Corrigez les phrases ci-dessous; 1. Quand viendras tu me visiter? 2. Il faut que je sort de la maison 3. J'ai fait une erreur
1. Quand viendras me rendre visite? 2. If faut que je sorte de la maison 3. J'ai commit une erreur
Solve the differential equation below: dy / x = y dx
The differential equation above is described as separable equation. A separable equation is one that allows you to put all alike terms together without being multiplied by a different term, ie; all x's one one side and all y's on the other side. In this case, we can divide y on both sides to get dy / (x*y) = dx Multiply ln x on both sides to get dy / y = x dx Now, we can integrate both sides of the equation lny = (1/2) x^2 + c Note that I did not add a constant when finding the derivative of y, yet I did so for x. This is because I am solving for y as a function of x. I could have a constant, let's say b, at y but move it to the right side and it adds up to the constant c, which becomes another constant. Now use expontial to remove the ln before y, e^(lny) = e^[(1/2) x^2 + c] We get y = e^[(1/2) x^2 + c] Note: e to the power of lna = a y = e^[(1/2) x^2]+ e^c e^c is a constant, let's call it k y = e^[(1/2) x^2]+ k The above is the solution to the differential equation.
Assume that you performed a sieve analysis for a type of soil and the result came out as follows; 65% material retained on No. 4 sieve, 32% retained on No. 200 sieve, Cu = 3 and Cc = 1. How would you classify the soil above, using USCS?
If less than 50% of material passes No. 200 sieve, that implies that the soil is coarse-grained, otherwise it would be fine-grained. A soil that is coarse grained can be either gravel or sand. To determine if it is gravel, the material that is retained at No. 4 sieve needs to be more than 50%, otherwise it is sand. The test results show that 65% is retained at No. 4 and 32% is retained at No. 200, thus only 3% passes No. 200. This implies that the soil is coarse grained. More than 50% is retained at No. 4, which means that the soil is gravel. According to USCS, Cu is equal or greater than 4 and Cc is between 1 and 3, then is it consider well-graded, otherwise it is poorly-graded. In this case, Cu is less than 4, thus the soil is poorly-graded. Therefore, the USCS classification is poorly-graded gravel, (GP).