1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
deff fn [24]
3 years ago
10

A soft drink can is h centimeters tall and has a radius of r cm. The cost of material in the can is 0.0005 cents per cm2 and the

soda itself costs 0.002 cents per cm3. The cans are currently 4 cm tall and have a radius of 4 cm. Use calculus to estimate the effect on costs of increasing the radius.
Mathematics
2 answers:
lord [1]3 years ago
7 0

Answer:

Step-by-step explanation:

Given:

Cost of material, Cm = 0.0005 cents per cm2

Cost of soda, Cs = 0.002 cents per cm3

Height, h = 4 cm

Radius, r = 4 cm

Surface area of a cylinder, Ac = 2πrh + 2πr^2

= 2π × 4 × (4 + 4)

= 64π cm^2

Volume of a cylinder, V = πr^2 × h

= π × (4^2) × 4

= 64π cm^3

dAs = dAs/dr ×dr + dAs/dh × dh

= 2πh + 4πr × dr + 2πr × dh

= 8π + 16π × dr + 8π × dh

= 24π dr + 8π dh

dr = 0.1 cm

dh = -0.8 cm

dAs = 2.4π - 6.4π

= -4π × 0.0005

Cost = -0.00628

dV = dV/dr ×dr + dV/dh × dh

= 2πrh× dr + πr^2 × dh

= 32π × dr + 16π × dh

dr = 0.1 cm

dh = -0.8 cm

dAs = 3.2π - 12.8π

= -9.6π × 0.002

Cost = -0.603

Total cost = -0.00628 - 0.603

= -0.609

kvasek [131]3 years ago
3 0

Answer:

Step-by-step explanation:

Given:

  • The cost of material in the can is 0.0005 cents per cm2
  • The soda itself costs 0.002 cents per cm3.

1. The Volume of the can is: V = Sh = πr^{2} h = 3.14*4^{2} *4 = 200.96 cm^{3}

2. The surface area of the can is

S = 2πr^{2} + 2rhπ = 2*3.14*4^{2} + 2*4*4*3.14

= 100.48 + 100.48

= 200.96 cm^{2}

The total cost of the can is:  0.0005*200.96cm^{2}  + 0.002*200.96 cm^{3}

If we increase the radius, the cost will be increased as well. Because the volume and the surface area will increase.

You might be interested in
If the function f(x)=-1/2x-7 were graphed, which of the following would be true? A. The y-values would be negative. B. As the x-
vagabundo [1.1K]

f(x)= -1/2x-7 (better expressed as   f(x) = (-1/2)x - 7  )   has a negative slope, so as x increases, y decreases.  Answer D is correct.


3 0
3 years ago
Read 2 more answers
John took a 5-mile walk to his friend's house.
lianna [129]

Answer:

2 hours

Step-by-step explanation:

add the time before and after adding 30 mins. (1 hour and 45 minutes/ 2 hours and 15 mins.) then divide by 2

7 0
3 years ago
9062016 in expanded form
Sloan [31]
9000000+60000+2000+10+6
Hope this is what you were looking for!!
6 0
3 years ago
Explore the opportunity district in the Expo school site. What are the geometric shapes we can include to utilize maximum space?
maxonik [38]
Area i would pack probably water and good and my phone and the main things you need to survive would be good and water and a shelter
5 0
3 years ago
3
weqwewe [10]

Answer:

The y-intercept is –2.

The slope is Negative three-fifths

Step-by-step explanation:

I got it right on edge

3 0
2 years ago
Other questions:
  • What is the GCF of 8,18
    5·1 answer
  • Let f = {(–2, 4), (–1, 2), (0, 0), (1, –2), (2, –5)}.
    15·2 answers
  • Can an expression like 2a+7 be true or false
    8·2 answers
  • Find the slope of the line whose equation is 8y = 2x 4.
    6·1 answer
  • What value is equivalent to 2³ · 3(4)?
    8·1 answer
  • Use the distributive property to remove the parentheses.<br> -5(-6y+4x-5)
    6·1 answer
  • What is the distance between the points (4,5) and (10,13) on a coordinate plane?
    15·1 answer
  • The cost of taking your pet aboard the air flight with you in the continental US varies according to the airlines. The five numb
    14·1 answer
  • Give 5 Examples of Linear Equation in Two Variables​
    9·2 answers
  • Here is Diya's work writing the expression 6 - 2x + 5 + 4x with fewer terms. Describe the mistake that Diya made.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!