Explanation

Square = 4 sides are equal

Rectangle = only 2 opposite sides are equal

In the case of 3-dimension,

If the hall is in Cube shape, the area of all 4 walls will be equal.

But, here we know that the hall is in a Rectangular Prism shape, so only the area of 2 opposite walls will be equal.

Area of two walls = 15*b + 15*b = 30b

Area of other two walls = 12*b + 12*b = 24b

Hence,

Their Sum = 30b + 24b = 54b

360 = 54b which means b = 360/54 = 20/3

Here, the breadth of the walls is equal to the height of the rectangular prism (Hall)

Hence,

Volume of Hall = l*b*h = 15*12*(20/3) = 1200 cu.m

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ND10-12-2022

Explanation

An equilateral triangle has three sides of equal length, and each interior angle measures 60 degrees.

Explanation

Sum = 8 + 6 + 7 + 2 + 0 + 4 + 7 + 2 + 3 = 39

Explanation

Question 

solution:

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Explanation

Let the breadth of the rectangular plot be x meters.

Since the length is thrice the breadth, the length is 3x meters.

The area of the rectangular plot is given as 867 sq m, which is equal to the product of the length and breadth: length × breadth = area.

So, we can write the equation: 3x × x = 867.

Simplifying the equation, we get: 3x^2 = 867.

Divide both sides by 3: x^2 = 289.

Take the square root of both sides: x = √289 = 17.

Therefore, the breadth of the rectangular plot is 17 meters.

Explanation

Since the sides are in the ratio 3:4:5, let's assume the common multiplier is x. Then, the sides can be written as 3x, 4x, and 5x.

The perimeter is the sum of all sides, so we can set up the equation:

3x + 4x + 5x = 24

Combine like terms:

12x = 24

Divide by 12:

x = 2

Now that we have the value of x, we can find the length of the longest side (5x):

5x = 5(2) = 10 cm

So, the length of the longest side is 10 cm.

Explanation

The given differential equation is:

dy/dx = 1/√(1+x^2)

To solve this equation, we can use the substitution u = 1+x^2, which implies du/dx = 2x. Then, we can rewrite the equation as:

dy/dx = 1/√u

dy = 1/√u du/2x

2y = ∫1/√u du

Now, we can recognize the integral as the inverse hyperbolic sine (arsinh or sinh^-1) function:

2y = sinh^-1(u) + C

2y = sinh^-1(1+x^2) + C

Dividing both sides by 2, we get:

y = (1/2)sinh^-1(1+x^2) + C/2

Since C/2 is also a constant, we can write the solution as:

y = (1/2)sinh^-1(1+x^2) + c

or simply: y = sinh^-1(x) + c

Explanation

Given:

Central angle = 180 degrees

1. Calculate the total angle of the pie graph:

The total angle of a pie graph is always 360 degrees since it represents the whole or 100% of the data.

2. Determine the proportion:

The proportion is the ratio of the given angle to the total angle of the pie graph.

In this case, it is 180 degrees divided by 360 degrees.

Proportion = 180 degrees / 360 degrees

Simplifying the division:

Proportion = 1/2

Therefore, the proportion of the central angle in the pie graph is 1/2, which can also be expressed as 50% or 0.5.

Explanation

The area of a circle can be expressed in terms of its circumference C as:

A = C^2 / 4π

This is because the circumference C is related to the radius r by:

C = 2πr

And the area A is related to the radius r by:

A = πr^2

Substituting the expression for r in terms of C, we get:

A = C^2 / 4π

Explanation

The tangent at any point of a circle is perpendicular to the radius through the point of contact.

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ND17-1-2023