A large sphere with radius R, supported near the earth's surface as shown has charge density p(r) that varies as r^n (where n is 0,1,2..) for 0<r<R and reaches a max value of p as you get to r=R. a non conducting uncharged string of length L with a second tiny sphere of radius b, mass m, and excess charge q is suspended from the large sphere as shown. suppose the string is cut gently without otherwise disturbing the setup and the ball begins to move. Derive a formula for the instantaneous acceleration of the small ball just after the string is cut.

c) Define the measurement system specifications to meet the above application requirements

d) Develop a feasible design: draw the measurement system block diagram and describe the function of all needed subsystems

Create an array of 10,000 elements, use sorted, near sorted, and unsorted arrays. Implement find the kth smallest item in an array. Use the first item as the pivot. Compare sets of results using a static call counter. Reset counter before running another search. Create a Test drive to exhaustively test the program.

// Assume all values in S are unique.

kSmall(int [] S, int k): int (value of k-smallest element)

pivot = arbitrary element from S:  let’s use the first element.

S1 = < all elements from S less than pivot > // these two steps will require some thought

S2 = < all elements from S greater than pivot > //  and need to be implemented

if k <= S1.length

    return kSmall(S1, k)

else if k == S1.length + 1

    return pivot

else

    return kSmall(S2, k – S1.length – 1)

The Yum and Yee food truck near the business school serves customers during lunch hour by taking orders and making fresh batches of stir-fry. Customers have only one choice during the lunch hour so that Y&Y can maximize the number of customers served. Assume that each customer places just one lunch order, and all lunch orders are the same size: one unit of stir-fry. The stir-fry cooking works in this manner. First, one person cooks a batch of orders in a wok. The cooking depends upon the number of orders in the batch. The time to cook just one order is 3.4 minutes. For each additional order in the batch, it takes 0.4 minute more to cook. Thus, cooking two orders in a batch takes 3.8 minutes, cooking three orders takes 4.2 minutes, and so on. The other process is bagging and accepting payments (done by a separate person), which takes 0.7 minute per order.

a.What is the Setup time

b.If Y&Y operates with bath sizes of 7 units, what is their process capacity (in orders per minute)?

c.If Yum an Yee operates with batch sizes of 12 units, what is the utilization of the wok?

d. Calculate the batch size (in orders) that maximizes the overall flow rat (assume there is ample demand)? Do NOT round the batch size (i.e., assume for this calculation that a noninteger batch size is possible.

The Yum and Yee food truck near the business school serves customers during lunch hour by taking orders and making fresh batches of stir-fry. Customers have only one choice during the lunch hour so that Y&Y can maximize the number of customers served. Assume that each customer places just one lunch order, and all lunch orders are the same size: one unit of stir-fry. The stir-fry cooking works in this manner. First, one person cooks a batch of orders in a wok. The cooking depends upon the number of orders in the batch. The time to cook just one order is 3 minutes. For each additional order in the batch, it takes 0.5 minute more to cook. Thus, cooking two orders in a batch takes 3.5 minutes, cooking three orders takes 4 minutes, and so on. The other process is bagging and accepting payments (done by a separate person), which takes 0.80 minute per order.

a. What is the setup time of this process?

b. If Y&Y operates with batch sizes of 6 units, what is their process capacity (in orders per minute)?

c. If Yum and Yee operates with sizes of 10 units, what is the utilization of the work (assume there is sample demand)?

d. Calculate the batch size (in orders) that maximizes the overall flow rate (assume these is sample demand)?

The Yum and Yee food truck near the business school serves customers during lunch hour by taking orders and making fresh batches of stir fry. Customers have only one choice during the lunch hour, since the objective is to maximize the number of customers served. Assume that each customer places just one lunch order, and all lunch orders are the same size –one unit of stir-fry. The stir fry cooking works in this manner. First, a batch of orders is cooked in a wok by one person. The cooking depends upon the number of orders in the batch. The time to cook just one order is 3 minutes. For each additional order in the batch, it takes 0.5 minutes more to cook. Thus, cooking two orders in a batch takes 3.5 minutes, cooking three orders takes 4 minutes, and so on. The other activity is bagging and accepting payments (done by a separate person), which takes 0.80 minutes per order.

If Yum and Yee operates with batch sizes of 9 units, what is their process capacity (in orders per miute)?

Low concentrations of Ni-EDTA near the detection limit gave the following counts in a mass spectral measurement: 184, 148, 148, 148, 136, 170., 196, 152, 156, 175. Ten measurements of a blank had a mean of 45 counts. A sample containing 1.00 µM Ni-EDTA gave 1797 counts.

(a) Find the mean.
___ counts

(b) Find the standard deviation.
___ counts

(c) Estimate the detection limit for Ni-EDTA.
___ counts
___ M

Near the equator, the Sun is approximately straight overhead at noon, and around 1000 W/m2 solar irradiance reaches Earth. Around this time of day, assuming ambient temperature of 40C, and a 10m x 10m x 2m-tall greenhouse with ¼”-thick glass walls that reflect away 20% of the incoming sunlight, and only thinking of conductive losses, estimate the maximum temperature reached in the interior of the greenhouse. Hint: when are losses and sources balanced?

glass conductivity is 1.05 W/(m k)

Thirty small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that σ is known to be 40.9 cases per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)