Question Solved1 Answer R is the region bounded by the functions f(x)=x/3+1 and g(x)=−x/4+7 over the interval [a,b] where a=−6 and b=−1. Find the area A of R. Enter an exact answer.

Let S be the solid of revolution obtained by revolving the region defined by the curves y=√x and y=(1/2)x of the xy plane about the line y=−2. We wish to compute the volume of S using the washer method. a) Find the smallest x value x1 and the largest x value x2 of the points in this region. x1= __________ x2= __________ b) Let x be a real number in the interval [x1,x2]. The section S of the plane of abscissa xx is a washer. What is the inner radius ri and the outer radius re of this washer? ri= __________ re= __________ c) Let x be as in (b) for Δx>0 small. The volume of the slice delimited by the planes of abscissa xx and x+Δx is approximately A(x)Δx. What is the function A(x)? A(x)= __________ Remark: there is no Δx in the answer. Also, keep in mind that π is written pi. For example, 2π∕3 in Maple is written 2*pi/3. d) Find the volume of S with ±0.001±0.001 precision. Answer: ________________________

JAVA language Given a sorted list of integers, output the middle integer. A negative number indicates the end of the input (the negative number is not a part of the sorted list). Assume the number of integers is always odd. Ex: If the input is: 2 3 4 8 11 - 1 the output is: Middle item: 4

8.50. An alpha particle of mass 4 u moving with a velocity 2000 m/s collides with a carbon atom of mass 12 u at rest. The alpha particle is scattered through an angle of 30°. Considering the collision to be perfectly elastic, calculate the velocities of both particles after collision and the scattering angle of the recoiling carbon. Describe this collision in the CMCS.

Show that if A and B are matrices which don’t commute, then eA+B = eAeB, but if they do commute then the relation holds. Hint: Write out several terms of the infinite series for eA, eB, and eA+B and do the multiplications carefully assuming that A and B don’t commute. Then see what happens if they do commute.

O 9. (05.09 MC) The amount of medicine m in the blood during a four-hour treatment is given as met 2t. Determine when the amount of medicine reaches maximum. (10 points) When the time is such that When the time is such that e-O When the time is such that 2-4me=0. When the time is such that meet = 0 O 9. (05.09 MC) The amount of medicine m in the blood during a four-hour treatment is given as met 2t. Determine when the amount of medicine reaches maximum. (10 points) When the time is such that When the time is such that e-O When the time is such that 2-4me=0. When the time is such that meet = 0

5.21 LAB: Middle item Given a sorted list of integers, output the middle integer. A negative number indicates the end of the input (the negative number is not a part of the sorted list). Assume the number of integers is always odd. Ex: If the input is: 2 3 4 8 11 -1 the output is: Middle item: 4 in C please