Sketch and label a clamping circuit. Use a 2.5 V rms source and an ideal diode. Explain how it works. Show the voltage wave forms in a diagram, giving numeric values where appropriate.

1. ) Determine if the set form the basis in R³

(1,1,2); (1,2,5); 5,3,4)

1. Write the vector v = (2,3,-5); as a linear combination of u₁= (1,2,-3), u₂= (2,3,-4) and u₃= (1,3,-5)

A solution containing 45.00 ml of 0.0500 M metal ion buffered to pH = 10.00 was titrated with 0.0400 M EDTA. Answer the following questions and enter your results with numerical value only.

Calculate the equivalence volume, V_e, in milliliters.

Calculate the concentration (M) of free metal ion at V = 1/2 V_e.

Calculate the fraction (α_Y^4-) of free EDTA in the form Y^4-. Keep 2 significant figures.

If the formation constant (K_f) is 10^12.00. Calculate the value of the conditional formation constant K_f’ (=α_Y^4- * K_f) and enter your result as scientific notation form.

Calculate the concentration (M) of free metal ion M⁺ at V = V_e. (Use the K_f' calculated above)

The following equation describes the horizontal range of a projectile, fired from a height of zero, at an angle of ?θ, with an initial velocity of v:

?= ?^2 sin(2?) / ?,

where g is the acceleration of gravity. Use kinematics to derive this equation by assuming the magnitude of the initial velocity to be v. Hint: the horizontal and vertical components of the initial velocity can be expressed as ??=????(?)vx=vcos(θ) and ??=????(?)vy=vsin(θ). Another hint: you aren't given any numbers but you can still proceed as usual (i.e., find an expression for t using kinematics in the y direction and then plug it into a kinematic equation in the x direction). A third hint: the double angle identity states: sin(2?)=2sin(?)cos(?)

The water in a 40-L tank is to be heated from 15°C to 45°C by a 25-cm-diameter spherical heater whose surface temperature is maintained at 85°C. Determine how long the heater should be kept on.

Given: The properties of air at 1 atm and the film temperature of 57.5°C.

Fluid temperature = Average temperature for water (15+45)/2=30°C

k = 0.6515 W/m.°C, v = 0.493 x 10^-6 m²/s, Pr = 3.12, and ? = 0.501 x 10^-3 K^-1

The properties of water at 30°C.
? = 996 kg/m³ and c_p = 4178 J/kg.°C, and volume, V = 0.040 m³

A mass of m=1kg of steam is contained in a closed rigid container. Initially the pressure and temperature of the steam are: p1= 1.5 MPa and t1=240?C, respectively. Then the temperature drops to T2 =100?C as the result of heat transfer to the surroundings. Determine: a) quality of the steam at the end of the process, b) percentage of volume that is occupied by the saturated liquid at the final state, c) heat transfer with the surroundings per unit mass of the system. For: p=1.5 MPa and T1=240?C: h1=2900KJ/kg, v1=0.1483 m3/kg while for T2=100?C: h’=419KJ/kg, v’=0.001043m3/kg and h”=2676 KJ/kg ,v”=1.672 m3/kg.

Consider the following cell reaction: Fe(s) + 2 H+(? M) Fe2+(1.00 M) + H2(g)(1.00 atm) If the cell potential at 298 K is 0.236 volts, what is the pH of the hydrogen electrode?

A voltaic cell is constructed in which the cathode is a standard hydrogen electrode and the anode is a hydrogen electrode ()= 1atm) immersed in a solution of unknown [H+]. If the cell potential is 0.202 V, what is the pH of the unknown solution at 298 K? pH =

A voltaic cell is constructed in which the cathode is a standard hydrogen electrode and the anode is a hydrogen electrode ()= 1atm) immersed in a solution of unknown [H+]. If the cell potential is 0.184 V, what is the pH of the unknown solution at 298 K?

Thank you!

Arteriosclerotic plaques forming on the inner walls of arteries can decrease the effective cross-sectional area of an artery. Even small changes in the effective area of an artery can lead to very large changes in the blood pressure in the artery and possibly to the collapse of the blood vessel. Imagine a healthy artery, with blood flow velocity of v 0 =0.14m/s and mass per unit volume of ρ=1050kg/ m 3 . The kinetic energy per unit volume of blood is given by K 0 = 1 2 ρ v 2 0 . Relative to its initial, healthy state, by what factor does the velocity of blood increase as the blood passes through this blockage? Express your answer numerically.