<span>2<span>x2</span>+xy+2<span>y2</span>=5</span>Implicit differentiation yields<span>4x+y+x<span>y′</span>+4y <span>y′</span>=0</span>Solve for <span>y′</span><span>.
answer is- y = 4x+ y /5x</span>
Ya, calculus and related rates, such fun!
everything is changing with respect to t
altitude rate will be dh/dt and that is 1cm/min
dh/dt=1cm/min
area will be da/dt which is increasing at 2cm²/min
da/dt=2cm²/min
base=db/dt
alright
area=1/2bh
take dervitivie of both sides
da/dt=1/2((db/dt)(h)+(dh/dt)(b))
solve for db/dt
distribute
da/dt=1/2(db/dt)(h)+1/2(dh/dt)(b)
move
da/dt-1/2(dh/dt)(b)=1/2(db/dt)(h)
times 2 both sides
2da/dt-(dh/dt)(b)=(db/dt)(h)
divide by h
(2da/dt-(dh/dt)(b))/h=db/dt
ok
we know
height=10
area=100
so
a=1/2bh
100=1/2b10
100=5b
20=b
so
h=10
b=20
da/dt=2cm²/min
dh/dt=1cm/min
therefor
(2(2cm²/min)-(1cm/min)(20cm))/10cm=db/dt
(4cm²/min-20cm²/min)/10cm=db/dt
(-16cm²/min)/10cm=db/dt
-1.6cm/min=db/dt
the base is decreasing at 1.6cm/min
Answer:
a
12=
−
3
n
2
−
n
Step-by-step explanation:
The radius of your cone is half of 18 units = 9 units.
The volume of any cone is <span><span>V = (1/3) · (pi) · (radius)² · (height) </span>
</span>
-- Take that formula for the volume of any cone.
-- Write '8' in place of 'height'.
-- Write '9' in place of 'radius'.
-- Write '3.142' in place of 'pi'.
-- Complete the arithmetic.
-- Bada-bing, you've got the volume.
