The radius is 5 (distance from (0,0) to (3,4)), so the equation is x² + y² = 5² = 25.

The radius is the distance from the center to the point, which is √(3² + 4²) = √25 = 5.

Radius = distance from center to point = √[(7-3)² + (1-4)²] = √[16 + 9] = √25 = 5 units.

The chance of not contracting the disease = 1 - (1/500) = 499/500 = 0.998 = 99.8%.

The electric field inside a non-conducting sphere with linearly increasing charge density varies linearly with radius.

At the center of a non-uniform spherical charge distribution, the electric field is zero due to symmetry.

The electric field inside a non-uniform charge distribution varies quadratically with radius due to the increasing charge density.

According to Gauss's law, the electric flux is directly proportional to the enclosed charge, so it doubles.

Capacitance C = Q/V. If Q is doubled and V remains constant, C must also double.

Capacitance C = Q/V; if Q is doubled and V remains constant, C must halve.

The electric field E between the plates of a capacitor is directly proportional to the charge. If the charge is doubled, the electric field also doubles.

The energy stored in a capacitor is given by U = 1/2 * C * V^2. If the charge is doubled, the energy stored quadruples.

The energy stored in a capacitor is proportional to the square of the charge (U = Q^2/(2C)). Doubling the charge increases the energy by a factor of 4.

The electric field E is directly proportional to the charge, so tripling the charge will triple the electric field.

Circumference = 2πr; 31.4 = 2 * π * r; r = 5 cm.

Circumference = 2πr, so r = circumference / (2π) = 31.4 / (2 * 3.14) = 5 cm.

Circumference = 2πr. Therefore, r = circumference / (2π) = 31.4 / (2 * 3.14) = 5 cm.

Using the formula C = 2πr, we find r = C/(2π) = 31.4/(2*3.14) = 5 cm.

Circumference = 2πr. Therefore, r = Circumference / (2π) = 31.4 cm / (2 * 3.14) = 5 cm.

Circumference = 2πr. Setting 31.4 = 2 × 3.14 × r gives r = 5 units.

The circumference C = 2πr. Setting 31.4 = 2 * 3.14 * r gives r = 5.

Circumference = 2πr. Measured circumference = 31.4 cm. Thus, r = 31.4 / (2π) ≈ 5.0 cm.

Percentage error = (Absolute error / Measured value) * 100 = (0.2 / 31.4) * 100 ≈ 0.64%.

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.