is simple to convert 125 kg to lb. Simply use our calculator above or the method to convert 125 kg to pounds. To convert 125 kg to pounds, multiply the kilogram mass by 2.2046226218. The formula for converting 125 kilograms to pounds is [lb] = 125 * 2.2046226218. Thus, 125 kilos is 275.577827731 pounds.

One pound is about equivalent to 0.45359237 kilos (kg). The pound to kilogram conversion is accomplished by multiplying the provided pound value by 0.45359237. In addition, one kilogram is about equal to 2.2046226218 pounds.

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Answer:

4q + 2

Step-by-step explanation:

4(q + 2) -6

4q + 8 -6

4q + 2

By Solving the given identity equation we get A = 32/5, B = 36/5, C = 1/10 and D = -7/2.

Given  (3x³ + 4x² - 6x)/(x² + 2x + 2)(x² - 1) = (Ax + B)/(x² + 2x + 2) + C/(x - 1) + D/(x + 1)

Taking LCM in RHS

(3x³ + 4x² - 6x)/(x² + 2x + 2)(x² - 1) = ((Ax + B)(x² - 1) + C(x² + 2x + 2)(x + 1)+ D(x² + 2x + 2)(x - 1))/(x² + 2x + 2)(x² - 1)

3x³ + 4x² - 6x = Ax³ - Ax+ Bx² - B + C(x³ + 3x² + 4x + 2)+ D(x³ + x² -2)

3x³ + 4x² - 6x = (A + C + D)x³ + (B + 3C + D)x² +(-A + 4C)x - B + 2C -2D

Comparing coefficients of RHS with LHS

So, A + C + D = 3     --(1)

B + 3C + D = 4       --(2)

- A + 4C = -6      --(3)

- B + 2C -2D = 0       --(4)

We have 4 variables and 4 equations. Solving them, we get

A = 32/5, B = 36/5, C = 1/10 and D = -7/2

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Answer:0.69

Step-by-step explanation:

Let z = e^(2x). Then your equation is

 z^2 +3z -28 = 0

 (z +7)(x -4) = 0

 z = -7 or 4

Taking the log of our definition of z, we have

 ln(z) = 2x

 x = ln(z)/2

So, the one real solution is

 x = ln(4)/2 = ln(√4)

 x = ln(2)

The decimal approximation is

 x ≈ 0.69

The complete solution of the given initial value problem  can be given by,

y(t) = [tex]\frac{7}{4} e^{3t} +\frac{7}{12} e^{-t} + -2te^{2t} -\frac{4}{3} e^{2t}[/tex]

A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable) dy/dx = f(x) Here “x” is an independent variable and “y” is a dependent variable. For example, dy/dx = 5x.

Therefore, the complete solution of the given  initial value problem  can be given by,

y(t) = [tex]\frac{7}{4} e^{3t} +\frac{7}{12} e^{-t} + -2te^{2t} -\frac{4}{3} e^{2t}[/tex]

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The full solution to the initial value problem can be provided by,

y(t) = 7/4e^3t + 7/12 e^ -t - 2e^2t- 4/3e^2t

A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable) dy/dx = f(x) Here “x” is an independent variable and “y” is a dependent variable. For example, dy/dx = 5x.

As a result, the full solution to the initial value problem can be provided by, y(t) =  7/4e^3t + 7/12 e^ -t - 2e^2t- 4/3e^2t

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To find the order and degree of a given differential equation, simply count the highest derivative and the highest power of the unknown function that appear in the equation.

What is a differential equation?

A differential equation is an equation that relates an unknown function and its derivatives to some given functions or constants.

The order of a differential equation is defined as the order of the highest derivative appearing in the equation. For example, if a differential equation contains only the first derivative of the unknown function, it is said to be a first-order differential equation. If it contains the second derivative, it is a second-order differential equation, and so on.

The degree of a differential equation is defined as the highest power of the unknown function in the equation. For example, if a differential equation is of the form y' + 2y = 0, the degree of the differential equation is 1 (the highest power of y is 1). If it is of the form y'' + 4y = 0, the degree of the differential equation is 2 (the highest power of y is y^2).

Hence, To find the order and degree of a given differential equation, simply count the highest derivative and the highest power of the unknown function that appear in the equation.

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System 1 has unique solution, System 2 have infinite solutions, System 3 has no solution and System 4 have infinite solutions.

Algebra requires the simultaneous solution of two or more equations. There must be an equal number of equations and unknowns for a system to have a singular solution. The several kinds of linear equation systems are as follows:

Independent: There is just one possible outcome for the system. The graphs of the equations come together at this one location.

Inconsistent: There is no solution for the system.

1. Given these 3 equations will yield a unique solution:

x = 32, y = 5, z = -9.  

So, a unique solution exists for this

2. This is yield many solutions. It is of the form:

x = 41n + 20, y = 55n + 27, z = 10n + 4, when n can take any values.

Hence, infinite solutions exist

3. There is no answer for any of the three equations when you try to solve them.

4. Multiply the first equation by two and subtract from the third equation. Basically, the equation is the same.

Three unknowns, but no three distinct equations Thus, there are an infinite number of combinations of x, y, and z.

Hence, infinite solutions exist.

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The 683.67 kilowatt-hour was charged while 1640 kilowatt-hour generated the credit by not being used.

The amount of electricity consumed will be calculated by the formula -

Amount of electricity consumed = total charged amount ÷ amount of unit electricity consumed

The amount of electricity that earned the credit will be calculated by the formula -

Amount of electricity that earned the credit = total reduction amount ÷ credit on unit electricity

Keep the values in formula

Amount of electricity consumed = 82.04/0.12

Performing division on Right Hand Side of the equation

Amount of electricity consumed = 683.67

Amount of electricity that earned the credit = 4.10/0.0025

Performing division on Right Hand Side of the equation

Amount of electricity that earned the credit = 1640

Thus, the amount of electricity consumed is 683.67 units and unused electricity is 1640 units.

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The following limits a) the limit does not exist. b) the limit does not exist and c) the limit does not exist.

a) limx→5+ 1/x−5 = 1/0 which is undefined. Therefore, the limit does not exist.

b) limx→5− 1/x−5 = −1/0 which is undefined. Therefore, the limit does not exist.

c) The two-sided limit of 1/x−5 as x approaches 5 from both the left and the right side is undefined. Therefore, the limit does not exist.

A limit in mathematics is a point at which a function approaches the output for the specified input values. Calculus and mathematical analysis both rely heavily on limits, which are also needed to describe concepts like continuity, derivatives, and integrals.

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The monument is made up of 150,124 blocks.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Monument:

50,123 sandstone blocks

100,001 limestone blocks.

Now,

The total number of blocks.

= 50,123 + 100,001

= 150124

Thus,

150,124 blocks.

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Answer:

Hence the correct answer is 256

Answer: $8.30

Step-by-step explanation:

Multiply: 83 times 10. If it's in a decimal put the decimal after 8

Answer:

(6,0), (0,9), (2,6)

Step-by-step explanation:

If a point is on a line, then the equation should be true when you plug in the x and y values.

(0,6): 3*0+2*6 = 18 -> 12 = 18, false

(6,0): 3*6+2*0 = 18 -> 18 = 18, true

(0,9): 3*0+2*9 = 18 -> 18 = 18, true

(9,0): 3*9+2*0 = 18 -> 27 = 18, false

(2,6): 3*2+2*6 = 18 -> 18 = 18, true

The number of people on the escalator during rush hour will depend on how long rush hour lasts, so it is not possible to provide a single answer without knowing the length of rush hour.

At rush hour, two people per second step onto the escalator, so in one second, 2 people get on the escalator.

The escalator takes 20 seconds to bring a person from the bottom to the top, so for every 20 seconds, 2 people get on the escalator and 2 people get off the escalator.

To find the number of people on the escalator during rush hour, we need to determine the number of people on the escalator after a certain amount of time, say t.

The number of people on the escalator at time t can be calculated as follows:

people on the escalator at time t = 2 * t - 2 * floor(t / 20)

where floor(t / 20) represents the number of complete cycles (20 seconds each) that have occurred.

For example, if t = 40 seconds, then floor(t / 20) = 2, so the number of people on the escalator would be:

people on the escalator at time 40 = 2 * 40 - 2 * 2 = 76

The number of people on the escalator will continue to increase as long as rush hour continues, so it is not possible to give a single answer to the question "how many people are on the escalator during rush hour?" without more information.

In general, the number of people on the escalator during rush hour will depend on how long rush hour lasts, so it is not possible to provide a single answer without knowing the length of rush hour.

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The number of people on the escalator during rush hour will depend on how long rush hour lasts, so it is not possible to provide a single answer without knowing the length of rush hour.

At rush hour, two people per second step onto the escalator, so in one second, 2 people get on the escalator.

The escalator takes 20 seconds to bring a person from the bottom to the top, so for every 20 seconds, 2 people get on the escalator and 2 people get off the escalator.

To find the number of people on the escalator during rush hour, we need to determine the number of people on the escalator after a certain amount of time, say t.

The number of people on the escalator at time t can be calculated as follows:

people on the escalator at time t = 2 * t - 2 * floor(t / 20)

where floor(t / 20) represents the number of complete cycles (20 seconds each) that have occurred.

For example, if t = 40 seconds, then floor(t / 20) = 2, so the number of people on the escalator would be:

people on the escalator at time 40 = 2 * 40 - 2 * 2 = 76

The number of people on the escalator will continue to increase as long as rush hour continues, so it is not possible to give a single answer to the question "how many people are on the escalator during rush hour?" without more information.

In general, the number of people on the escalator during rush hour will depend on how long rush hour lasts, so it is not possible to provide a single answer without knowing the length of rush hour.

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The height of the rectangle is equal to -2x² - 3x + 35.

The height of a rectangle can be found by subtracting the value of one of its side lengths from the value of the other side length.

We know that the height is equal to the difference between two side lengths, which are represented by the expressions y1 = -2x²+20 and y2 = 3x-15.

To find the height, we subtract y2 from y1:

y1 - y2 = (-2x²+20) - (3x-15) = -2x² - 3x + 35

So, the height of the rectangle is equal to -2x² - 3x + 35.

It is important to note that rectangles have four sides and all their internal angles are exactly 90 degrees. Additionally, opposite sides of a rectangle have equal lengths and its perimeter is the total distance covered by its outside boundary.

Complete Question:

The shaded region between the graphs of y = − 2 x 2 + 20 and y = 3 x − 15 is displayed below. In the shaded region lies between x = -5 x = 7/2. A typical rectangle is shown in the diagram located at position x. What is the height of this rectangle, in terms of x?

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The height of the rectangle is equal to -2x² - 3x + 35.

The height of a rectangle can be found by subtracting the value of one of its side lengths from the value of the other side length.

We know that the height is equal to the difference between two side lengths, which are represented by the expressions y1 = -2x²+20 and y2 = 3x-15.

To find the height, we subtract y2 from y1:

y1 - y2 = (-2x²+20) - (3x-15) = -2x² - 3x + 35

So, the height of the rectangle is equal to -2x² - 3x + 35.

It is important to note that rectangles have four sides and all their internal angles are exactly 90 degrees. Additionally, opposite sides of a rectangle have equal lengths and its perimeter is the total distance covered by its outside boundary.

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Complete Question:

The shaded region between the graphs of y = − 2 x 2 + 20 and y = 3 x − 15 is displayed below. In the shaded region lies between x = -5 x = 7/2. A typical rectangle is shown in the diagram located at position x. What is the height of this rectangle, in terms of x?

The total surface area of the prism is 204 cm²

Prism is a three-dimensional solid object in which the two ends are identical. It is the combination of the flat faces, identical bases and equal cross-sections. The faces of the prism are parallelograms or rectangles without the bases.

Given here: A prism with triangular base with three of its faces as rectangle and its bases triangles.

Thus total surface area is the sum of areas of all these 5 faces

TSA= Sum of the area of the two slanted rectangles + Sum of the two bases + the sum of the rectangle the prism is resting on in the figure

Now dimensions of the slanted rectangles are given by length =12 and breadth =5 and the dimensions of the last rectangle are length =12 and breadth = 6

∴ TSA= 2×12×5 +1/2 ×6×4 +12×6

         = 120+12+72

        =204 cm²

Hence, The total surface area of the prism is 204 cm²

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==============================================

Explanation:

We have a proportion in the form:

A/B = C/D

where,

Each is measured in feet.

In this case,

Let's solve for D.

A/B = C/D

18/6 = 15/D

3 = 15/D

3D = 15

D = 15/3

D = 5

Ariadne is 5 feet tall.

The required money she will have at the end of the week for 10, 15, and 20 hours is $250, $375, and $500.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

The equation to show how much money Mary will have at the end of the week would be:

M = 100 + (15 * h), where M is the total money Mary will have at the end of the week and h is the number of hours she works.

If Mary works 10 hours, she will have:

M = 100 + (15 * 10) = 250 dollars.

If Mary works 15 hours, she will have:

M = 100 + (15 * 15) = 375 dollars.

If Mary works 20 hours, she will have:

M = 100 + (15 * 20) = 500 dollars.

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Answer:

using the random numbers, we can determine that 5 servers will be correct.

Step-by-step explanation:

(this may be incorrect, but the if their success rate is 60% then it should be 7.2, but this is not what the question is asking)

Coefficient estimates from WLS (weighted least squares) are interpreted in a similar manner to those from an un-weighted, original model. The main difference is the weights used to scale the observations.

Therefore, correct answer will be:-  Coefficient estimates from the un-weighted, original model should be used for prediction

This can cause estimates to differ depending on the weight chosen. When interpreting the coefficient estimates, it is important to consider the weights used when calculating the model. This is because they can affect the magnitude of the coefficient estimates.

Additionally, the weights should be taken into account when calculating the marginal effects of the coefficients. This can be done by scaling up the coefficients by the weight used. Ultimately, the interpretation of coefficient estimates from WLS should be done in the same manner as those from an un-weighted model, but the weights should be taken into account when considering their magnitude and when calculating marginal effects.

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The common region to the graph of both inequality represents the possible solution sets to the inequality.

An inequality is used to make unequal comparisons between two expressions.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is a system of inequality as -

4x - 5y ≥ -35

y > - x - 2

Refer to the graph attached. The common region to the graph of both inequality represents the possible solution set to the inequality.

Therefore, the common region to the graph of both inequality represents the possible solution sets to the inequality.

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Answer:

Multiplying

Step-by-step explanation:

The Multiplying of a positive integer is negative.

The quotient of the rational expression given is [tex]\frac{2x - 1}{3x}[/tex] , and option A is the correct answer.

The ratio of two polynomials is displayed in rational expressions. It indicates that the denominator and numerator are polynomials. It is an algebraic expression that has a ratio and an unknown variable, just like a fraction. Although we can simplify this kind of equation with the aid of a calculator.

Polynomial expressions must be set equal to zero in order to find the root or zero. However, once the expression has been condensed to its simplest form, we must only set the numerator equal to zero in order to obtain the zeros of rational functions or expressions.

The given rational expression is:

[tex]\frac{2x - 1}{x + 1}[/tex] ÷ [tex]\frac{3x^2}{x^2 + x}[/tex]

The rational expression can be written as follows:

[tex]\frac{2x - 1}{x + 1} * \frac{x^2 + x }{3x^2} \\\\\frac{2x - 1}{x + 1} * \frac{x (x+ 1) }{3x^2}\\\\\frac{2x - 1}{3x}[/tex]

Hence, the quotient of the rational expression given is [tex]\frac{2x - 1}{3x}[/tex] , and option A is the correct answer.

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The  speed describes as :  A scalar quantity with magnitude only.

What is speed?

Speed is distance travelled by the object per unit time. Due to having no direction and only having magnitude, speed is a scalar quantity With SI unit meter/second.

Some more information about speed:

When an object travels the same distance in the same amount of time, it is said to be moving at a uniform speed.

When an object travels a different distance at regular intervals, it is said to have variable speed.

Average speed is the constant speed determined by the ratio of the total distance travelled by an object to the total amount of time it took to travel that distance.

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The required values are sin θ = -55/73, cos θ = -48/73, tan θ = 55/48, cosec θ = 73/-55, sec θ = 73/-48, cot θ =48/55

Trigonometry is one of the most important branches in mathematics. The word trigonometry is formed by clubbing words 'Trigonon' and 'Metron' which means triangle and measure respectively. It is the study of the relation between the sides and angles of a right-angled triangle. It thus helps in finding the measure of unknown dimensions of a right-angled triangle using formulas and identities based on this relationship. Trigonometry basics deal with the measurement of angles and problems related to angles. There are three basic functions in trigonometry: sine, cosine, and tangent. These three basic ratios or functions can be used to derive other important trigonometric functions: cotangent, secant, and cosecant. All the important concepts covered under trigonometry are based on these functions. Hence, further, we need to learn these functions and their respective formulas at first to understand trigonometry.

Given the terminal point we know the following:

Adjacent = -48

Opposite = -55

Hypotenuse can use the Pythagorean Theorem to find:

c²=(-48)²+(-55)² = 5329

Take the square root of both sides

c=√5329 = 73

So, sin θ = -55/73

cos θ = -48/73

tan θ = 55/48

csc θ = 73/-55

sec θ = 73/-48

cot θ =48/55

Thus, the required values are sin θ = -55/73, cos θ = -48/73, tan θ = 55/48, csc θ = 73/-55, sec θ = 73/-48, cot θ =48/55

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