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koban [17]
3 years ago
13

Garwnicy nim

Mathematics
1 answer:
Vika [28.1K]3 years ago
8 0

Answer:

What is the equation of a circle with a radius of 7 and centered at point (3, -4)?

Step-by-step explanation:

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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
Find the product of 17892 and 36
solniwko [45]
The answer to 17892•36 is 644,112
6 0
3 years ago
Read 2 more answers
5. Solve v = w - 20 for w.​
slava [35]

v = w - 20

move -20 to the other side

sign changes from -20 to +20

to get w by itself

v+20= w-20+20

Answer:

w= v+20 or w= 20+v

5 0
3 years ago
Read 2 more answers
Stanley, the skunk, is traveling from point A to point B by taking a shortcut through the pond.A path that avoids the pond is 25
san4es73 [151]
Stanley the skunk will save about 15.5 feet.

This problem can be solve with the Pythagorean Theorem. The possible paths that Stanley can take make a right triangle. The legs of the triangle are 25 and 28, and the hypotenuse would be 37.5.

If Stanley went the long way, he would travel 25 + 28 = 53 feet. Taking the short way (hypotenuse) is 53 - 37.5 = 15.5 feet shorter.
7 0
3 years ago
Kira walks 8hole and one half blocks in 17 minutes.if kira continues to walk at the steady pace, how many blocks will she walk e
ZanzabumX [31]
8 1-and-a-half blocks would be 12 blocks, and so 12/17, because 12 blocks in 17 mins., so you divide 12 by 17 to get ---- blocks per minute, which is 12/17 as a fraction, or approx. 0.705882353 blocks per minute.
7 0
3 years ago
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