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cluponka [151]
3 years ago
15

Coughing forces the trachea (windpipe) to contract, which in turn affects the velocity of the air through the trachea. The veloc

ity of the air during coughing can be modeled by v = k(R – r)r2, 0 ≤ r < R, where k is a constant, R is the normal radius of the trachea, and r is the radius during coughing. What radius r will produce the maximum air velocity?
Mathematics
1 answer:
Rzqust [24]3 years ago
8 0
To find the maximum velocity you have to differentiate the function respect to r.

v = k(R - r)r^2 = kRr^2 - krr^2 = kRr^2 - kr^3

k and R are constants.

=> v' = 2kRr - 3kr^2 = kr(2R - 3r)

maximum velocity => v' = 0 => kr(2R - 3r) = 0

r = 0 or 2R - 3r = 0 => r = 2R / 3

Answer: r = 2R / 3




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Answer:

The cost of per ounce of oat cereal is $0.04 less than per ounce cost of rice.

Step-by-step explanation:

Given:

Cost of 15 ounces of oat cereal box = $3.90

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To compare the unit prices of the the boxes.

Solution:

Using unitary method to find the unit prices:

If 15 ounce of oat box cost =$3.90

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∴ 1 ounce of rice would cost = \$\frac{3.30}{11}=\$0.3

∴ Per ounce cost of rice = $0.3

Difference in unit costs of oat and rice = \$0.3-\$0.26=\$0.04

On comparing the the unit costs of oats and rice, we find out that the cost of per ounce of oat cereal is $0.04 less than per ounce cost of rice.

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