Answer:
the rate of change in volume is dV/dt = 4π mm³/s = 12.56 mm³/s
Step-by-step explanation:
since the volume V of a cylinder is related with the height H and the radius R through:
V = πR²*H
then the change in time is given by the derivative with respect to time t
dV/dt = (∂V/∂R)*(dR/dt) + (∂V/∂H)*(dH/dt)
the change in volume with radius at constant height is
(∂V/∂R) = 2*πR*H
the change in volume with height at constant radius is
(∂V/∂H) = πR²
then
dV/dt = 2π*R*H *(dR/dt) + πR²*(dH/dt)
replacing values
dV/dt = 2π* 2 mm * 20 mm * (-0.1 mm/s) + π (2 mm) ²* 3 mm/s = 4π mm³/s
dV/dt = 4π mm³/s = 12.56 mm³/s
Converting feet to inches, 8*12=96 and 96*4=384. Next, 40*12=480. Since 384*x (if x represents the cost per inch of crown molding)=16*100=1600 cents due to that for every inch, we add x amount of money, we can find x to be 1600/384=800/192=400/96=200/48=100/24=50/12=25/6 by simply dividing both the numerator and denominator by 2 each time. Since we add x amount of money for every inch, and we have 480 inches, 480*x=480*25/6=2000 cents=2000/100=20 dollars is our answer
Step-by-step explanation:
OA=AC=OC=2 (equal triangle)
which means angle O =60 degree
tan 60 = AB / 2
AB = 2 tan 60 =
