Explanation

A scalar quantity has only magnitude and no direction.

Examples include mass, time, temperature, and speed.

Explanation

Cohesion is the attractive force between molecules of the same substance.

It is strongest in solids due to tightly packed molecules.

Explanation

The argument of the product of two complex numbers is the sum of their arguments.

This property comes from the multiplication of complex numbers in polar form.

Explanation

To find the median, let's arrange the weights in order:

27, 29, 30, 32, 33, 35, 37, 47, 48

Since there are 9 values (an odd number), the middle value is the median:

The median is the 5th value: 33

Explanation

The number of diagonals in a polygon can be calculated using the formula:

n(n-3)/2

where n is the number of sides.

For a 12-sided polygon (dodecagon):

n = 12

Number of diagonals = 12(12-3)/2

= 12(9)/2

= 108/2

= 54

Explanation

Given ∫12x⁻⁵ √(-3x⁻⁴ + 1) dx

Let u = -3x⁻⁴ + 1

du/dx = 12x⁻⁵

du = 12x⁻⁵ dx

∫√u du = ∫u^(1/2) du

= (2/3)u^(3/2) + C

Substituting back u = -3x⁻⁴ + 1:

= (2/3)(-3x⁻⁴ + 1)^(3/2) + C

Explanation

The function y = x + 100 is in the slope-intercept form y = mx + c, where:

m = 1 (slope)

c = 100 (y-intercept)

This confirms that the graph of the function is a straight line.

Explanation

- Magnetic Induction (B) is also called Magnetic Flux Density.  

- It represents the strength of the magnetic field over a given area.  

- Unit: Tesla (T) → 1 T = 1 Weber/m²  

- Formula: B = Φ / A  

  (Where Φ = magnetic flux, A = area)  

- It indicates how much magnetic field passes through a surface.  

- It's a vector quantity (has both magnitude and direction).  

- Higher B → stronger magnetic field at that point.

Explanation

Given y = 2/x

Let's find the first and second derivatives:

dy/dx = -2/x²

d²y/dx² = 4/x³

Now, let's evaluate y + 1/2 * d²y/dx²:

y + 1/2 * d²y/dx² = 2/x + 1/2 * 4/x³

= 2/x + 2/x³

= (2x² + 2)/x³

= 2(x² + 1)/x³

= 2(1 + x²)/x³

Explanation

The atomic number of silver (Ag) is 47. Its electronic configuration is [Kr] 4d¹⁰ 5s¹.

The valence electrons are in the outermost shell, which is the 5s orbital with 1 electron.

The number of valence electrons is 1.