What are the data modeling concepts used in MongoDB? What are the main CRUD operations of MongoDB?

Perform the indicated operation or operations.

$$\frac { ( 5 x - 3 ) ^ { 6 } } { ( 5 x - 3 ) ^ { 4 } }$$

How many 4-m-high flights of stairs must an overweight person weighing $75 \mathrm{~kg}$ climb to atone for the indiscretion of eating a 500-Cal hamburger? Assume that there is a $20 \%$ efficiency in converting nutritional energy to mechanical energy. The gravitational force of an object of mass $m \mathrm{~kg}$ is $F=m g$, where the gravitational constant $g$ is $9.8 \mathrm{~m} \cdot \mathrm{s}^{-2}$.

A $1.40-\mathrm{kg}$ block slides with a speed of $0.950 \mathrm{~m} / \mathrm{s}$ on a frictionless horizontal surface until it encounters a spring with a force constant of $734 \mathrm{~N} / \mathrm{m}$. The block comes to rest after compressing the spring $4.15 \mathrm{~cm}$. Calculate the spring potential energy, $U$, the kinetic energy of the block, $K$, and the total mechanical energy of the system, $E_f$ for compression of $2.00 \mathrm{~cm}$.

Why is it important to know how to use algebraic operations by hand when calculators are available?

A $100-\mathrm{kg}$ patient walks the treadmill at a speed of $3 \mathrm{~m} / \mathrm{s}$, and $\theta_{\text {in }}=30^{\circ}$ for $5 \mathrm{~min}(300 \mathrm{~s})$. What is the mechanical power output of the patient in watts? (Use $g=10 \mathrm{~m} / \mathrm{s}^2$.) A. $300 \mathrm{~W}$ B. $1500 \mathrm{~W}$ C. $3000 \mathrm{~W}$ D. $7500 \mathrm{~W}$

Servers can be designed to limit the number of open connections. For example, a server may wish to have only N socket connections at any point in time. As soon as N connections are made, the server will not accept another incoming connection until an existing connection is released. Explain how semaphores can be used by a server to limit the number of concurrent connections.

A $1.20\ \mathrm{kg}$ ball is projected straight upward with an initial speed of $18.5\ \mathrm{m/ s}$ and reaches a maximum height of $14.7\ \mathrm{m}$. (a) Show numerically that total mechanical energy is not conserved during this part of the ball's motion. (b) Determine the work done on the ball by the force of air resistance. (c) Calculate the average air resistance force on the ball and the ball 's average acceleration.

An oil pump is drawing 44 kW of electric power while pumping oil with $\rho=860 \mathrm{kg} / \mathrm{m}^{3}$ at a rate of $0.1 \mathrm{m}^{3} / \mathrm{s}.$ The inlet and outlet diameters of the pipe are 8 cm and 12 cm, respectively. If the pressure rise of oil in the pump is measured to be 500 kPa and the motor efficiency is 90 percent, determine the mechanical efficiency of the pump.

It takes $15 \mathrm{~s}$ to raise a $1200-\mathrm{kg}$ car and the supporting $300-\mathrm{kg}$ hydraulic car-lift platform to a height of $2.8 \mathrm{~m}$. Determine (a) the average output power delivered by the hydraulic pump to lift the system, (b) the average electric power required, knowing that the overall conversion efficiency from electric to mechanical power for the system is 82 percent.

Perform the operations and simplify as much as possible. $\frac{\frac{X^{2}}{8}}{\frac{X}{4}}$

Perform the operations. Write the answer in the form

$$\frac { - 4 i } { 2 - 6 i }$$

Perform the operations and simplify as much as possible. $\frac{\frac{x^{2}+6 x+9}{x}}{x+3}$

In the case of work done against friction, the internal energy change is independent of the velocity (or inertial reference frame) of the observer. That is, different observers would assign the same quantity of mechanical energy transformed into inter- nal energy due to friction. How can this be explained, consider- ing that such observers measure different quantities of total work done and different changes in kinetic energy in general?