Help with calculus question? do you know what test it is from/ can you help?
A particle moving along a curve in the xy-plane has position (x(t), y(t)) at time t>0 where dx/dt = ((6/t)-3)^(1/3) and dy/dt = te^-t At time t = 3, the particle is at the point (5,4) Is there a time t at which the particle is farthest to the right? If yes, explain why and give the value of t and the x-coordinate of the position of the particle at that time. If no, explain why not. Describe the behavior of the path of the particle as t increases without bound.
How do I calculate quantity of steel in R.C.C slab/column/beam?
If you wish to know some thumb rules,(This is purely based on my experience.)You need to calculate how much concrete is required to cast the member first.Example: Consider slab area is 400 square meter, thickness of the slab is 150 mm.Concrete quantity required to cast this slab is 400*0.15 = 60 Cubic meter. After calculating concrete quantity, you can remember these thumb rules just for getting a basic idea of how much quantity of steel is required in those structural members.Steel quantity in a conventional slab (excluding its beams) will be around 60 to 65 Kg per Cubic meter.In beams it will be around 200 to 220 kg per cubic meter.In columns it'll be around 200 to 250 kg per cubic meter.For raft footings it'll be around 100 to 120 kg per cubic meter.If you wish to know the detailed answer in simple terms, go through this link below:Kasee Sreenivas's answer to Can anyone tell me how steel quantity is calculated in the construction of a building, like footings, beams, columns, and slabs? How would you explain the formula?If you have any ambiguity, feel free to drop in a message. I would be happy tohelp
Calc 2 helpp!!!!! i don't know where to begin?
1. Consider the area shown below. The top curve (in blue) is y=x^(1/4), and the bottom curve (in red) is y=x , and we have used the notation Dy for delta y. here's a picture http://i29.photobucket.com/albums/c274/xxspotchxx/homeworkk/1.png #2 Consider the volume of the region shown below, which shows a right circular cone with top radius 1 cm and height 5 cm. We have used the notation Dy for delta y http://i29.photobucket.com/albums/c274/xxspotchxx/homeworkk/2.png http://i29.photobucket.com/albums/c274/xxspotchxx/homeworkk/22.png please helppp fill in the blanks for eachh picturee
Mathematics: What is the most beautiful theorem proof, and why?
Though their are lot of elegant proofs in Mathematics, here I am posting two of those.1. Proof by contradiction of an infinite number of primes, which is fairly simple:Assume that there is a finite number of primes.Let G be the set of all primes [math]P_1, P_2, P_3... P_n[/math]Compute [math]K= P_1 \times P_2 \times P_3 \times ... \times P_n +1[/math].If K is prime, then it is obviously not in G.Otherwise, none of its prime factors are in G.Conclusion: G is not the set of all primes.For more detail one can look at thisEuclid's theorem2. There exist two irrational numbers x, y such that [math]x^y[/math] is rational. If [math]x=y=\sqrt{2}[/math] is an example, then we are done; otherwise [math]\sqrt{2}^\sqrt{2}[/math] is irrational, in which case taking [math]x=\sqrt{2}^\sqrt{2}[/math] and [math]y=\sqrt{2}[/math] gives us:[math]\left(\sqrt{2}^\sqrt{2} \right)^\sqrt{2} = \sqrt{2}^\left(\sqrt{2}\sqrt{2} \right) = \sqrt{2}^2 = 2[/math]Though now we have Gelfond-Schneider Theorem which implies this.Edit 1: One more proof which is a bit geometrically intuitive. In number theory, there is a curious relationship between the sum of consecutive cubes of the set of natural numbers and the square of the sum of the corresponding numbers themselves. It can be stated as: [math]\left(1 + 2 + 3 + ... +n \right)^2 = 1^3 + 2^3 +3^3 + ... + n^3 [/math] [math]n\varepsilon N[/math]In the picture below I have made a square that is 15 by 15. The bars on the side and bottom of the square show that the square has an area equal to, 1 + 2 + 3 + 4 + 5. (Notice that I have colour coded the numbers). The total area of the square is equal to the sum of these numbers, squared (The left hand side of the problem.). I have arranged the squares of these numbers in the large square. This leaves an area to account for.In the next picture you will see that I have divided the remainder into squares. The two rectangles can be rearranged into squares.The total area can be written as shown.This is the right hand side of the problem and completes the solution.This, of course is interesting because the solution requires an area model, when we would expect an volume problem.Source:http://users.tru.eastlink.ca/~br...This page has some more interesting problems you can look at.