Question Solved1 Answer 3. Determine first and second derivative of the function f(x) = e -0.5x2 3. Determine first and second derivative of the function f(x) = e -0.5x2

7. Suppose a large gasoline tank has the shape of a halfcylinder 8 feet in diameter and 10 feet long (Figure 6.45). If the tank is full, find the work \( W \) necessary to pump all the gasoline to the top of the tank. Assume the gasoline weighs 42 pounds per cubic foot.

Q2) Simplify the following expressions as much as you can using Boolean algebra theorems and postulates. (A + BC) + (DE + F) (A + BC)′

  A skateboarder is attempting to make a circular arc of radius r = 19 m in a parking lot. The total mass of the skateboard and skateboarder is m = 94 kg. The coefficient of static friction between the surface of the parking lot and the wheels of the skateboard is μs = 0.68 .   A.)  What is the maximum speed, in meters per second, he can travel through the arc without slipping?   (b)  He speeds up very slightly and begins to slide. The coefficient of kinetic friction is μk = 0.27. What is the new magnitude, in meters per squared second, of his radial acceleration? 

Two charged particles, q1 and q2, are located on the x-axis, with q1 at the origin and q2 initially at x1 = 14.5 mm. In this configuration, q1 exerts a repulsive force of 2.62 µN on q2. Particle q2 is then moved to x2 = 18.6 mm. What is the force (magnitude and direction) that q2 exerts on q1 at this new location? (Give the magnitude in µN.) magnitude µN direction −î 6. [1/2 Points] DETAILS PREVIOUS ANSWERS SERPSE 10 22.3.OP.003. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Two charged particles, 94 and 92, are located on the x-axis, with q, at the origin and q2 initially at x2 = 14.5 mm. In this configuration, q, exerts a repulsive force of 2.62 UN on 42. Particle qz is then moved to x2 = 18.6 mm. What is the force (magnitude and direction) that qz exerts on 9, at this new location? (Give the magnitude in uN.) magnitude μΝ direction -i

Given that the area immersed in the gap is changing as the coil enters the gap, what is the correct expression of Faraday's Law for this situation? That is, find the induced voltage as a function of the velocity of the glider, \( v \), the flux density inside the magnetic gap, \( B \), and other quantities you can measure from the video. Hint: This is an Given that the area immersed in the gap is changing as the coil enters the gap, what is the correct expression of Faraday's Law for this situation? That is, find the induced voltage as a function of the velocity of the glider, v, the flux density inside the magnetic gap, B, and other quantities you can measure from the video. Hint: This is an example of a motional emf, which is something that we covered in the lecture. You should already know the equation for this.

3.77 If P 20 lb in the figure, replace the three couples with a single equivalent couple, specifying its magnitude and the direction of its axis.