The product of the roots is given by c/a = 24/1 = 24.

The product of the roots is given by c/a = 15/1 = 15.

proj_B(A) = (A · B / |B|^2)B = ((3*1 + 4*1) / (1^2 + 1^2))(i + j) = (7/2)(i + j) = 3.5.

Circumference = 2πr; 62.8 = 2πr; r = 10 cm.

Area = πr²; 154 = 22/7 * r²; r² = 154 * 7/22 = 49; r = 7 units.

Circumference = 2πr; 31.4 = 2πr; r = 31.4/(2π) ≈ 5 m.

Circumference = 2πr; 62.8 = 2πr; r = 62.8/(2π) ≈ 10 cm.

Radius is half of the diameter. Therefore, radius = 14 cm / 2 = 7 cm.

For a first-order reaction, k = 0.693 / t₁/₂. Here, t₁/₂ = 10 min, so k = 0.693 / 10 = 0.0693 min⁻¹.

The rate law for a reaction is determined by the order with respect to each reactant. For a first order with respect to A and second order with respect to B, the rate law is Rate = k[A][B]^2.

For a first order reaction, the rate law is directly proportional to the concentration of the reactant, hence Rate = k[A].

For a second order reaction with respect to A, the rate law is expressed as Rate = k[A]^2.

The rate law is determined by the order of the reaction with respect to each reactant. For first order in A and second order in B, the rate law is Rate = k[A][B]^2.

For a second order reaction with respect to A, the rate law is expressed as Rate = k[A]^2.

The real part of the complex number 4 + 5i is 4.

The real part of the complex number 7 - 4i is 7.

The standard reduction potential for 2H⁺ + 2e⁻ → H₂ is 0.00 V.

The relationship is ΔG = -nFE, where n is the number of moles of electrons transferred.

The period T is the reciprocal of frequency f, given by T = 1/f.

According to the Arrhenius equation, the rate of reaction increases exponentially with temperature.

1 Joule is defined as the work done when a force of one Newton moves an object one meter, hence 1 J = 1 N·m.

The angle of diffraction is directly proportional to the wavelength of light used in a diffraction grating, as described by the grating equation.

The angle of diffraction is inversely proportional to the wavelength; as the wavelength increases, the angle of diffraction decreases.

Using Ohm's law (R = V/I), R = 25V / 5A = 5Ω.

(15 + 5) = 20, then 20 × 2 = 40.

(15 + 5) = 20, so 20 × 2 = 40.

15 ÷ 3 = 5, then 5 × 4 = 20.

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

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

The s orbital has a spherical shape.