Question

The cranial nerves generally innervate structures of the head and neck. Which pair of cranial nerves also innervates various structures in the ventral body cavity?

To what parts of the body is this nerve connecting the brain?

Question 5496: Solve the equation below for b:

|3b + 4| = 11

Explain it using any of these vocab words:

Polynomial expressions
Graphing polynomial expressions
Dividing polynomials
Solving polynomial equations
Rational functions

Answer 1

1. The vagus nerve (cranial nerve X) is the pair of cranial nerves that innervates various structures in the ventral body cavity, connecting the brain to organs such as the heart, lungs, and digestive system.

2. The value of b is
`\[ b = (-7)/(3), \, (7)/(3) \]`.

Step-by-step explanation:

1. The vagus nerve, also known as cranial nerve X, plays a crucial role in innervating structures beyond the head and neck. Emerging from the medulla oblongata, it descends through the neck and chest into the abdominal cavity. The vagus nerve branches out extensively, forming connections with organs in the ventral body cavity. It innervates the heart, influencing heart rate and contraction, and reaches the lungs, regulating bronchial smooth muscle. Additionally, the vagus nerve extends into the digestive system, where it contributes to the function of organs such as the stomach and intestines.

2. To solve the equation |3b + 4| = 11, we'll consider two cases:

1. 3b + 4 = 11: In this case, subtract 4 from both sides and divide by 3 to find
`\(b = (7)/(3)\).`

2. -(3b + 4) = 11: Here, multiply through by -1, subtract 4, and then divide by 3, resulting in
`\(b = (-7)/(3)\).`

These two solutions cover all possibilities, as the absolute value expression |3b + 4| can either be 3b + 4 or -(3b + 4) depending on the sign of 3b + 4.