The eight ball, which has a mass of m=0.5kg, is initially moving with a velocity v=4.9i m/s. It the strikes the six ball, which has an identical mass and is initially at rest. After the collision the eight ball is deflected by an angle of theta 27 degrees and the six ball is deflected by an angle psi 31 degrees. (a) Write an expression for the magnitude of six ball's velocity, in terms of the angles given in the eight ball's initial velocity, v.
In: Physics
A cylindrical container is to be made from certain solid material with the following constraints: It has a fixed inner volume of V mm3, has a 2 mm thick solid wall, and is open at the top. The bottom of the container is a solid circular disc of thickness 2 mm and is of radius equal to the outer radius of the container. If the volume of the material used to make the container is minimum when the inner radius of the container is 10 mm, then the value of V/250 π is
In: Math
Standard reduction potentials are provided for two half reactions that involve the hypothetical metal "M" and sulfide ion. Use them to calculate the value of the solubility product constant for the metal sulfide. (Hint: what is the balanced chemical reaction equation for the equilibrium reaction that gives Ksp?)
| M2+ + 2 e- ⇌ M(s) | Eo = -0.057 V |
| MS(s) + 2 e- ⇌ M(s) + S2- | Eo = -1.208 V |
| Ksp of MS(s) = |
In: Chemistry
Let V be the vector space of 2 × 2 real matrices and let P2 be the vector space of polynomials of degree less than or equal to 2. Write down a linear transformation T : V ? P2 with rank 2. You do not need to prove that the function you write down is a linear transformation, but you may want to check this yourself. You do, however, need to prove that your transformation has rank 2.
In: Math
In: Biology
In this week's lecture #3, Walter Lewin lit a fluorescent bulb by holding it near a Van de Graaff generator, charged to 300,000 V. Suppose that the spherical conductor of the Van de Graaff has a diameter of 68.69 cm, that the bulb is 100.56 cm in length, and Prof. Lewin is holding the near end of the bulb 32.23 cm from the surface of the Van der Graaff. What is the potential difference (V) between the two ends of the bulb?
In: Physics
Let T and S be linear transformations of a vector space V, and TS=ST
(a) Show that T preserves the generalized eigenspace and eigenspace of S.
(b) Suppose V is a vector space on R and dimV = 4. S has a minimal polynomial of (t-2)2 (t-3)2?. What is the jordan canonical form of S.
(c) Show that the characteristic polynomial of T has at most 2 distinct roots and splits completely.
In: Math
The coenzyme NADP+ is the terminal electron acceptor in chloroplasts, according the reaction
2 H2O + 2 NADP+ → 2 NADPH + 2 H+ + O2
NADP+ + H+ + 2 e- → NADPH E˚'= -0.315 V
O2 + 4 H+ + 4 e- → 2 H2O E˚'= 0.816 V
Given the information above, calculate the equilibrium constant for this reaction at 25˚C and pH 7.0.
How can the chloroplast overcome this unfavorable equilibrium?
In: Biology
A mass of 0.3 kg of saturated refrigerant-134a is
contained in a piston-cylinder device at 240 kPa.
Initially, 70 percent of the mass is in the liquid phase. Now heat
is transferred to the refrigerant at
constant pressure until the cylinder contains vapor only.
(a) show the process on a P-v and T-v diagrams with respect to
saturation lines. Determine;
(b) the volume occupied by the refrigerant initially,
(c) the work done, and
(d) the total heat transfer.
In: Mechanical Engineering
2A. The label on a 1.00-L bottle of wine states that the alcohol content is 12.5% (v/v). How much alcohol is present in the bottle?
2B. How do you make 2.50 L of 3.25 M NaHC03?
2C. How do you make 2.50 L of 0.200 M NaOH?
2D.Tell the type of solution(solid-in-liquid, etc) represented by each of the following: Gasohol, Wax in gasoline, and Gas mixture used as anesthesia
In: Chemistry