The scientific name of the domestic cat is Felis catus, following the binomial nomenclature system.

Biology is the scientific study of living organisms.

First derivative f'(x) = 8x^3 - 9x^2 + 1. Second derivative f''(x) = 24x^2 - 18x.

First derivative f'(x) = 8x^3 - 12x^2. Second derivative f''(x) = 24x^2 - 24x.

Using the product rule and chain rule, the second derivative is f''(x) = e^x (sin(x) + cos(x)).

The second derivative f''(x) = e^x.

f''(x) = 12x - 12.

First derivative f'(x) = 8x^3 - 12x^2. Second derivative f''(x) = 24x^2 - 24x.

A liquid droplet takes a spherical shape because a sphere has the minimum surface area for a given volume, minimizing the energy associated with surface tension.

A tetrahedral geometry has a central atom bonded to four other atoms, forming a shape like a pyramid with a triangular base.

AX3E indicates three bonding pairs and one lone pair, resulting in a trigonal pyramidal shape.

The s orbital has a spherical shape.

Ammonia has a trigonal pyramidal shape due to the presence of a lone pair on the nitrogen atom.

The d orbitals have a double dumbbell shape.

The equipotential surfaces around a point mass are spherical.

The gravitational field lines around a point mass are radial, pointing towards the mass.

The magnetic field lines around a bar magnet form closed loops, exiting from the north pole and entering the south pole.

The magnetic field lines around a circular loop of wire carrying current are in the shape of concentric circles, with the center of the loop being the point of maximum field strength.

The magnetic field lines around a long straight conductor are concentric circles centered on the wire.

Methane (CH4) has a tetrahedral shape due to the four pairs of bonding electrons around the central carbon atom.

π bonds are formed by the side-to-side overlap of p orbitals, resulting in a planar shape.

The HOMO of benzene is cyclic due to the delocalization of π electrons in the ring structure.

The highest energy molecular orbital in O2 is a π* orbital, which has a dumbbell shape.

The highest energy molecular orbital in O2 is a diatomic molecular orbital, specifically a π* orbital.

PCl5 has a trigonal bipyramidal shape due to five bonding pairs around the phosphorus atom.

SF6 has six bonding pairs and no lone pairs, leading to an octahedral shape.

AX2E2 indicates two bonding pairs and two lone pairs, resulting in a bent shape.

AX3E indicates three bonding pairs and one lone pair, resulting in a trigonal pyramidal shape.

AX4 indicates four bonding pairs and no lone pairs, resulting in a tetrahedral shape.

The p-orbital has a dumbbell shape.