Questions
Suppose that Ω ⊆ R n is bounded, and path-connected, and u ∈ C2 (Ω) ∩...

Suppose that Ω ⊆ R n is bounded, and path-connected, and u ∈ C2 (Ω) ∩ C(∂Ω) satisfies ( −∆u = 0 in Ω, u = g on ∂Ω. Prove that if g ∈ C(∂Ω) with g(x) = ( ≥ 0 for all x ∈ ∂Ω, > 0 for some x ∈ ∂Ω, then u(x) > 0 for all x ∈ Ω

In: Advanced Math

prove the intermediate value theoerom using a) Nested interval property b) Axiom of completeness

prove the intermediate value theoerom using

a) Nested interval property

b) Axiom of completeness

In: Advanced Math

1. An 8-inch diameter (I.D.) pipe is filled to a depth equal to one-third of its...

1. An 8-inch diameter (I.D.) pipe is filled to a depth equal to one-third of its diameter. What is the area in flow?

2. Find the area of a washer formed by two concentric circles whose chord outside the small circle is 10 cm.

3. A goat is tied to a corner of a 30 ft by 35 ft building. If the rope is 40 ft. long and the goat can reach 1 ft. farther than the rope length, what is the maximum area of the goat can cover?

I need solution pleaseeee

In: Advanced Math

Solve by separation variables (2x-5y-2)dx+(5x-y-5)dy=0

Solve by separation variables (2x-5y-2)dx+(5x-y-5)dy=0

In: Advanced Math

An experiment is given together with an event. Find the (modeled) probability of each event, assuming...

An experiment is given together with an event. Find the (modeled) probability of each event, assuming that the coins are distinguishable and fair, and that what is observed are the faces uppermost.

Three coins are tossed; the result is at most one tail.

An experiment is given together with an event. Find the (modeled) probability of each event, assuming that the dice are distinguishable and fair, and that what is observed are the numbers uppermost.

Two dice are rolled; the numbers add to 3.

An experiment is given together with an event. Find the (modeled) probability of each event, assuming that the dice are distinguishable and fair, and that what is observed are the numbers uppermost.

Two dice are rolled; the numbers add to 11.

An experiment is given together with an event. Find the (modeled) probability of each event, assuming that the dice are distinguishable and fair, and that what is observed are the numbers uppermost.

Two dice are rolled; the numbers add to 13.

An experiment is given together with an event. Find the (modeled) probability of each event, assuming that the dice are distinguishable and fair, and that what is observed are the numbers uppermost.

Two dice are rolled; both numbers are prime. (A positive integer is prime if it is neither 1 nor a product of smaller integers.)

Use the given information to find the indicated probability.

P(AB) = .8, P(B) = .7, P(AB) = .4.

Find P(A).

Use the given information to find the indicated probability.

P(A) = .78.

Find P(A').

P(A') =

In: Advanced Math

6. Let V be the vector space above. Consider the maps T : V → V...

6. Let V be the vector space above. Consider the maps T : V → V And S : V → V

defined by T(a1,a2,a3,...) = (a2,a3,a4,...) and S(a1,a2,a3,...) = (0,a1,a2,...).

(a) [optional] Show that T and S are linear.
(b) Show that T is surjective but not injective.
(c) Show that S is injective but not surjective.

(d) Show that V = im(T) + ker(T) but im(T) ∩ ker(T) ̸= {0}.

(e) Show that im(S) ∩ ker(S) = {0} but V ̸= im(S) + ker(S).

In: Advanced Math

4. Consider bit strings with length l and weight k (so strings of l 0’s and...

4. Consider bit strings with length l and weight k (so strings of l 0’s and 1’s, including k 1’s). We know how to count the number of these for a fixed l and k. Now, we will count the number of strings for which the sum of the length and the weight is fixed. For example, let’s count all the bit strings for which l + k = 11.

(a) Find examples of these strings of different lengths. What is the longest string possible? What is the shortest?

(b) How many strings are there of each of these lengths. Use this to count the total number of strings (with sum 11).

(c) The other approach: Let n = l + p vary. How many strings have sum n = 1? How many have sum n = 2? And so on. Find and explain a recurrence relation for the sequence (an) which gives the number of strings with sum n.

(d) Describe what you have found above in terms of Pascal’s Triangle. What patter have you discovered?

I'd really appreciate the help on solving this problem as there were no similar example problems in the book to even help me start this problem. Thank you!

Also some background information on this problem to hopefully help someone at least start answering this problem. For this problem we previously went over sequences such as recursive and closed. Also if they were arithmetic or geometric. The last chapter did cover binomial coefficients if that has some prevalence here.

In: Advanced Math

A researcher believes that female stray cats are more cautious when approaching people than male cats....

A researcher believes that female stray cats are more cautious when approaching people than male cats. He knows that the stray cat population is 50% male and 50% female. In order to test this, visits 15 different areas where stray cats live and records the gender of the first cat to approach him. He finds that 12 of the 15 cats that approach him are male. Using a sign test:

D) What is the critical value? (In number of female cats)

In: Advanced Math

Explain how loss to follow-up could bias findings in a cohort study of physical activity in...

  1. Explain how loss to follow-up could bias findings in a cohort study of physical activity in college and subsequent diagnosis of diabetes.
  2. Explain how recall bias could affect a case-control study of type 2 diabetes diagnosed in adults age 45 to 64 years and physical activity during young adulthood (while age 18 to 24 years)
  3. Explain how selection bias could affect a case-control study of type 2 diabetes diagnosed in adults age 45 to 64 years and physical activity during young adulthood. Assume cases are identified as adult diabetic patients attending a diabetes management seminar at a local hospital and controls are selected from non-diabetic patients admitted to the hospital during the week the seminar was offered. Further assume that cases and controls are matched on age and sex.

In: Advanced Math

solve the differential equation a) ? ′′ − ? ′ = 1 1 + ? −?...

solve the differential equation

a) ? ′′ − ? ′ = 1 1 + ? −?

b) ? ′′ + 3? ′ + 2? = cos(?x )

c) 10) ? ′′ − 2? ′ + ? = exsqrtx

In: Advanced Math

Use the Cauchy Criterion to prove the Bolzano–Weierstrass Theorem, and find the point in the argument...

Use the Cauchy Criterion to prove the Bolzano–Weierstrass Theorem, and find the point in the argument where the Archimedean Property is implictly required. This establishes the final link in the equivalence of the five characterizations of completeness discussed at the end of Section 2.6.

In: Advanced Math

Consider the following subsets of the set of all students: A = set of all science...

Consider the following subsets of the set of all students:

A = set of all science majors
B = set of all art majors
C = set of all math majors

D = set of all female students


Using set operations, describe each of the following sets in terms of A, B, C, and D:

a) set of all female physics majors

b) set of all students majoring in both science and art

In: Advanced Math

Lamia's House of Software (LHS) wants to prepare a cash budget for months of September through...

Lamia's House of Software (LHS) wants to prepare a cash budget for months of
September through Dêcember. Using the following information,
Sales were $50,000 in June and $60,000 in July. Sales have been
forecasted to be $65,000, $72,000, $63,000, $59,000, and $56,000 for months
of August, September, October, November, and December, respectively. In the
past, 10 percent of sales were on cash basis, and the collection were 50
percent in the first month, 30 percent in the second month, and 10 percent in
the third month following the sales.
n
Every four months (three times a year) $500 of dividends from investments
are expected. The first dividend payment was received in January.
Purchases are 60 percent of sales, 15 percent of which are paid in cash, 65
percent are paid one month later, and the rest is paid two months after
purchase.
$8,000 dividends are paid twice a year (in March and September).
The monthly rent is $2,000.
Taxes are $6,500 payable in December.
A new machine will be purchased in October for $2,300
$1,500 interest will be paid in November
$1,000 loan payments are paid every month.
Wages and salaries are $1,000 plus 5 percent of sales in each month.
August's ending cash balance is $3,000.
LHS would like to maintain a minimum cash balance of $10,000.
October Cash.
$1,570 ExcessCash
November Cash
$36,900 Excess cash
September cash
$1,570 Required Financing

In: Advanced Math

Derive the Catmull-Rom Spline blending function in your own words step by step.

Derive the Catmull-Rom Spline blending function in your own words step by step.

In: Advanced Math

A company manufactures Products A, B, and C. Each product is processed in three departments: I,...

A company manufactures Products A, B, and C. Each product is processed in three departments: I, II, and III. The total available labor-hours per week for Departments I, II, and III are 900, 1080, and 840, respectively. The time requirements (in hours per unit) and profit per unit for each product are as follows. (For example, to make 1 unit of product A requires 2 hours of work from Dept. I, 3 hours of work from Dept. II, and 2 hours of work from Dept. III.)

Product A Product B Product C
Dept. I 2 1 2
Dept. II 3 1 2
Dept. III 2 2 1
Profit $18 $12 $15

How many units of each product should the company produce in order to maximize its profit?

Product A     units
Product B     units
Product C     units


What is the largest profit the company can realize?
$

Are there any resources left over? (If so, enter the amount remaining. If not, enter 0.)

labor in Dept. I     labor-hours
labor in Dept. II     labor-hours
labor in Dept. III     labor-hours

In: Advanced Math