Using the formula R = (abc)/(4 * Area), we can find the side opposite to angle A. Let a = side opposite to A. Then, a = (4 * Area * R) / (bc) = (4 * 48 * 10) / (b * c).

The maximum area of a triangle with circumradius R is given by the formula Area = (abc)/(4R). For maximum area, the triangle should be equilateral, thus Area = (3√3/4) * (R^2) = (3√3/4) * (5^2) = 25√3/4 cm².

C(n,k) represents the number of ways to choose k items from n, which corresponds to the coefficient of x^k.

In a GP with a negative common ratio, the terms will alternate in sign, starting from the sign of the first term.

Let the principal be P. Then, CI = P(1 + r)^n - P = P(1.1^2 - 1) = 220. Solving gives P = $2000.

Using the formula CI = P[(1 + r)^n - 1], we can set up the equation 400 = 1600[(1 + r)^2 - 1]. Solving gives r = 12.5%.

According to Le Chatelier's principle, if a change is made to a system at equilibrium, the system will adjust to counteract that change. Increasing the concentration of a reactant will shift the equilibrium to the right, favoring the formation of products.

For a second-order reaction, if concentration is tripled, the rate increases by 3² = 9 times.

Increasing the concentration of Cu²⁺ increases the cell potential according to the Nernst equation.

According to Le Chatelier's principle, increasing the concentration of reactants will shift the equilibrium position to the right, favoring the formation of products.

Lifting constraints typically leads to increased freedom and opportunities.

Substituting x = 2: 2(2) + 3y = 12 => 4 + 3y = 12 => 3y = 8 => y = 8/3 ≈ 2.67, closest is 3.

Substituting x = 0 in 2(0) + 3y = 6 gives 3y = 6, so y = 2.

Substituting x = 0: 3(0) + 4y = 12 => 4y = 12 => y = 3.

Solving the equations x + y = 10 and x - y = 2 simultaneously gives x = 6 and y = 4.

Reflection across the yz-plane changes the sign of the x-coordinate. So, Q = (-1, -1, 2).

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

Slope = (6-2)/(4-1) = 4/3.

Slope = (7-3)/(4-2) = 4/2 = 2.

Slope = (5-1)/(5-1) = 4/4 = 1

Distance CD = |10 - 5| = 5.

Length CD = |10 - 5| = 5.

Using point-slope form: y - 5 = 1(x - 5) => y = x

Using point-slope form: y - 5 = 1(x - 5) => y = x.

Setting y = 0 in the equation -3x + 6 = 0 gives x = 2.

Distance AB = √((3-1)² + (4-2)²) = √(4) = 2.

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

The slope m is calculated as (y2 - y1) / (x2 - x1) = (7 - 3) / (4 - 2) = 4/2 = 2.

Calculate distances AB, BC, CA and sum them: AB = 5, BC = 5, CA = 7. Perimeter = 5 + 5 + 7 = 17.

Perimeter = AB + BC + CA = √[(3-1)² + (4-2)²] + √[(5-3)² + (2-4)²] + √[(1-5)² + (2-2)²] = 2.83 + 2.83 + 4 = 10.