Water is leaking out of a conical tank At 500 cm³/min. The tank has a height of
24 cm and a radius of 6 cm. Find the rate at which water is being poured into the
tank if the water level is rising at 15 cm/min when the height of the water is 9cm.
SMU the water level
dh
is
rising ,
• DI IS the rate level
=
that enters
of water
Into the tank exceeds the rate
h=q
H of water that leaves the tank
H =
24
& r 6 E
notice ratio between
height 4: I
=
radius =
24
a h=4r 24=416)
r
-
-
I V= 's Trh f- It #12h
4
Oo V =
'T IT h
ddtf Igt
'
V h
Ig
=
= .
3h 2. DI
dt
du
Te
=
Tig °
IT .
3195 .
lls )
# =
V' in -
V' out
d¥ =
IT .
1215
16
✓ DI
'
out =
-
500 = 238.56
dt
238.56 =
Vin -
500
V' in = 738.56
Simultaneity
'
Water
'
is
being poured In @ rate of 738.56cm Im in 1h ,
500cm Im in flows So tank 238
'
out net of 56cm Im in
.
,
gains a .
, A 13 feet ladder is leaning against a house. The ladder slides down the wall at a rate
of 3 ft/min. How fast is the ladder moving away from the base of the wall when the
foot of the latter is currently 5 ft from the wall?
Y ? 52
' ' '
of
=
y ez t
y 13 12
+
y
-
-_ =
=
1=13
µ
X=s If =-3
FI = ? =-3
'
Ii = ?
⇐ Cx
Y
-15=11*91%17.7 : !÷:
.
shame .
2x .
II t
2g It
. =
0 215 ) .IE ,
+2112) .
-
3=0
5
×
10 -
II -
72=0 fit =
351=7.2 ftlmin
How fast is the area of the triangle changing?
Area D=
of BIH
⇐ ( A- ( Xy)
'
X. y
) (2) (
Xy) 121
'
A-
-
= =
-2 .
2
# ' 2)
=¥igt¥;¥H= Its 35¥
3)
IF
' ' -
= =
35.7 =
How fast is the angle between ladder and the ground changing?
* Hottel 'm't # in
(
'
.
SOH
#
FAH TOA =o+ He )
l Sth
-
-
tf I -
-
Ft( Sino F ) -
-
13 O
my coso.IT?-- f. fit ¥ .
=
( Ee)
need to find O
⑦
TIA 5 daff
- =
Cos @
=f=E
5 (5/13)
'
O COS
-
=
}
0=67.380
×
d§
-
=
radians linin
,
24 cm and a radius of 6 cm. Find the rate at which water is being poured into the
tank if the water level is rising at 15 cm/min when the height of the water is 9cm.
SMU the water level
dh
is
rising ,
• DI IS the rate level
=
that enters
of water
Into the tank exceeds the rate
h=q
H of water that leaves the tank
H =
24
& r 6 E
notice ratio between
height 4: I
=
radius =
24
a h=4r 24=416)
r
-
-
I V= 's Trh f- It #12h
4
Oo V =
'T IT h
ddtf Igt
'
V h
Ig
=
= .
3h 2. DI
dt
du
Te
=
Tig °
IT .
3195 .
lls )
# =
V' in -
V' out
d¥ =
IT .
1215
16
✓ DI
'
out =
-
500 = 238.56
dt
238.56 =
Vin -
500
V' in = 738.56
Simultaneity
'
Water
'
is
being poured In @ rate of 738.56cm Im in 1h ,
500cm Im in flows So tank 238
'
out net of 56cm Im in
.
,
gains a .
, A 13 feet ladder is leaning against a house. The ladder slides down the wall at a rate
of 3 ft/min. How fast is the ladder moving away from the base of the wall when the
foot of the latter is currently 5 ft from the wall?
Y ? 52
' ' '
of
=
y ez t
y 13 12
+
y
-
-_ =
=
1=13
µ
X=s If =-3
FI = ? =-3
'
Ii = ?
⇐ Cx
Y
-15=11*91%17.7 : !÷:
.
shame .
2x .
II t
2g It
. =
0 215 ) .IE ,
+2112) .
-
3=0
5
×
10 -
II -
72=0 fit =
351=7.2 ftlmin
How fast is the area of the triangle changing?
Area D=
of BIH
⇐ ( A- ( Xy)
'
X. y
) (2) (
Xy) 121
'
A-
-
= =
-2 .
2
# ' 2)
=¥igt¥;¥H= Its 35¥
3)
IF
' ' -
= =
35.7 =
How fast is the angle between ladder and the ground changing?
* Hottel 'm't # in
(
'
.
SOH
#
FAH TOA =o+ He )
l Sth
-
-
tf I -
-
Ft( Sino F ) -
-
13 O
my coso.IT?-- f. fit ¥ .
=
( Ee)
need to find O
⑦
TIA 5 daff
- =
Cos @
=f=E
5 (5/13)
'
O COS
-
=
}
0=67.380
×
d§
-
=
radians linin
,
