Which of the following integrals are improper integrals? 1. int_0^3(3-x)^2 3dx 2. int_1^16 (e^sqrtx)/sqrtx dx

The boom weighs 2600N. The boom is attached with a frictionless pivot at its lower end. It is not uniform; the distance of its center of gravity from the pivot is 35% of its length. a) Find the tension in the guy wire and the horizontal and vertical components of the force exerted on the boom at its lower end. b) Does the line of action of the force exerted on the boom a tits lower end lie along the boom?

Flux through a Cube (Eigure 1) A cube has one corner at the origin and the opposite corner at the point (L, L, L). The sides of the cube are parallel to the coordinate planes

A 2.0-kg projectile is fired with initial velocity components ${\displaystyle v_{0x}=30}$ m/s and ${\displaystyle v_{0y}=40}$ m/s from a point on the earth's surface. Neglect any effects due to air resistance. What is the kinetic energy of the projectile when it reaches the highest point in its trajectory? How much work was done in firing the projectile?

Two snowcats tow a housing unit to a new location at McMurdo Base, Antarctica, as shown in the figure. The sum of the forces ${\displaystyle F_A}$ and ${\displaystyle F_B}$ exerted on the unit by the horizontal cables is parallel to the line L, and ${\displaystyle F_A=4200}$ N. Determine ${\displaystyle F_B}$? Determine the magnitude of ${\displaystyle F_A+F_B}$?

A convex lens is held over a piece of paper outdoors on a sunnyday. When the paper is held 26cm below the lens, the sunlight isfocused on the paper and the paper ignites. What is the focallength of the lens?

Some advanced textbooks define entropy by the formula ${\displaystyle S=-k\sum _s\rho \left(S\right)\ln \rho \left(S\right)}$. Where the sum runs over all microstates accessible to the system and P(s) is the probability of the system being in microstate s. (a) For an isolated system, ${\displaystyle \mathcal{P}\left(s\right)=\frac{1}{x^2}.\mathrm{\Omega }}$ for all accessible states s. Show that in this case the preceding formula reduces to our familiar definition of entropy. (b) For a system in thermal equilibrium with a reservoir at temperature T ${\displaystyle \mathcal{P}\left(s\right)=e^{-E\left(s\right)x^2.kT}{x}^2}$ Z. Show that in this case as well, the preceding formula agrees with what we already know about entropy.

The electric field strength between two parallel conducting plates separated by 4.00 cm is ${\displaystyle 7.50\times {10}^{4}V}$. (a) What is the potential difference between the plates? (b) The plate with the lowest potential is taken to be zero volts. What is the potential 1.00 cm from that plate and 3.00 cm from the other?