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Show that improper integral ∫ x^2/((e^x)-1) is converging.(integral limit 0 to positive infinity)
Determine the domain of the function f(x)=-x-10/-3x^3+5x^2+10x
A computer retailing company specializes in the sale of jump drives to community college students.
The demand function for jump drives is P= X2 +10X +1000
dollars
For the same company the average cost function is given as: c= 22 +36x +100 -2/x
dollars
Where p is the price in dollars and x represents units of output.
i) Determine the revenue function
ii) Determine the cost function
iii) Determine the profit function
iv) Find the price and output that will maximize profit.
v) Find the maximum profit
Suppose you are buying face mask for yourself, your friends, and family during this covid-19
pandemic. The face mask shop has a deal going, if you buy one facemask for 35 pesos, then
additional face masks are only 30 pesos each. Using a short bond paper, do the following:
a. Represent this situation into a rational equation showing the price per face mask based
on the number of face masks.
b. Determine the horizontal asymptote and explain what the horizontal asymptote
represents.
c. Graph the function appropriately and determine its domain and range.
d. Is the original function one-to-one? Explain
Use the Chain Rule to determine an equation for the acceleration when 𝑎 = 𝑑𝑣/ 𝑑𝑡
When 𝑣 = (2𝑡2 + 3)4
and
When 𝑣 = ln(4𝑡3 − 1)
The gain of an amplifier is found to be 𝐺 = 20 ln(𝑉𝑜𝑢𝑡). The tasks are to find equations for: a) Draw a graph of Gain against Vout between 𝑉𝑜𝑢𝑡 = 1 and 𝑉𝑜𝑢𝑡 = 10 b) Determine the gradient of the graph at 𝑉𝑜𝑢𝑡 = 2 and 𝑉𝑜𝑢𝑡 = 5 c) Find the derivative 𝑑𝐺/ 𝑑𝑉𝑂𝑢𝑡 and calculate its value at 𝑉𝑜𝑢𝑡 = 2 and 𝑉𝑜𝑢𝑡 = 5 d) Compare your answers for part b) and part c) e) Find the second derivative 𝑑2𝐺/ 𝑑𝑉𝑂𝑢𝑡 2
Given the function f(x)=x^1/3 + x sqrt x - 1, find formulas to
(a) compress the graph horizontally by a factor of 2 followed by a reflection across the y-axis.
(b) Stress the graph vertically by a factor of 1.5 followed by a reflection across the y-axis.
Write a Mathematica code to display the functions in (a) and (b). Your Mathematica code should produce the graph as displayed in Fig. I(a) and I (b), where the blue, red and brown curves refer to the function f(x),g1(x),g2(x) respectively. g2(x) is the final function while g1(x) is the intermediate function.
F. Determine the length of the parametric curve given by the following parametric equations. x=3sin(t) y=3cos(t) 0<t<2π
Currently the sowing of wheat is taking place in Pakistan till December, the harvesting season will
begin in March. So, the farmers wants to build a silo in the form of cylinder to keep the wheat inside
the silo after harvesting. For this purpose, they have to built silo of different sizes having 2000 cubic
units and 4000 cubic units. Moreover, the top of the cylinder is hemi-sphere. The cost of construction
of per unit surface area is thrice as great for the hemisphere as it is for the cylindrical sidewall.
Determine the dimensions to be used and cost of construction is to be kept to a minimum. Neglect the
thickness of the silo and waste in construction. Finally, use MATLAB to write a program which will
provide you the optimal dimensions subject to the constraint of cost. The program will take dimensions
of the Silo as input and return the cost and quantity of each size.
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
