The Gaia satellite will measure parallaxes with an accuracy of 2 × 10⁻⁵ arcsec for stars with V < 15.
(a) What is the distance d of an M5 I supergiant with log(L/L_ʘ) = 5.50 and BC = −3.70 that has V = 12, if the effect of interstellar extinction is ignored?
(b) What is the relative distance accuracy σ(d)/d of such a star?
(c) Assuming that T_eff is known, what is the relative accuracy in radius σ(R)/R?

A spherical capacitor has vacuum between its conducting shells and a capacitance of 125 pF. The outer shell has inner radius 9.00 cm.

a. If the potential of the inner shell is 355 V higher than the potential of the outer shell, what is the surface charge density on the outer shell?

b. If the potential of the inner shell is 355 V higher than the potential of the outer shell, what is the surface charge density on the inner shell?

Consider a myelinated nerve with axon of radius, a = 10 micrometers, and Myelin sheath of thickness b = 0.4a. A) Calculate the space constant. B) Assume that a potential change of ∆V = 10mV is required to initiate an action potential, and that the distance between two nodes of Ranvier is D = 200a. If the maximum potential change is ∆V = 100mV, how many nodes of Ranvier can be triggered

the specific values are right in the question if you actually read it

Starting with the exact differential for S (entropy, treated as a state function of P, pressure, and T, temperature), the definition of entropy, S, definition of heat, q, and the definition of enthalpy, H, show that

dS= (Cp/T)dT - alpha*V*dP

where

alpha= (1/V)*(dV/dT) when P is held constant

.Using the Helmholtz free energy, A, given by

A=U - TS

express dS in terms of dT and dV

Consider the surface S described by r(u,v) =〈2 cosusinv,3 sinusinv,4 cosv〉,0≤u≤2π, 0≤v≤π, and consider the vector field F(x,y,z)=〈−2x,y,z〉.(a) Sketch or name S.

(b) Set up (DO NOT EVALUATE) ∫ ∫S F·n dS over S.

(c) Using the divergence theorem, deduce the value of the surface integral.

1a) If the ventilation/perfusion ( V/Q) ratio of a lung region decreases, how will the P_O2 and P_CO2 in the blood in that region change?

1b) In perfusion-limited O₂ exchange, is the P_O2 at the end of the pulmonary capillary closer to P_A,O2 or P_V,O2?

1c) Which of the following is/are higher at the base of the lung than at the apex: blood flow, V/Q, ventilation, P_O2, P_CO2?

Please explain your answers briefly and accurately.

Use the following pair of reduction half-reactions to design a galvanic cell. Then write in the proper coefficient for each of the species involved in the overall reaction. Water molecules and protons are not shown in the half-reactions, but may be needed in the overall reaction.

MnO4- (aq) ? MnO2 (s) ?o = 0.59 V NO3- (aq) ? NO (g) ?o = 0.96 V

NO₃^- (aq)
MnO₄^- (aq)
NO (g)
MnO₂ (s)
H⁺ (aq)
H₂O (l)

Let X1,…,Xn∼i.i.d.N(0,σ2), for some σ2>0. Let σ2ˆ=1n∑i=1nX2i,andσ2˜=1n∑i=1n(Xi−Xnbar)2. Argue that both proposed estimators σ2ˆ and σ2˜ below are consistent and asymptotically normal. Then, give their asymptotic variances V(σ2ˆ) and V(σ2˜) and decide if one of them is always bigger than the other. Hint: Use the multivariate Delta method.

A homemade capacitor is assembled by placing two 9-in. pie pans 4cm apart and connecting them to the opposite terminals of a 6-Vbattery.

Part A:

Estimate the capacitance.

C= ?? V

Part B:

Estimate the charge on each plate.

Q= ?? C

Part C:

Estimate the electric field halfway between the plates.

E = V/m

Part D:

Estimate the work done by the battery to charge the plates.

W= ?? J