Find the directional derivative of the f(x, y) x2 ex

Find the directional derivative of the f(x, y) = x^2 e^x at the point (2,0) in the direction of the vector v vector = (1,1).

Solution

fx=2x ex+x2ex and f y=0

At (2,0)

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If the length of the Achilles tendon increases 0.52 cm

If the length of the Achilles tendon increases 0.52 cm when the force exerted on it by the muscle increases from 2200 N to 5500 N, what is the \”spring constant\” of the tendon?
Answer in N/m .

(b) How much work is done by the muscle in stretching the tendon 0.52 cm as the force increases from 2200 N to 5500 N?
Answer in J

Solution

a)del x ( change in length) = 0.52 cm

del F ( change in force) = 5500-2200 = 3300 N

k ( spring constant) = del F / del x

k= 3300 / 0.52*10-2 = 634.61*103 N/m

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IF – child 1 pulls with F1 40 N force making an angle

IF;

– child 1 pulls with F1 = 40 N force making an angle of 30 degrees north from east

– Child 2 pulls with F2 = 30 N force making an angle of 60 degrees north from west

– Child 3 pulls with F3 force making an angle south from west

What does the force F3and the angle have to be for the net force to be ZERO, i.e., for the toy to be in equilibrium?

Solution

the horizontal forces are equal in either side

so

F3 cos60 + 30 cos 60 = 40 cos 30

F3 X 0.5 + 30 X 0.5 = 40 X 0.866

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prevous l 41 roblem 11.110 What is the OH in solution X

prevous l 41 roblem 11.110 What is the [OH in solution X? Express your answer to tone significant figure and include the appropriate units Solution X has a pH of 9.70, and solution Y has a pH of 7.8 Value M Submit My Answers Give Up Incorrect: Try Again; 4 attempts remaining Part E What is the [OH ] in solution Y? Express your answer to one significant figure and include the appropriate units. Value Units Submit My Answers Give Up Incorrect: Try Again; 6 attempts remaining

Solution

D)

we have below equation to be used:

pH = -log [H+]

9.7 = -log [H+]

log [H+] = -9.7

[H+] = 10^(-9.7)

[H+] = 1.995*10^-10 M

we have below equation to be used:

[OH-] = Kw/[H+]

Kw is dissociation constant of water whose value is 1.0*10^-14 at 25 oC

[OH-] = (1.0*10^-14)/[H+]

[OH-] = (1.0*10^-14)/(1.995*10^-10)

[OH-] = 5*10^-5 M

Answer: 5*10^-5 M

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A circuit has a resistor R and a capacitor C wired in s

A circuit has a resistor R and a capacitor C wired in series with a battery that supplies a potential difference V. The capacitor is initially uncharged. (a) Calculate the time constant. (b) Find the maximum charge that will appear on the capacitor during the charging process. (c) How long does it take for the charge on the capacitor to build up to an intermediate value Q?

Solution

A)

Time constant = Rc

B)Q= C(V)

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Gallium is produced by the electrolysis of a solution o

Gallium is produced by the electrolysis of a solution obtained by dissolving gallium oxide in concentrated NaOH(aq). Calculate the amount of Ga(s) that can be deposited from a Ga(III) solution by a current of 0.530 A that flows for 70.0 min.

Solution

the electrolysis expression is:

Ga3+ + 3e- ——> Ga

1 mol of Ga requires 3 mol of electron

1 mol of electron = 96485 C

So,1 mol of Ga requires 289455 C

let us calculate the charge passed:

t = 70.0 min = 70.0*60 s = 4200 s

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Consider the capacitor shown below If L 87.8 cm, H 3

Consider the capacitor shown below: If L = 87.8 cm, H = 36.7 cm, and d = 0.849 mm, calculate the capacitance. Enter your answer in nF: 1nF = 10^-9 F: do NOT enter the units.

Solution

c=e0.A/d

=e0*87.8cm*36.7cm/0.0849cm

=e0*37953.5924

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l Questions (Total points 20) D-1 Lights Relationship t

l Questions: (Total points 20) D-1 Light\’s Relationship to Matter: ow we can relate the existence of any color to electrons being on different level of energy? (6 points) D-2 Electron Configurations: Describe electron configuration theory. How we would be able to use both the ground state and diagram configuration to present valance and core electrons for sodium and calcium atoms. (8 points)

Solution

1. Electrons of an atoms have different level of energy depending upon the distance of their orbital from the nucleus. Electrons can get excited to higher energy levels farther from nucleus and when they fall back to lower energy they emit radiation in the form of quanta (photon). ███████ █████████ ███████ ████████████████ ██████ ████████████████████████ ███ █████████████ ████ ██████ ███████████████████ █████ ████████████ █████████████ ██████, ████████████ ████████ █████████████ ███ ███████ ███████████████████ ███████████ █████████████ ███████ ████████ █████ ██████████ ███ █████ ██████████████████ ████████████████ █████████ █████████ ████████████ ██████ ██████████ ███ █████████████ ██████████████████ ████ ████████████████ ████████████ ██████████████ ████████ █████ ██████████████

C-2 Draw conductivity of an ionic agueou wtion Alsn a s

C-2 Draw conductivity of an ionic agueou wtion Alsn a simple dingram of n instrumsent which,uldh s (2 pointsy decaneThen you have shaken the test tubes vigorously, for 30 seconds. After leaving it (2 points) A) Into a 20 mL stoppered test tube, you have added 5 ml. of each water, and to stand still, for 5 minutes, explain your observation. Which one would stay on top of B) Now to this mixture add 1mL of saturated iodine solution in water and repeat the above procedure and explain your findings. other, and why? (2 points)

Solution

C-3

A.

Decane is a non polar molecule and water is polar molecule. So, they are immiscible. When two immiscible liquids are mixed, the liquid with lower density stays on top of the high dens liquid.

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In all parts, make sure to explain your answers (a) Wha

In all parts, make sure to explain your answers:

(a) What is the largest possible number of coexisting phases you would expect to find for a mixture of water and glucose (C6H12O6)? Describe what these phases might be. (Assume that no chemical reactions can take place; the only two molecules present are H2O and glucose.)

(b) Suppose that you combine glucose and water together with some mole fractions at some T and P and that you find the system exhibits coexistence between two phases (a sugar water solution and a vapor phase) under these conditions. Is it within the realm of thermodynamic possibility that you can slightly adjust both T & P in some arbitrary manner and always find coexistence between these two phases? Is it necessarily the case that you will remain in a state of coexistence between these two phases for arbitrary small adjustments to T & P?

(c) What about if you slightly adjusted all three of T,P,Xsugar in an arbitrary manner from the coexistence point found in part b (Xsugar is the mole fraction of glucose in the system)? Do you still expect to find coexistence between the two phases?

Solution

a) The largest possible no. of phases when you mix water with glucose = 1

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