A helicopter makes a force landing at sea. The last radio signal received at station C gives the bearing of the helicopter from C as at an N 57.1 degrees. E altitude of 423 feet. An observer at C sights the helicopter and gives <DCB as 12.1 degrees. How far will a rescue boat at A have to travel to reach any survivors at B? Apply the rules regarding the use of significant digits when determining your answer. Round your answer to the nearest ten feet.

Distance rescue boat travels = ________ ft

Convert the following to a decimal, scientific notation, and engineering notation

Decimal to scientific and engineering notation: 270, 14600, 0.000456, 0.022, 0.000000051, 66500000, 423000, 0.78

Scientific notation to decimal and engineering notation,4.5x10^4, 6.8x10^-8, 2.7x10^5, 7.22x10^-2, 9.52x10^-5, 1.89x10^2, 3.6x10^7, 8.62x10^-10

engineering notation to decimal and scientific notation,12k, 68p, 2.1G, 82T, 7.1n, 100m, 1.8k

In a particular card​ game, each player begins with a hand of 3 ​cards, and then draws 6 more. Calculate the probability that the hand will contain one pair​ (2 cards of one​ value, with the other cards of 7 different​ values).

Consider the following set of vectors in R6

S={[-9 7 -8 3 0 -5], [1 -7 3 2 -8 -8], [-6 -14 1 9 -23 -29], [11 -21 14 1 -16 -11], [8 16 -8 8 10 1], [17 -7 13 -8 8 18]

(a) (2 points) Demonstrate that S is not a basis for R6.

(b) (4 points) Let H = Span S. Find a basis for H and determine its dimension.

(c) (2 points) Determine whether v= [1,1,1,−1,−1,−1] ^T belongs in H or not.

(d) (6 points) Find a basis for R6 consists of the basis vectors of H found in part (b) and some additional linearly independent vectors.

(e) (4 points)Suppose A is a 6×6 matrix and T(x) =Ax. Show that T(H), the set of images of vectors of H, is a subspace of R6.

(f) (3 points) Show that dimT(H)≤dimH

(g) (4 points) Suppose A is invertible. Show that dimT(H) = dimH.

(h) (5 points)Suppose K is a 4 dimensional subspace of R6. Show that Hand K must have a nonzero vector in common.Hint: Start with bases for the two subspaces. If H andKonly have the trivial vector in common, then what’s a basis for the subspace H+K?

A population, obeying the logistic equation, begins with 1000 bacteria, then doubles itself in 10 hours. The population is observed eventually to stabilize at 20,000 bacteria. Find the number of bacteria present after 25 hours and the time it takes the population to reach one-half of its carrying capacity.

Please show all work and steps clearly so I can follow your logic and learn to solve similar ones myself. I will rate your answer for you and provide positive feedback. Thank you kindly!

You have 10 friends: 3 couples and 4 singles. How many ways can you invite 7 of them to your house, such that the two people of every couple are either both invited or not?

Use Matlab to find a subset of the set of vectors that forms a basis for the span of the vectors.

(a) {(1, 2, −1, 0), (−3, −6, 3, 0), (1, 0, 0, 1), (−2, −2, 1, −1)}

The zoo is building a new polar bear exhibit, and wants to put a semi-circular window in the concrete wall of the swimming tank. (Note: picture is not to scale)



If the semi-circle has diameter 80 centimeters, and the bottom of the window is at a depth of 3 meters, find the hydrostatic force on the window.



   Newtons

A=[ 7 8 -2 -6 7 4 1 ; 2 4 -4 -13 9 9 -12 ; 6 6 0 -9 8 9 -4 ; 1 8 -14 -22 5 8 -1 ; 4 9 -10 -14 7 4 -1]

B=[ 19 4 4 14 -3 -7 -5 ; 21 -6 -5 10 14 -2 4 ; 22 -4 5 13 5 -6 4 ; 41 20 0 26 11 -1 -27 ; 29 14 -2 20 3 -4 -19]

Remark: You may only use rref , or commands that are covered in our MATLAB guides, and no other special MATLAB functions for this problem.

(a) (3 points) Find a basis for Col(A) and determine its dimension.

(b) (5 points) Find a basis for Nul(A) and determine its dimension.

(c) (3 points) Find a basis for Row(A) and determine its dimension.

(d) (5 points) Find a basis for the left nullspace of A and determine its dimension.

(e) (2 points) Find a basis for Col(B) and determine its dimension.

(f) (6 points) Determine whether Col(A) = Col(B), i.e. determine whether the two given subspaces of R 5 are the same or not. If not, find a vector v

that belongs in one of the subspaces and not the other.

(g) (6 points) Determine whether Nul(A) = Nul(B). If not, find a vector v that belongs in one of the subspaces and not the other.

Use generating functions to solve the following recurrence relation: an = 2an−1 + 3n , n ≥ 1 a0 = 2

Assume you have been given $400,000 CAD with access to all listed stocks, bonds, futures, and options worldwide. You can trade in options and futures, in combination with the underlying asset. Assume today is Feb 1, 2020 and you have been given $400,000 CAD fake money to trade until April 20, 2020.

Perform a bear spread (either call or put) strategy.

Describe the trade and provide the reason for such trade.

Please provide table and or/ graph.

Kolkmeyer Manufacturing Company is considering adding two machines to its manufacturing operation. This addition will bring the number of machines to ten. The president of Kolkmeyer asked for a study of the need to add a second employee to the repair operation. The arrival rate is 0.05 machines per hour for each machine, and the service rate for each individual assigned to the repair operation is 0.4 machines per hour.

Compute the operating characteristics if the company retains the single-employee repair operation. If required, round your answers to four decimal places. P0 = Lq = L = Wq = hours W = hours

Compute the operating characteristics if a second employee is added to the machine repair operation. If required, round your answers to four decimal places. P0 = Lq = L = Wq = hours W = hours

Each employee is paid $20 per hour. Machine downtime is valued at $70 per hour. From an economic point of view, should one or two employees handle the machine repair operation? Explain. If required, round your answers to two decimal places. Cost of one employee system: $ Cost of two employees system: $ From an economic point of view, should handle the machine repair operation.

Can anyone help?

Given n ∈N and p prime number and consider the polynomial f (x) = xn  (xn-2)+1-p

1)Prove that f (x) is irreducible in Q [x]

2) If n = 1 and p = 3, find Q [x] / f (x))

3) Show that indeed Q [x] / (f (x)) is a field in the previous paragraph

PLEASE answer all subsections