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 […]

A particle moves along the curve y=2 sin(pi x/2). As the particle passes through the point (1/3, 1), its x-coordinate increases at a rate of sqrt{10} cm/s. How fast is the distance from the particle to the origin changing at this instant?

The question aims to find the rate of change in distance of the particle from the origin as it moves along the given curve and its movement increases. The background concepts needed for this question include basic calculus, which includes derivatives and calculating distance by using distance formula and some trigonometric ratios. Expert Answer Read […]

If xy+8e^y=8e , find the value of y” at the point where x=0.

This question aims to find the value of the second derivative of the given non-linear equation.  Nonlinear equations are those which show up as curved lines when graphed. The degree of such an equation is two or more, but not less than two. The curvature of the graph increases as the value of the degree […]

If xy+6e^y=6e, find the value of y” at the point where x=0.

This question aims to find the second derivative of the given implicit function. A function’s derivatives describe the rate of change of that function at a given point. If the dependent variable, say $y$, is a function of the independent variable, say $x$, we usually express $y$ in terms of $x$. When this occurs, $y$ […]

Each limit represents the derivative of some function f at some number a.

Find the number $a$ and the function $f$ given the following limit: [lim_{tto 1} frac{t^4 + t – 2}{t-1}] Read moreSolve the equation explicitly for y and differentiate to get y’ in terms of x.The aim of this question is to learn the differentiation (calculation of derivative) from first principles (also called by definition or […]