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cluponka [151]
4 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]4 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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JulijaS [17]

Answer:

Robin's age is n - 5

Step-by-step explanation:

Let n represent Nathan's age. Robin is younger, 5 years younger. Robin's age should be a smaller number than Nathan's age. So we'll take away 5 years from Nathan's age:

n - 5

This is Robin's age in terms of Nathan's age.

4 0
2 years ago
Which number is a rational number, but not an integer? - 144−−−√- square root 218/12 184/4 99
iris [78.8K]

Answer:

184/4

Step-by-step explanation:

A rational number is a number in the form p/q where the numerator and denominator (p and q) are both integers but the denominator q is not equal to zero (q ≠ 0)

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From the question:

-144 is an integer because it is a negative whole number. Also -144 can be represented as -144 / 1, hence it is a rational number

√218/12 is neither a rational number or integer

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99 is an integer because it is a positive whole number. Also 99 can be represented as 99 / 1, hence it is a rational number

6 0
3 years ago
The sum of two numbers is 72 and one of them is five times the other
NeTakaya

Answer:

60+12

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8 0
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PLEASE HELP!!!
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Coordinates after 270 clockwise rotation is (-6,-2), (-3,-5) and  (-8, -5).

<h3>What is graph?</h3>

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given coordinates are: (-2,6) , (-5, 3) and (-5, 8)

For 270° clockwise about the origin, we have the following rule:

(x, y)= (-y, x)

So,

coordinates  (-2,6) change into (-6,-2)

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coordinates  (-5, 8) change into (-8, -5).

Learn more about this concept here:

brainly.com/question/12673036

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What is equivalent to 6/8
sineoko [7]
The answer is 3/4 because I divided the fraction by two
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