Question

1. slope the slope m between two points (x1, y1) and (x2, y2) is m = (y2 - y1)/(x2 - x1). solve for y2.
2. cylinders the surface area of a cylinder a is given by a = 2πr² + 2πrh, where r is radius and h is height. solve for h.
3. physics the height h of a falling object is given by h = vt - gt², where v is the initial velocity of the object, t is time, and g is the gravitational constant. solve for v.

Explanation:

14.

Step1: Multiply both sides by $(x_2 - x_1)$

$m(x_2 - x_1)=y_2 - y_1$

Step2: Add $y_1$ to both sides

$y_2=m(x_2 - x_1)+y_1$

Step1: Subtract $2\pi r^{2}$ from both sides

$A - 2\pi r^{2}=2\pi rh$

Step2: Divide both sides by $2\pi r$

$h=\frac{A - 2\pi r^{2}}{2\pi r}$

Step1: Add $gt^{2}$ to both sides

$h+gt^{2}=vt$

Step2: Divide both sides by $t$ (assuming $t

eq0$)
$v=\frac{h + gt^{2}}{t}$

Answer:

$y_2=m(x_2 - x_1)+y_1$

15.