MAC 2311C Lecture Notes - Lecture 7: Xio, Normandy Landings
22 Jun 2018
School
Department
Course
Professor
3.9 Related Rates
° Find an equation that relates the
two quantities and then use the
Chain Rule to differentiate both
Sides with respect to tim
Example l:Air Is being pumped into
aSpherical balloon So that its
Volume increases at a rate of 1oo cm%
How fast is the radius Of the bauoh increasing
when diameter is 50cm ?
Solution :
given :±✓ =100 cm31S -
ssooay
dt 5
unknown :Iwhen r =25cm
dt
dif ✓=¥#r3
both
Sides dv CV dr 2I
-=--=4cTr at
dt dr ⇒
±=±
idt
de 4Tr2
g÷=(
1007 .it#zs5=zt@
100 =4#✓
2D=
de
100
=D= =100 -1-
⇒
72 dt 4(zg2)eT ZST
3.9 HW
1.
6¥ |15ft
III µ
dx
y×
Given
.
.-=4FECS
dt
at 40ft
unknown :I(xty )
DE
X=horizontal distance
1s40 Of man from pole
to
= I
t =time
y
=horizontal distance
Is =
-6 from the man to
Xty Ythe tip of his Shadow
lsy =Gxtay
4g
- -ax £C×+g7=F€( + + Ex )
y= }×
=§da±
=5- is
3
gdecxty )
=¥-@
2.PV =C
IV=800cm
3
/volume {onstant
Pressure p =100 1hPa
Pincrease
(0(apg
min
at what rate is the volume decreasing at
this instant
DP
G:-=co Kpalm
DE
F:d✓
=>at ✓=800cm }
-
.
dt p=100 hPa
p✓=C
dp
pI+v-=o
DE DE
DI =-vdp
dt To -
DE
800
=--(10 )
100
du
-=-
80 -answer format
dt Tdecreasing @
I80 Antonin
dont keep
veg in answer
