Using point-slope form: y - y1 = m(x - x1) => y - 2 = 3(x - 1).

Using point-slope form: y - 2 = 5(x - 1) gives y = 5x - 3.

The vertex form of a parabola is y = ax^2. Since it passes through (2, 8), we have 8 = a(2^2) => 8 = 4a => a = 2. Thus, the equation is y = 4x^2.

The distance from the focus to the directrix is 4, so the equation is y = (1/4)(x - 0)^2 + 0, which simplifies to x^2 = 8y.

The distance from the focus to the directrix is 6, so p = 3. The equation is y^2 = 4px = 12y.

f'(x) = 2x + 2. At x = 1, f'(1) = 4. The tangent line is y - 3 = 4(x - 1) => y = 4x - 1.

f'(x) = 2x + 2. At x = 1, f'(1) = 4. The point is (1, 3). The tangent line is y - 3 = 4(x - 1) => y = 4x - 1.

The equation xy = c represents a family of hyperbolas with varying constant c.

The equation x^2/a^2 + y^2/b^2 = 1 represents a family of ellipses with semi-major axis a and semi-minor axis b.

The equation y = a sin(bx + c) represents a family of sine waves with amplitude a and phase shift c.

The equation y = e^(kx) represents a family of exponential functions where 'k' determines the growth rate.

The equation y = k/x represents a family of hyperbolas with varying asymptotes depending on the value of 'k'.

Using the chain rule, f'(x) = 2e^(2x).

The equation x^2 + y^2 = r^2 represents a family of circles with varying radii (r).

The equation x^2 + y^2 = r^2 represents a family of circles with radius r centered at the origin.

The equation y = mx^2 + c represents a family of parabolas that open upwards or downwards depending on the sign of m.

The equation y^2 = 4ax represents a family of parabolas that open to the right with varying values of 'a'.

The differential equation is separable. Integrating both sides gives ln|y| = 3x + C, hence y = Ce^(3x).

Using the formula r = A/s, where A is the area and s is the semi-perimeter. Area = 26 cm², s = 12 cm, so r = 26/12 = 4 cm.

The integral of cos(x) is sin(x) + C.

∫(2x)dx from 0 to 3 = [x^2] from 0 to 3 = 9 - 0 = 9.

∫2x dx = x^2 + C.

The integral is sin(x) + C.

The integrating factor is e^(∫2dx) = e^(2x).

The integrating factor is e^(∫3dx) = e^(3x).

Q1 = 4, Q3 = 10. IQR = Q3 - Q1 = 10 - 4 = 6.

IQR = Q3 - Q1; Q1 = 3, Q3 = 8; IQR = 8 - 3 = 5.

Q1 = 3, Q3 = 8. IQR = Q3 - Q1 = 8 - 3 = 5.

Q1 = 3, Q3 = 7; IQR = Q3 - Q1 = 7 - 3 = 4.

Q1 = 3, Q3 = 9. IQR = Q3 - Q1 = 9 - 3 = 6.