The direction of the magnetic field produced by a current-carrying wire is perpendicular to both the wire and the direction of the current.

Using the right-hand rule, the magnetic field direction is counterclockwise around the wire.

The standard form of a parabola is (y - k)^2 = 4p(x - h). Here, p = 2, so the directrix is x = -2.

For the parabola y^2 = 4px, here 4p = 8, so p = 2. The directrix is x = -p = -2.

The distance between centers (1, 2) and (-3, -4) is calculated using the distance formula.

The distance between the foci is 6, calculated using the formula 2c where c = √(a^2 - b^2).

The distance between the foci is given by 2c, where c = √(a^2 - b^2) = √(25 - 16) = 3, so the total distance is 2c = 6.

Distance = √[(4-1)² + (6-2)²] = √[9 + 16] = √25 = 5.

Distance = √[(7-3)² + (1-4)²] = √[16 + 9] = √25 = 5.

Distance = √((4-1)² + (5-2)² + (6-3)²) = √(9 + 9 + 9) = 3√3.

Distance = |3(1) + 4(2) - 10| / √(3² + 4²) = |3 + 8 - 10| / 5 = 1.

Distance = |2(3) + 3(4) - 6| / √(2² + 3²) = |6 + 12 - 6| / √13 = 12/√13.

The function is undefined at x = 2, so the domain is all real numbers except 2.

The function is undefined at x = 3, so the domain is x ≠ 3.

The expression under the square root must be non-negative, so x - 1 >= 0, hence x >= 1.

The Doppler effect refers to the change in frequency of a wave in relation to an observer moving relative to the wave source.

Dot product = 1*3 + 2*4 = 3 + 8 = 11

A . B = 2*1 + 3*0 + 4*(-1) = 2 + 0 - 4 = -2.

The eccentricity e of a hyperbola is given by e = √(1 + b^2/a^2).

The phenomenon of two sound waves of slightly different frequencies interfering is called beats.

-NO2 is a strong electron-withdrawing group and destabilizes benzene derivatives.

-CF3 is a strong electron-withdrawing group, which destabilizes the benzene ring.

The -CH3 group is an electron-donating group and stabilizes the carbocation through hyperconjugation.

The -COOH group is a strong electron-withdrawing group, thus it destabilizes the benzene ring.

A -I group increases the acidity of a carboxylic acid by stabilizing the negative charge on the conjugate base.

A -I group increases the acidity of carboxylic acids by stabilizing the negative charge on the conjugate base.

The -NO2 group is a strong electron-withdrawing group, which destabilizes the benzene ring.

A catalyst does not affect the equilibrium constant; it only speeds up the rate at which equilibrium is reached.

A catalyst does not affect the position of equilibrium; it only speeds up the rate at which equilibrium is reached.

Inserting a dielectric material between the plates of a capacitor decreases the electric field due to polarization.