### Find the centroid of the region in the first quadrant bounded by the given curves y=x^3 and x=y^3

This question aims to find the centroid of the region which is bounded by curves in the first quadrant. A centroid is the center point of any shape

### 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”

### The current in a wire varies with time according to the relation $I=55A-\left(0.65\dfrac{A}{s^2}\right)t^2$.

How many coulombs of charge pass a cross-section of the wire in the time interval between $t=0,s$ and $t=8.5,s$? Express your answer using two

### The integral represents the volume of a solid. Describe the solid. $\pi\int\limits_0^1(y^4−y^8)\,dy$

The integral represents the volume of the solid obtained by rotating the region $R={{x, y}| 0leq yleq 1, y^4leq xleq y^2}$of the $xy-$plane about the

### At a certain college, $6\%$ of all students come from outside the United States. Incoming students there are assigned at random to freshman dorms, where students live in residential clusters of $40$ freshmen sharing a common lounge area.

How many international students would you expect to find in a typical cluster? With what standard deviation? This question aims to find the expected