You are the building manager for a cylindrical skyscraper with a slanted roof. You must contract a window cleaner fwho works for $35 an hour and can clean 1 square meter of glass per minute. If you know the building is 120m tall at its highest point and 100m tall at its lowest point, and 20m wide, how much should you budget for the contract? Use a line integral of a scalar function to solve. Assume there are no windows to be cleaned on the roof.

Show which of the following models can be estimated by the OLS, where X, y and Z are variables and α,β,γ are parameters to be estimated. The models can be rearranged if necessary.

(1) y_t=α+βx_t+u_t [5 marks]

(2) y_t=e^α x_t^β e^(u_t ) [5 marks]

(3) y_t=α+βγx_t+u_t [5 marks]

(4) y_t=α+βx_t Z_t+u_t [5 marks]

Use normal vectors to determine the intersection, if any, for each of the following groups of three planes. Give a geometric interpretation in each case and the number of solutions for the corresponding linear system of equations. If the planes intersect in a line, determine a vector equation of the line. If the planes intersect in a point, determine the coordinates of the point.

a x + 2y + 3z = −4

b x + 2y + 3z = −4

2x + 4y + 6z = 7

2x + 4y + 6z = 7

x + 3y + 2z = −3

3x + 6y + 9z = 5

c x + 2y + z = −2

d x − 2y − 2z = 6 2x + 4y + 2z = 4 2x − 5y + 3z = −10 3x + 6y + 3z = −6 3x − 4y + z = −1

e. x − y + 3z = 4 x + y + 2z = 2 3x + y + 7z = 9

Let X be a set containing infinitely many elements, and let d be a metrio on X. Prove that X contains an open set U such that U and its complement Uc = X\U are both infinite

Suppose an electrical circuit contains a 1 H inductor, a 10 Ω resistor and a capacitor rated at 1/7 F. If the circuit is hooked up to an alternating voltage source described by E(t) = 68 cost V and initially q(0) = 1 C and i(0) = 0 A, find a function that describes the charge as a function of time.  Lq'' + Rq' + q/C = E(t).  

Please show work using a complementary and particular solution if possible.

Use the variation of parameters method to solve the differential equation:

y''' - 16y' = 2

Answer correctly supporting with clear explanation.

Classify the set Q( √ 5i) as a ring or a field. To justify your answer, show that the set satisfies the axioms for ring or field.

National Highways Authority (NHA) is considering a public-private partnership with Friends construction as main contractor using a DBOMF contract for a new 50-mile motorway on the outskirts of Baluchistan Province. The design includes seven 10-mile-long commercial/retail corridors on both sides of the road. Motorway construction is expected to require 6 years at an average cost of $4 million per mile. The discount rate is 11% per year, and the study period is 30 years. Initial investment is $200 million distributed over 5 years; $50 million now and in year 6 and remaining amount equally in rest of the years. Annual operating cost is $10 million per year, plus an additional $5 million every six years. Annual revenues Include tolls and retail/commercial growth; start at $5 million in first year, increasing by a constant $2 million annually through year 10, and then increasing by a constant $3 million per year through year 20 and remaining constant thereafter. Disbenefits include loss of income to people in surrounding areas; start at $15 million in year 1, decrease by $2 million per year through year 21, and remain at zero thereafter.

Required: Evaluate the economics of the proposal using (a) the modified B/C analysis from the NHA’s perspective and (b) the profitability index from the Friends construction viewpoint in which disbenefits are included and not included.

can we have two limit cycles in a 2d state space? if possible how can we draw them?

Definition Call a number eld super-constructible if there is a tower of eld extensions,

=0 1 =, where[+1 ]=1,2,or3.

1) Give an example of a eld that is not super-constructible. Prove that your example is correct.

2) Give an example of a super-constructible eld that is not a constructible number eld. Prove that your answer is correct.

Derive a formula relating the angle sum of a quadrilateral on a sphere of radius R to its area.

find the general solution of the given differential equation.

1. y'' + y = tan t, 0 < t < π/2

2. y'' + 4y' + 4y = t^-2 e^-2t , t > 0

find the solution of the given initial value problem.

3. y'' + y' − 2y = 2t, y(0) = 0, y'(0) = 1

Question#1
How many positive integers between 100 and 888 inclusive,

a) are divisible by 7?

b) are odd?

c) have distinct digits?

d) are not divisible by 6?

e) are divisible by either 4 or 7?

f) are not divisible by either 4 or 7?

g) are divisible by 4 but not by 7?

h) are divisible by 4 and 7?

Question#1
How many positive integers between 100 and 888 inclusive,

a) are divisible by 7?

b) are odd?

c) have distinct digits?

d) are not divisible by 6?

e) are divisible by either 4 or 7?

f) are not divisible by either 4 or 7?

g) are divisible by 4 but not by 7?

h) are divisible by 4 and 7?

please type the answers if possible! I've been having trouble reading the handwriting lately!

PLEASE MAKE SURE IS A "MINITAB" ANSWER, OTHERWISE... DON'T BOTHER. THANK YOU.

A company that stamps gaskets out of cork sheets and wants to compare the mean number of gaskets produced per hour for three different types of stamping machines. The company wants to use the data to determine whether one machine is more productive than the other. To answer these questions, the manufacturer decides to conduct an experiment with each of the machines operating for six 1-hour time periods assigned in a random order to eliminate the possibility of bias. The data for the experiment, the number of gaskets (in thousands) produced per hour is shown below. (a) State the hypotheses and conduct an analysis of variance at α = 0.05 to test the hypotheses. Create a boxplots of the data as part of the oneway ANOVA. (b) Plot and analyze the residuals from the experiment and comment on model adequacy. (c) Is there sufficient evidence to indicate that any machine is more productive than the others? Machine 1 Machine 2 Machine 3 431 427 440 436 442 448 401 394 389 404 441 418 421 409 418 425 393 422