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Answers by Richard P.

Volume integral (answer)

This problems is a bit tricky because the resulting solid should be viewed as being into two parts joined together.   The first part corresponds to 0 ≤ x < 1 and the second to   1 ≤ x  ≤ 9   The volume of the first part can be computed...

Chem Question (answer)

With the addition of the 350 mL of water, the concentration of acetic acid is (0.1) 0.035 /(.035 + .35) = 0.00909   The equilibrium is :     1.8 x 10-5  =  [ H+ ] [ Ac-]/ [H Ac]   but [Ac-] = [ H+]      call this x...

I will use an ordered triplet (  ,   ,  ) notation to describe vectors.   The direction of line l  is specified by (1 , - 1, 2)   and the direction of line my by ( 1 , 2, -2)  A direction perpendicular to both of these is the cross product   (...

Center of Mass (answer)

For part a)   The x coordinate of the center of mass is      xcm =  ∫∫ dθ r dr  r cos(θ)  /   M    where M = ∫∫ dθ r dr        The y coordinate of the center of mass is    ycm...

Rewrite the equation as    y2 (1+ sin2x)2 = cos22x      Then replace cos22x with 1 - sin22x    The result is an equation quadratic in sin2x   The quadratic formula can then be used to get two values for sin2x  One is  sin2x =...

First work out the molar mass of glucose   MM = 6 x 12 + 12 x 1 + 6 x 16 =  180 g   The number of moles of glucose is  2.2 x 10-2 / 160 =  0.0001222 moles of glucose.   The number of molecules is this number multiplied by the Avogadro...

At the top if the curve, the occupants of the car are accelerating downward with ac = v2 /R  where v is the velocity and R = 91 m  ((centripetal acceleration)    The free body diagram for an occupant shows two forces:  1) , the downward force of gravity = mg ...

For the case of an equal mass elastic collision, the angle between the exit velocities is 90 degrees.  Hence second ball moves at an angle 90 - 37 = 53 degrees with respect to the original line of motion.

To see what is going on,  work backwards from the answer. Long division (or synthetic division)  of   (-2s^3-8s^2+4s+40)/(s^3+4s^2+3s)   Works out to be -2 with a remainder of (10 s +40) /(s^3 +4 s^2 + 3s)   The -2...