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kipiarov [429]
2 years ago
10

PLEASE I don't understand how to do this, 50 Points for anyone who solves it!

Mathematics
1 answer:
Lana71 [14]2 years ago
3 0

Answer:

  • 170°

Step-by-step explanation:

<u>∠WYX is the inscribed angle and equal to half of the intercepted arc WX</u>

  • mWX = 2m∠WYX = 2(42x + 1) = 84x + 2

<u>Sum of arc measures add to 360°:</u>

  • 29x - 1 + 65x + 3 + 84x + 2 = 360
  • 178x + 4 = 360
  • 178x = 356
  • x = 2

<u>Plug in the value of x and find measure of the arc WX:</u>

  • mWX = 84*2 + 2 = 170°
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A cardboard box without a lid is to have a volume of 8,788 cm3. Find the dimensions that minimize the amount of cardboard used.
Montano1993 [528]

Answer:

  x = y = 26 cm; z = 13 cm

Step-by-step explanation:

The generic solution for the minimum material in an open-top box is that the box is square and half as high as it is wide. It is half a cube of twice the volume.

The dimensions of the square base are ...

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Then the height is half that, or 13 cm.

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_____

If you need to see the development, you can use the method of Lagrange multipliers to find the minimum area for the given volume;

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We require each of the partial derivatives of L with respect to x, y, z, and λ to be zero.

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  partial with respect to x: 0 = y+2z +λyz

  partial with respect to y: 0 = x +2z +λxz

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  partial with respect to λ: 0 = xyz -8788

From the first two equations, we have ...

  λ = (y +2z)/(yz) = 1/z +2/y

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Equating these expressions for λ, we find ...

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The third equation then tells us ...

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Comparing this to either of the first two expressions for λ, we see ...

  1/z +2y = 2/x +2/y   ⇒   z = x/2

This is the result we started the answer with:

  x = y = 2z = ∛(2·8788 cm³)

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Step-by-step explanation:

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