256. [T] The formula for the area of a circle is A = ar², where r is the radius of the circle. Suppose a circle is expanding, meaning that both the area A and the radius r (in inches) are expanding. a. Suppose r = 2-100 (t+7)² b. (0)1 where this time in seconds. Use the chain rule A = d.dr dAdA dt dt to find the rate at which the area is expanding. Use a. to find the rate at which the area is expanding at t = 4 s. 89 90gmont
256. [T] The formula for the area of a circle is A = ar², where r is the radius of the circle. Suppose a circle is expanding, meaning that both the area A and the radius r (in inches) are expanding. a. Suppose r = 2-100 (t+7)² b. (0)1 where this time in seconds. Use the chain rule A = d.dr dAdA dt dt to find the rate at which the area is expanding. Use a. to find the rate at which the area is expanding at t = 4 s. 89 90gmont
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please solve 256. Thank you!
![5
-2
4
-3
a=0
=0
=3
)²²; a=1
=0
a=1
=2
a = 1
g(x)
0
3
1
24
2
0
-1
3
OLS
On of a freight train is given by
- in meters and t in seconds.
's
Cain speeding up or slowing
om a vertical spring is in
by the following
is C
dollars,
255. [T] The total cost to produce x boxes of Thin Mint
where
In
Scout cookies
weeks
Girl
C=0.0001x³-0.02x² + 3x + 300.
production is estimated to be x = 1600 + 100t boxes.
a. Find the marginal cost C'(x).
b.
()
b. Use Leibniz's notation for the chain rule,
dC = dc. dx,
dt
dx
time that the cost is changing.. -
c. Use b. to determine how fast costs are increasing
when t= 2 weeks. Include units with the answer.
Chapter 31 Derivatives
256. [T] The formula for the area of a circle is A = r,
where r is the radius of the circle. Suppose a circle is
expanding, meaning that both the area A and the radius r
(in inches) are expanding.
a. Suppose r = 2-
to find the rate with respect to
100
(t+7)
t
seconds. Use the chain rule
where t is time in
dA
di = dA. dr
the rate at which the area is expanding.
Use a. to find the rate at which the area is
expanding at t = 4 s.
257. [T] The formula for the volume of a sphere is
S=r³, where r (in feet) is the radius of the sphere.
Suppose a spherical snowball is melting in the sun.
a. Suppose r =
to find
(t+1)²-12 where t is time in
1:1
minutes. Use the chain rule d dS
=
dt
the rate at which the snowball is melting.
b. Use a. to find the rate at which the volume is
changing at t= 1 min.
dr dt
to find
258. [T] The daily temperature in degrees Fahrenheit of
Phoenix in the summer can be modeled by the function
T(x) = 94 - 10 cos[(x-2)] where x is hours after
midnight. Find the rato t
is
chau
the temperature
Chapter 31 Derivatives
3.7| Deri
3.7.1 Ca
3.7.2 Re
In this section we
whose derivative
limit definition a
functions. This f
The Deriv
We begin by co
the inverse of
f-¹(x). Look
point correspo
51 0
Thus, if f¹(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b1ec9e1-71c5-41a7-88e5-1ec0b0e62692%2F9b5348a0-5c38-4123-9ca1-751a64dc061b%2Fw7z895t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5
-2
4
-3
a=0
=0
=3
)²²; a=1
=0
a=1
=2
a = 1
g(x)
0
3
1
24
2
0
-1
3
OLS
On of a freight train is given by
- in meters and t in seconds.
's
Cain speeding up or slowing
om a vertical spring is in
by the following
is C
dollars,
255. [T] The total cost to produce x boxes of Thin Mint
where
In
Scout cookies
weeks
Girl
C=0.0001x³-0.02x² + 3x + 300.
production is estimated to be x = 1600 + 100t boxes.
a. Find the marginal cost C'(x).
b.
()
b. Use Leibniz's notation for the chain rule,
dC = dc. dx,
dt
dx
time that the cost is changing.. -
c. Use b. to determine how fast costs are increasing
when t= 2 weeks. Include units with the answer.
Chapter 31 Derivatives
256. [T] The formula for the area of a circle is A = r,
where r is the radius of the circle. Suppose a circle is
expanding, meaning that both the area A and the radius r
(in inches) are expanding.
a. Suppose r = 2-
to find the rate with respect to
100
(t+7)
t
seconds. Use the chain rule
where t is time in
dA
di = dA. dr
the rate at which the area is expanding.
Use a. to find the rate at which the area is
expanding at t = 4 s.
257. [T] The formula for the volume of a sphere is
S=r³, where r (in feet) is the radius of the sphere.
Suppose a spherical snowball is melting in the sun.
a. Suppose r =
to find
(t+1)²-12 where t is time in
1:1
minutes. Use the chain rule d dS
=
dt
the rate at which the snowball is melting.
b. Use a. to find the rate at which the volume is
changing at t= 1 min.
dr dt
to find
258. [T] The daily temperature in degrees Fahrenheit of
Phoenix in the summer can be modeled by the function
T(x) = 94 - 10 cos[(x-2)] where x is hours after
midnight. Find the rato t
is
chau
the temperature
Chapter 31 Derivatives
3.7| Deri
3.7.1 Ca
3.7.2 Re
In this section we
whose derivative
limit definition a
functions. This f
The Deriv
We begin by co
the inverse of
f-¹(x). Look
point correspo
51 0
Thus, if f¹(
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