PLEASE HELP ASAPShade the following: (B - A') intersects (A - C)

Mathematics

1 answer:

Alexeev081 [22]2 years ago

5 0

Step-by-step explanation:

Look at the picture.

A' - The complement of a set is the set of all elements in the given universal set U that are not in A.

B - A - The set difference of sets A and B is the set of all elements in A that are not in B.

A ∩ B - The intersection of sets A and B is the set of all distinct elements that are in both A and B.

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igor_vitrenko [27]

Answer: 30 cm

Step-by-step explanation:

The volume of the composite solid is 17000 cm³. To find h, we must first subtract the volume of the half cylinder from the composite volume.

From the figure, AE = MK, and so the radius of the half cylinder is 10cm. The volume of the half cylinder is thus $\frac{1}{2}$ the volume of a cylinder. The volume of a cylinder is πr²h. So a half cylinder is 1/2 πr²h. This gives us a volume of $\frac{1}{2} (\frac{22}{7})(10 cm)^2(28 cm) = 4400 cm^3$ .

Thus, the volume of the right prism is 17000cm³ - 4400cm³ = 12600cm³. Consider the cross-section ABKJ. If we multiply this by AE, we'll have the volume of the right prism.

The ABKJ is a trapezoid so it's area is $\frac{1}{2}(AJ + BK) \cdot AB$ . Thus the volume of the right prism is $\frac{1}{2}(AJ + BK) \cdot AB \cdot AE$ . This gives us $\frac{1}{2}(28 + 14) \cdot h \cdot 20 = 12600$ , and thus h = 30 cm.