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Musya8 [376]
3 years ago
5

Short on time, please help!

Mathematics
1 answer:
kvv77 [185]3 years ago
3 0
56.3% hope it helped ok
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A cone-shaped paper drinking cup is to be made to hold 27 cm of water. Find the height h and radius r of the cup that will use t
andreyandreev [35.5K]

Answer:

  • r = 2.632 cm
  • h = 3.722 cm

Step-by-step explanation:

The formula for the volume of a cone of radius r and height h is ...

  V = (1/3)πr²h

Then r² can be found in terms of h and V as ...

  r² = 3V/(πh)

The lateral surface area of the cone is ...

  A = (1/2)(2πr)√(r² +h²) = πr√(r² +h²)

The square of the area is ...

  T = A² = π²r²(r² +h²)

Substituting for r² using the expression above, we have ...

  T = π²(3V/(πh))((3V/(πh) +h²) = 9V²/h² +3πVh

We want to find the minimum, which we can do by setting the derivative to zero.

  dT/dh = -18V²/h³ +3πV

This will be zero when ...

  3πV = 18V²/h³

  h³ = 6V/π . . . . . multiply by h³/(3πV)

For V = 27 cm³, the value of h that minimizes paper area is ...

  h = 3∛(6/π) ≈ 3.7221029

The corresponding value of r is ...

  r = √(3V/(πh)) = 9/√(π·h) ≈ 2.6319242

The optimal radius is 2.632 cm; the optimal height is 3.722 cm.

_____

The second derivative test applied to T finds that T is always concave upward, so the value we found is a minimum.

__

Interestingly, the ratio of h to r is √2.

8 0
3 years ago
Y + 8 = 2 i need help!!!!!
sergey [27]

Answer:

y = -6

Step-by-step explanation:

-6 + 8 = 2

3 0
3 years ago
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What’s the measure of X in this short answers are fine
miv72 [106K]

Answer:

28 = x

Step-by-step explanation:

62 =  angle BAC  since they are vertical angles

angle ABC is a right angle since KL is perpendicular to FG

Adding the angles in triangle ABC

BAC + ABC + BCA = 180

62 + 90 + BCA = 180

152 + BCA = 180

BCA = 180-152

BCA = 28

BCA = x since they are vertical angles

28 = x

3 0
3 years ago
Classify Angle 1 & Angle 2 by choosing the correct term from the choices below.
Elena L [17]

Answer:

complementary

Step-by-step explanation

Im not positive but theres a high chance its B

8 0
2 years ago
Use your plan to find the temperature at the top of Mt Everest.
Dmitry [639]

Answer:

- 61

Step-by-step explanation:

-3 - 58 = -61

times 1 is

is -61

7 0
3 years ago
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