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Express as a triple iterated integral the volume of the solid Q in the first octant bounded by the coordinate planes and the graphs of y^2+z^2=4 and 2z+x=4.Be certain to sketch the region Q for full credit


Water is being poured at the rate of 2\pi m^(3) min into an inverted conical tank that is 12-meter deep with a radius of 6 meters at the top. if the water level is rising at the rate of 1/6 m/min and there is a leak at the bottom of the tank, how fast is the water leaking the water is 6-meter deep?


The function,f: [-1,1]×[2,1] → R, defined by

f(x,y)= { x ; y is rational


{ 0 ; y is irrational


is integrable or not.


True or false with full explanation


The function,f is defined by F(x,y)=x^2+xy+y^2 is integrable over [2,1]×[1,2]. True or false with full explanation


Your classmate requests you to help him/her in understanding the solutions of the

lim

t→0

(1−cos3t)/

(3t)

= 0, via writing. How do you apply your knowledge based on what you have


learned from this module in doing the task?


  1. List any TWO materials that you can include in the appendix of a long essay.
  2. In a single paragraph, describe what an abstract is.

How to complete rational numbers? Mention processes.


Solve for the confidence interval estimate of the population proportion.


Mikay conducted poll survey in which 520 of 1200 randomly selected voters indicated their preference for a certain candidate. What is the true population proportion of voters who prefer the candidate using 95% confidence interval?


The function,

f(x,y)= { x ; y is rational

{ 0 ; y is irrational

is integrable or not

True or false with full explanation


4.The profit function and the average cost function for a product of a company are

p(x) = - 4000 + 194x - 0.149x2 in ringgit and ________ 4000

C(x) = 6 - 0.001x + ________

x

ringgit respectively, when x is the quantity sold in units. Find


(a) the total cost function

(b) the revenue function

(c) the quantity which will maximize the profit

(d) the maximum profit

(e) the price at maximum profit


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