The indicated function y₁(x) is a solution of the given differential equation. Use reduction of order to find y_2(x)

x²y'' − xy' + 17y = 0 ;   y₁=xsin(4In(x))

Adele Weiss manages the campus flower shop. Flowers must be ordered three days in advance from her supplier in Mexico. Although Valentine’s Day is fast approaching, sales are almost entirely last-minute, impulse purchases. Advance sales are so small that Weiss has no way to estimate the probability of low (25 dozen), medium (60 dozen), or high (130 dozen) demand for red roses on the big day. She buys roses for $15 per dozen and sells them for $40 per dozen.  Payoff table is given below.

Which decision is indicated by each of the following decision criteria?

• Maximin (pessimistic)  

• Maximax (optimistic)

• Laplace (Equally likely)

• Minimax regret

Define φ : Z[ √ 2] → Z[ √ 2] defined by φ(a + b √ 2) = a − b √ 2 for all a, b ∈ R is an automorphism of rings.

a passbook savings account has a 7% . Find the annual yield

Elk, Fire and Aspen – Quaking aspen (Populus tremuloides) is one of the most widespread tree species in North America. Although quaking aspen has been a key component of forest ecosystems for more than ten thousand years, it is currently in decline across broad portions of its range. Historically, aspen recruitment has been favored by the occurrence of low intensity fires, which create openings that allow young aspens to grow and eventually reproduce. In recent decades, however, the number of fires per year and the area burned per fire has increased; these increases in the frequency and magnitude of fires are thought to be caused by the “hotter droughts” that have resulted from climate change and by previous fire suppression policies. Some recent fires have destroyed more than 400 km2 of forest; such fires are referred to as “mega-fires.” In addition to fire, browsing by elk can prevent young aspen trees from becoming large enough to reproduce. Field Experiment – Suppose that researchers wanted to examine the combined effects of a mega- fire and browsing by elk (Cervus elaphus) as factors that may be affecting the decline of quaking aspen. Immediately after a mega-fire, the researchers established fenced-in plots that prevented by browsing by elk (the “Elk absent” treatment) along with nearby plots from which elk were not excluded (the “Elk present” treatment). Five fenced-in plots and five unfenced plots were established in each of two areas: A section of forest that was burned in the mega-fire (the “burned” treatment), and a nearby section of forest that was not burned (the “unburned” treatment). After 6 years, the number and mean height of young aspen trees in each plot are shown in table

1. What is the total number of plots that were established in this experiment? How many of these plots were burned? How many were unburned?

2. The aspen height data were used draw the bar graph shown in Fig. 1. Summarize how elk and fire affect the height of young aspen trees by answering the following questions: 2.1. What are the overall effects of elk and fire on aspen height? 2.2. Does the impact of fire on aspen height depend on whether elk were present?

3. Summarize how elk and fire affect the number of young aspen trees by answering the following questions: What are the overall effects of fire and elk on the number of aspen? Does the impact of elk on aspen number depend on whether the plots were burned? Does the impact of burning on aspen depend on whether elk were present?

Please show all steps!!!!

1. Let Q1=y(1.1),Q2=y(1.2),Q3=y(1.3), where y=y(x) solves y′′+ (−3.75)y′+(3.125)y= 0, y(0) = 1.5, y′(0) =−0.625

2. Let Q1=y(1.1),Q2=y(1.2),Q3=y(1.3), where y=y(x) solves y′′+ (−3.75)y′+(3.125)y= 114e−3.5x, y(0) = 5.5, y′(0) =−14.625.

3. Let Q1=y(1.1),Q2=y(1.2),Q3=y(1.3), where y=y(x) solves y′′+ (−3.75)y′+(3.125)y=−5e1.25x, y(0) = 1.5, y′(0) = 3.375

For all of the above Let Q= ln(3 +|Q1|+ 2|Q2|+ 3|Q3|). Then T= 5 sin2(100Q)

prove Pascal's mystic hexagon theorem and Brianchon's theorem which is the dual to Pascal's

Prove or disprove the statements: (a) If x is a real number such that |x + 2| + |x| ≤ 1, then x 2 + 2x − 1 ≤ 2.

(b) If x is a real number such that |x + 2| + |x| ≤ 2, then x 2 + 2x − 1 ≤ 2.

(c) If x is a real number such that |x + 2| + |x| ≤ 3, then x 2 + 2x − 1 ≤ 2.

(d) If x is a real number such that |x + 2| + |x| ≤ 5, then x 2 + 2x − 1 ≤ 2.

(2) Prove or disprove the statements: (a) If z is a complex number such that |z + 1| + |z − 1| ≤ 3, then |z 2 − 1| ≤ 2.

(b) If z is a complex number such that if |z 2 − 1| ≤ 2, then |z + 1| + |z − 1| ≤ 3.

(3) A clock with a face that has the numbers 1 through 12 has three hands that indicate the second, minute and hour of the day.

Assume that the center of the clock is at position (0, 0), and at noon the end points of the hands are (respectively) at (0, 1), (0, 3/4), (0, 1/2).

(a) Give the position of the end points of each of the hands at time t where t represents the number of seconds after noon in both polar and rectangular coordinates (make sure that you label which you are using clearly).

(b) At what times do your equations say that the hands of the clock will all align?

step by step solution, please

For each of the following vector fields F, decide whether it is conservative or not by computing curl F. Type in a potential function f (that is, ∇f=F). Assume the potential function has a value of zero at the origin. If the vector field is not conservative, type N.

A. F(x,y)=(−14x−6y)i+(−6x+6y)j

f(x,y)=

C. F(x,y,z)=−7xi−6yj+k

f(x,y,z)=

D. F(x,y)=(−7siny)i+(−12y−7xcosy)j

f(x,y)=

E. F(x,y,z)=−7x^2i−6y^2j+3z^2k

f(x,y,z)=

Section 8.1 Expanded: Constructing the nonlinear profit contribution expression Let PSand PDrepresent the prices charged for each standard golf bag and deluxe golf bag respectively. Assume that “S” and “D” are demands for standard and deluxe bags respectively. S = 2250 – 15PS (8.1) D = 1500 – 5PD (8.2) Revenue generated from the sale of S number of standard bags is PS*S. Cost per unit production is $70 and the cost for producing S number of standard bags is 70*S. So the profit for producing and selling S number of standard bags = revenue – cost = PSS – 70S (8.3) By rearranging 8.1 we get 15PS= 2250 – S or PS= 2250/15 – S/15 or PS= 150 – S/15 (8.3a) Substituting the value of PSfrom 8.3a in 8.3 we get the profit contribution of the standard bag: (150 –S/15)S – 70S = 150S – S2/15 – 70S = 80S – S2/15 (8.4) Revenue generated from the sale of D number of deluxe bags is PD*D. Cost per unit production is $150 and the cost for producing D number of deluxe bags is 150*D. So the profit for producing and selling D number of deluxe bags = revenue – cost = PDD – 150D (8.4a) By rearranging 8.2 we get 5PD= 1500 – D or PD= 1500/5 – D/5 or PD= 300 – D/5 (8.4b) Substituting the value of PDfrom 8.4b in 8.4a we get the profit contribution of the deluxe bags: (300 -D/5)D – 150D = 300D – D2/5 – 150D = 150D – D2/5 (8.4c) By adding 8.4 and 8.4c we get the total profit contribution for selling S standard bags and D deluxe bags. Total profit contribution = 80S –S2/15 + 150D – D2/5 (8.5) Reconstruct new objective function for 8.5 by changing “15PS” to “8PS” in 8.1, “5PD” to “10PD” in 8.2, cost per unit standard bagfrom 70 to “last two digits of your UTEP student ID” and cost per unit deluxe bagfrom 150 to 125. Keep other parameter values unchanged. Use up to 2 decimal points accuracy. Substitute the new expression for 8.5 in the excel solver workbook as explained in the class and solve for the optimal combination values for S and D. Student ID last two numbers 52, I NEED THE EXAMPLE IN EXCEL SHEET FORMAT.

1. Use cardinality to show that between any two rational numbers there is an irrational number. Hint: Given rational numbers a < b, first show that [a,b] is uncountable. Now use a proof by contradiction.

2. Let X be any set. Show that X and P(X) do not have the same cardinality. Here P(X) denote the power set of X. Hint: Use a proof by contradiction. If a bijection:X→P(X)exists, use it to construct a set Y ∈P(X) for which Y is not in the range of f.

Using the definition of a young function, prove that the conjugate phi^* of a young function phi is a young function