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a. When we cough, the trachea (windpipe) contracts to increase the velocity of the air going out. This raises the questions of how much it should contract to maximize the velocity and whether it really contracts that much when we cough.
Under reasonable assumptions about the elasticity of the tracheal wall and about how the air near the wall is slowed by friction, the average flow velocity y can be modeled by the equation , , where is the rest radius of the trachea in centimeters and is a positive constant whose value depends in part on the length of the trachea. Show that is greatest when that is, when the trachea is about contracted. The remarkable fact is that ray photographs confirm that the trachea contracts about this much during a cough.
b. Take to be and to be and graph over the interval . Compare what you see with the claim that is at a maximum.
this question needs to be done pn matlab. Can anybody do this entire question on matlab and send the graph and graph codes
A spring is such that a 16 lb weight stretches it by 1.5 in. The weight is pulled down to a point
4 in below the equilibrium point and given an initial downward velocity of 4 ft/sec. An impressed
force of F(t) = 2 cos 74t is acting on the spring. Describe the motion.
Change the following point from polar to rectangular coordinate.
(3/2, n/12)
II. Evaluate f²(3ײ- 6x ‐2)dx
A small factory producing a single product has weekly fixed costs of production of $2,112 and weekly variable costs of $52x + 3/4 x2, where x is the quantity produced. the capacity of the factory is about 600 units.
Past experience suggests that the product’s price and quantity are linked by the following demand equation: p = 200 - 1/4 x (p, x > 0) where p = $ price/unit and x = quantity sold. You are required to:
(a) Find the level of production at which revenue is maximized
(b) Find any break-even points
Apply separation of variable to solve
x2uxy+9y2u=0
Evaluate the integral ∮c= 1 /(z-1)(z-2)(z-4) dz where C is |z| = 3 ?
A builder has 2400 feed of barrier and wants to barricade off a rectangular ground that borderlands a straight water flow. No barrier is required along the entire length of the water flow.
Find the dimension of the ground that has the largest area
Let f
f be a function such that at each point (x,y)
(x,y) on the graph of f
f, the slope is given by dy
dx
=1
2
x−1
4
y
2
dydx=12x−14y2. The graph of f
f passes through the point (1,−2)
(1,−2) and is concave up on the interval 1<x<1.5
1<x<1.5. Let k
k be the approximation for f(1.3)
f(1.3) found by using the locally linear approximation of f
f at x=1
x=1. Which of the following statements about k
k is true?
The velocity of a moving object is given by the function
𝒅𝑽=𝟓𝒕^2+2t-4/t^2
a) Integrate the function and find the distance travelled in metres between t=2 and t=5
b) Calculate the distance travelled using a numerical method and compare your answer with part A.
01) Identify the X intercepts of this quadratic function y = 2x- x²
(02) Find the coordinates of maximum point of y = -4x + 8x – 2 by using equation y by using equetion method.
(03) Graph the quadratic function y = -3x +x+1 and you are required to answer the followings by using the graph:
(i) Coordinates of maximum point
(ii) Axis of symmetry
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