Use the Divergence Theorem to evaluate
| S |
F · dS,
where
F(x, y, z) = z2xi +
| y3 |
| 3 |
+ cos z
j + (x2z + y2)k
and S is the top half of the sphere
x2 + y2 + z2 = 4.
(Hint: Note that S is not a closed surface. First compute integrals over S1 and S2, where S1 is the disk
x2 + y2 ≤ 4,
oriented downward, and S2 = S1 ∪ S.)
In: Math
Using only real numbers between 0 and 100, inclusive, show the set of three numbers whose product is 64 and whose sum is minimal is give by {4, 4, 4}.
(a) When is an absolute minimum or maximum guaranteed?
(b) State the steps to find an absolute minimum and maximum.
(c) Is the space closed and bounded? Explain.
(d) Use Lagrange Multipliers to find the minimum and maximum
please label and write neatly.
In: Advanced Math
Suppose that Federal Reserve policy leads to higher interest rates in United States
a. How will this policy affect real GDP in short run if the United States is a closed economy (no exports and imports)?
b. How will this policy affect real GDP in short run if the United States is an open economy?
c. How will your answer to part b change if interest rates also rise in the other countries around the world?
In: Economics
On a particular summer day, the temperature is 30 degrees Celsius and the relative humidity is 80% (which means that the partial pressure of water vapor in the ambient air is 80% of the equilibrium vapor pressure of water). A sample of this air is placed in a 1 Liter flask which is then closed and cooled to 5 degrees Celsius. What is the mass in grams of water that still exists as vapor in the flask? How much liquid water in grams condenses out?
In: Chemistry
A closed rectangular tank 1.2 m high, 2.4 m long and 1.5 m wide is two-thirds full of gasoline (specic gravity 0.8). Calculate the acceleration which may be imparted to the tank so that the bottom front end of the tank is just exposed. Also calculate the total forces on each end of the tank and show that the dierence between these forces equals the unbalanced force necessary to accelerate the liquid mass in the tank.
In: Mechanical Engineering
1. Find the derivative.
f(x) = x6 · 3x
2. Find the absolute maximum and minimum values on the closed interval [-1,8] for the function below. If a maximum or minimum value does not exist, enter NONE.
f(x) = 1 − x2/3
3. Find the derivative.
f(x) = x5 · e6x
Consider the following.
f(x) = -19ln(84x)
Compute f '(x), then find the exact value of f ' (3).
In: Math
Five kg of oxygen (O2), initially at 430°C, fills a closed,
rigid tank. Heat transfer from the oxygen occurs at the rate 425 W
for 10 minutes. Assuming the ideal gas model with k
= 1.350 for the oxygen, determine its final temperature, in
°C.
Can't seem to find the right equations to use for this one, so I'm getting pretty stumped. Any help would be greatly appreciated
In: Mechanical Engineering
At 22°C, Kp = 0.070 for the equilibrium:
NH4HS (s) NH3 (g) + H2S (g)
a) A sample of solid NH4HS is placed in a closed vessel and allowed to equilibrate. Calculate the equilibrium partial pressure (atm) of ammonia, assuming that some solid NH4HS remains.
b) After the equilibrium in part a) was established, the reaction flask is then charged with an additional 0.59 atm of NH3. When the system has equilibrated, what is the partial pressure of hydrogen sulfide?
In: Chemistry
A wire bent with two right angles (forming a u-shape) sits in the xy-plane. The closed end (where the right angles are) is on the x-axis. The sides parallel to the y-axis run in the -y direction. A movable wire, parallel to the x-axis but not on the x-axis at any time, moves in the +y direction. If a magnetic field going in the -z direction baths the circuit, what is the direction of the induced current in the movable wire?
In: Physics
Suppose you are invested in an (excellent) account that pays 50% interest per year, paid monthly. The account is closed to new investment, so you cannot reinvest the interest. Do you prefer this account to one that pays a single payment of 50% at the end of the year, rather than monthly? Why or why not? Explain your reasoning (you may wish to reference ideas like compounding, NPV, IRR, etc.)
In: Finance