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
Write 100 times 100as multiplying 10 to a power by 10 to a power?<br>​
SCORPION-xisa [38]

Answer:

10^2 × 10^2

Step-by-step explanation:

Given that

Write 100 times 100 that would be multiplying  to the power by 10

So based on the above information

The equation that would be developed is

10^2 × 10^2

The same would be represented as an answer

4 0
3 years ago
4(x-1) + (x+2) + 3(x+1)
dusya [7]

Answer:

8x+1

Step-by-step explanation:

4(x-1) + (x+2) + 3(x+1)

4x-4 + x+2 + 3x+3

combine all x

4x+x+3x= 8x

combine all numbers without variables

(-4) + 2+3=1

8x+1

8 0
3 years ago
Write a how many units in 1 group word Problem for 4 divided by 2/3
Nastasia [14]

       

\displaystyle\bf\\4:\frac{2}{3}=4\times\frac{3}{2}=\frac{4\times3}{2}=2\times3=6



4 0
3 years ago
Name the three similar triangles correspondingly. Start with the original right triangle LMK, then the remaining two right trian
aleksandr82 [10.1K]

Answer:

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
PLEASE HELP!!!
kvasek [131]

Answer:

D

Step-by-step explanation:

Then you find the intersection and get the bisector without a protractor :)

7 0
3 years ago
Read 2 more answers
Other questions:
  • What is the opposite reciprocal for -1/5
    6·2 answers
  • Find the cosine of T.
    13·1 answer
  • You roll a number cube twice what is the probability of rolling a 2
    5·2 answers
  • Of the cartons produced by a​ company, ​% have a​ puncture, ​% have a smashed​ corner, and ​% have both a puncture and a smashed
    9·1 answer
  • Veronica's family is getting ready for
    11·1 answer
  • 8
    13·1 answer
  • Find the perimeter of the image below
    11·2 answers
  • Which digit in the following number is the one that determines its precision?
    9·1 answer
  • What is 129.392 rounded to nearest Ten?<br>​
    12·2 answers
  • (3,4) and (0, 5)<br> write a linear equation
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!