# Cups A and B are cone shaped and have heights of #39 cm# and #22 cm# and openings with radii of #17 cm# and #13 cm#, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?

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No, cup A will not overflow. When cup B is poured into cup A, the volume of cup B will fit within cup A because the volume of cup B is less than the volume of cup A. The final height of cup A will be the sum of its original height and the height of the liquid poured from cup B. To find the height of the liquid in cup A after pouring from cup B, you need to calculate the volume of cup B and then use the formula for the volume of a cone to find the height of the liquid in cup A. The formula for the volume of a cone is V = (1/3) * π * r^2 * h, where V is the volume, π is pi (approximately 3.14159), r is the radius, and h is the height. Calculate the volume of cup B using its dimensions and then use the volume to find the height of the liquid in cup A.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- Al-Khwarizmi, the father of modern mathematics try to solve the following: One square and ten roots of the same are equal to thirty-nine dirhems - What must be the square that when increased by ten of its own roots, amounts to thirty-nine?
- A triangle has two corners with angles of # ( pi ) / 4 # and # ( 7 pi )/ 12 #. If one side of the triangle has a length of #12 #, what is the largest possible area of the triangle?
- A triangular pyramid has a height of #x#, a side length of #2sqrt3#, and a volume of #7sqrt3#. What are the steps in order to find the height of the pyramid?
- A rectangle has perimeter 88 cm and length 38 cm. What is its width?

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