Acone with radius 5 units is shown below. its volume is 105 cubic units. find the height of the cone.

height of the cone  = 4.01273885 units

Step-by-step explanation:

Volume of a cone(V) is given by:

            ....[1]

where,

r is the radius and h is the height of the cone.

As per the statement:

A cone with radius 5 units and ts volume is 105 cubic units

⇒r = 5 units and V = 105 cubic units

Substitute these given values and use in [1] we have;

Multiply both sides by 3 we have;

⇒

Divide both sides by 78.5 we have;

or

h = 4.01273885 units

Therefore, the height of the cone is, 4.01273885 units

y=1/4x-4

step-by-step explanation:

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is