Find the Number B Such That the Line $y=b$ Divides the Region Bounded by the Curves

question 43

Multiple Choice

Find the number b such that the line $y=b$ divides the region bounded by the curves $y=x^{2}$ and $y=5$ into two regions with equal area.

• A) \(5^{1 / 2}\)
• B) \(5^{2 / 3}\)
• C) \(\frac{2}{3}\)
• D) \(5^{1 / 3}\)
• E) \(\frac{1}{3}\)

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Definitions:

Aneurysm

An abnormal bulge in the wall of a blood vessel, usually an artery, which can lead to the risk of rupture.

Claudication

Pain and cramping in the lower leg due to inadequate blood flow to the muscles, often associated with peripheral artery disease.

Infarction

The death of tissue due to a lack of blood supply, often resulting from a blockage in the vasculature serving the affected area.

Fibrillation

A rapid, irregular, and unsynchronized contraction of muscle fibers, particularly in the heart.