The radius of a spherical is decreasing at a constant rate of 3 cm per second. find, in cubic centimeters per second, the rate of change of the volume of the ball when the radius is 5cm.

DV/dt  =  942 cm³/sec  (decreasing )

Step-by-step explanation:

Volume of the sphere    V = 4/3π*r³    

r   ⇒ r(t)

DV/ dt    =  DV/dr * Dr/dt       so

DV/dt  = 4*π*r²*Dr/dt

and we know   Dr/dt  = - 3 cm/sec    and r = 5 cm

Then   radius decreasing   V  also decreases

by substitution

DV/dt  = - 4*π*(5)²* (3)

DV/dt   = - 942 cm³/sec

side xy = 10

sin(x) = 4/5

cos(x) = 3/5

tan(x) = 4/3

step-by-step explanation:

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.