Find dy/dx and d²y/dx². For x = et, y = te−t [Solved]

The first derivative dy/dx gives us the rate of change of y with respect to x which is $(e^{(-t)} – t * e^{(-t)})$ / $e^t$ and the second derivative d²y/dx² is [(- $e^{(-t)} + t * e^{(-t)}) * e^t – (e^{(-t)} – t * e^{(-t)}) * e^t] / e^{(2t)}$ = -2. To find dy/dx and d²y/dx² at […]

Evaluate the line integral where c is the given curve.

[ boldsymbol{ oint xy ds text{ where s is defined by } x = t^2 text{ and } y = 2t text{ over the interval } 0 leq t leq 4 } ] The aim of this question is to learn how to solve line integrals over some closed surfaces. To solve this question, we […]

A hurricane wind blows across a $6.00 \,m\times 15.0\, m$ flat roof at a speed of $130\, km/h$. Is the air pressure above the roof higher or lower than the pressure inside the house? Explain.

What is the pressure difference? How much force is exerted on the roof? If the roof cannot withstand this much force, will it “blow in” or “blow out?” The main objective of this problem is to determine the air pressure, pressure difference, and the force exerted by hurricane wind on the roof. Bernoulli’s equation is being […]