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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?

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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Find the equation of line b described below, in slope-intercept form

Serjik [45]

Given:

Line a is perpendicular to line b .

Line a passes through the points (1,-8) and (9,-12) .

Line b passes through the point (-8, -16).

To find:

The equation of b.

Solution:

Line a passes through the points (1,-8) and (9,-12) . So, slope of line a is

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m_a=\dfrac{-12-(-8)}{9-1}$

$m_a=\dfrac{-12+8}{8}$

$m_a=\dfrac{-4}{8}$

$m_a=-\dfrac{1}{2}$

Product of slopes of two perpendicular lines is -1.

$m_a\times a_b=-1$

$-\dfrac{1}{2}\times a_b=-1$

$b=2$

Slope of line b is 2.

If a line passing through a point $(x_1,y_1)$ with slope m, then equation of line is

$y-y_1=m(x-x_1)$

Line b passing through (-8,-16) with slope 2. So, equation of line b is

$y-(-16)=2(x-(-8))$

$y+16=2(x+8)$

$y+16=2x+16$

Subtract 16 from both sides.

$y=2x$

Therefore, the equation of line b is $y=2x$ .

7 0

3 years ago

In the diagram below segment DEF is shown(since all three letters are shown, they are collinear). If DE=3x+2, EF= x+5, and DF= 2

amm1812

The value of $x$ is 4.

By Geometry, we know that line segment $DF = DE + EF$ , which is equivalent to:

$DF = 3\cdot x + 2 + x + 5$

$DF = 4\cdot x + 7$ (1)

Now we solve algebraically the resulting expression.

If we know that $DF = 23$ , then we solve the equation for $x$ :

$4\cdot x + 7 = 23$

$4\cdot x = 16$

$x = 4$

The value of $x$ is 4.

We kindly invite to see this question on line segments: brainly.com/question/23297288

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3 years ago

A = 1/2ha +1/2hb solve for b

meriva

Answer:

A=1+1+2ha+2hb

A=2+2ha+2hb

A=2ha+2+2hb

A=<u>4ha</u>+<u>2hb</u>

4 = 4

A=½

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4 years ago

What is the measure of EG?

IrinaVladis [17]

The first thing you should know in this case is that a circumference has a total measure in 360 degrees.
We have then that the formula to find EG in this case is:
EG + GF + FE = 360
We cleared EG:
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We substitute the values:
EG = 360-83-66
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3 years ago

Can anyone help me with this

Natalka [10]

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5 0

3 years ago

Read 2 more answers