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blondinia [14]
2 years ago
9

Suppose that 6 years ago, Alice was four times as old as Betty. In 4 years from now, Alice will only be three times as old as Be

tty. How old is Betty today.
Mathematics
1 answer:
N76 [4]2 years ago
5 0
4b=a then plus 10 to see if the age holds true to 3b=a in ten years. Then since the question is how old is she today? You must either add 6 to young age (of20) or minus 4 from the older (of 30).
So Betty would be 26 today.
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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
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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.

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