The formula to determine the period of one swing of a simple pendulum is T=2\pi\sqrt{\frac{L}{g}},T=2π g L , where LL is the length of the string and gg is the acceleration due to gravity. Solve the formula to solve for LL in terms of \pi,π, TT and g. G.

L = (T² × g) / 4π²

Step-by-step explanation:

T = 2π√L/g

Where,

L = length of the string

g = acceleration due to gravity

T = 2π√L/g

square both sides of the equation to eliminate the square root

T² = (2π)²√(L/g)²

T² = (2π)²(L/g)

(2π)²

= 2π × 2π

= 4π²

T² = 4π²(L/g)

Multiply both sides by g

T² × g = 4π²(L/g) × g

T² × g = 4π²L

Divide both sides by 4π² to get L

L = (T² × g) / 4π²

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be