Aconical tank is 10 feet across and 12 feet deep if water is flowing into the tank at a rate of 10 cubic feet per minute find the rate of change of the depth of the water when the water is 8 feet deep

0.286 ft per minute ( approx )

Step-by-step explanation:

Let r represents the radius and h represents the height of the cone,

If the conical tank is 10 feet across and 12 ft deep,

Diameter = 10 ft, h = 10 ft

⇒ 2r = 10 ⇒ r = 5 feet,

Now, radius of a cone and its height is always in same proportion,

Now, volume of a cone,

From equation (1),

Differentiating with respect to t ( time ),

Here,

Hence, the rate of change of the depth of the water would be 0.286 ft per minute

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c