Explanation

Given:

a - b = 4

ab = 5

The formula for a³ - b³ is:

a³ - b³ = (a - b)(a² + ab + b²)

We can also use the identity:

a³ - b³ = (a - b)³ + 3ab(a - b)

Substituting the given values:

a³ - b³ = (4)³ + 3 * 5 * 4

= 64 + 60

= 124

Explanation

To find the distance traveled by the rider, we need to calculate the arc length:

Given:

Radius (r) = 49 meters

Angle (θ) = 150°

First, convert the angle to radians:

θ = 150° * (π / 180)

= 150 * π / 180

= 5π/6 radians

Now, calculate the arc length (s):

s = r * θ

= 49 * (5π/6)

= 49 * 5 * 3.14159 / 6

≈ 128.33 meters

Explanation

Given:

1. 6x + 2y = 6300

2. 2x + y = 2600

Multiplying equation (2) by 2:

4x + 2y = 5200

Subtracting:

(6x + 2y) - (4x + 2y) = 6300 - 5200

2x = 1100

x = 550

Explanation

The absolute value of a number is its distance from zero, regardless of direction. Therefore:

|-3| = 3

Explanation

Given:

p^(a - b) × p^(b - c) × p^(c - a)

Using the property of exponents that states a^(m) × a^(n) = a^(m + n), we can simplify:

p^(a - b + b - c + c - a)

= p^(0)

= 1

Explanation

1 divided by 1000 equals 0.001.

It represents one-thousandth in decimal form.

Explanation

Let's denote the number as x. According to the problem:

133 added to a number (x) is equal to 75 more than 4 times the number (4x + 75)

The correct equation is:

133 + x = 4x + 75

Now, let's solve for x:

133 - 75 = 4x - x

58 = 3x

x = 58 / 3

x = 19.33

The correct equation is indeed:

133 + x = 4x + 75

Explanation

A ray extends infinitely in one direction from its starting point.

Unlike a line which extends in both directions.

It has a definite starting point but no end, traveling in a single direction.

Explanation

Given:

Z1 = 2 - i

Z2 = 3 + i

Product of Z1 and Z2:

Z1 * Z2 = (2 - i) * (3 + i)

= 6 + 2i - 3i - i²

Since i² = -1,

= 6 - i + 1

= 7 - i

Explanation

نبی کریم صلی اللہ علیہ وآلہ وسلم نے حضرت دحیہ بن خلیفہ کلبی رضی اللہ عنہ کو قیصر روم کے پاس سفیر بنا کر بھیجا تھا۔

حضرت دحیہ نے قیصر روم کے دربار میں نبی صلی اللہ علیہ وآلہ وسلم کا پیغام پہنچایا تھا۔