a) Prove stereographic projection maps circles not containing (0,0,1) from the upper half sphere’s surface into circles on the z = 0 projection plane. b) What happens under stereographic projection to circles containing (0,0,1), or otherwise the North Pole? Draw a sketch showing this.

In: Math

The number of consumer complaints against the top U.S. airlines in 2013 in given in the following table.

Airline | Complaints |
Complaints per 100,000 Passengers Boarding |

Southwest Airlines | 397 | 0.34 |

Alaska Airlines | 86 | 0.44 |

Delta Airlines | 713 | 0.59 |

JetBlue Airways | 192 | 0.63 |

AirTran Airways | 130 | 0.73 |

SkyWest Airlines | 217 | 0.80 |

Mesa Airlines | 71 | 0.85 |

Endeavor Air | 113 | 0.86 |

ExpressJet Airlines | 319 | 0.96 |

Hawaiian Airlines | 105 | 1.06 |

Virgin America | 81 | 1.28 |

US Airways | 806 | 1.42 |

American Eagle Airlines | 303 | 1.70 |

American Airlines | 1730 | 1.99 |

United Airlines | 1935 | 2.14 |

Frontier Airlines | 316 | 3.09 |

(a) By considering the numbers in the colum labeled "Complaints," caclulate the mean and median number of complaints per airline.

(b) Explain why the averages found in part (a) are not meaningful.

(c) Find the mean and median of the numbers in the column labeled "Complaints per 100,000 Passengers Boarding." Discuss whether these averages are meaningful.

In: Math

Define a subspace of a vector space V . Take the set of vectors
in Rn such that th

coordinates add up to 0. I that a subspace. What about the set
whose coordinates add

up to 1. Explain your answers.

In: Math

Write an equation in slope-intercept form of the line that
satisfies the given conditions .

Through (-2,-2); parrallel to -x + 2y = 10

In: Math

An auto dealer's sales numbers are shown in the table below. Find for each month the mean, median, and mode prices of the cars she sold. Round your answers to the nearest dollar.

Number sold |
|||

Price |
May | June | July |
---|---|---|---|

$25,000 | 22 | 25 | 24 |

$15,000 | 49 | 24 | 24 |

$13,500 | 25 | 49 | 49 |

June

mean | $ |

median | $ |

mode | $ |

July

mean | $ |

median | $ |

mode | $ |

In: Math

Solve 8 cos ( 2 β ) = 8 sin 2 ( β ) + 3 for all solutions 0 ≤ β < 2 π

β=

In: Math

A doctor administers a drug to a

33-kg

patient, using a dosage formula of

55

mg/kg/day. Assume that the drug is available in a

100

mg per 5 mL suspension or in

200

mg tablets. a. How many tablets should a

33-kg

patient take every four hours?

b. The suspension with a drop factor of 10 ggt/mL delivers the drug intravenously to the patient over a twelve-hour period. What flow rate should be used in units of ggt/hr?

a. The patient should take

nothing

pills every four hours.

(Type an integer or decimal rounded to the nearest hundredth as needed.)

b. The intravenous suspension flow should be set to

nothing

ggt/hour.

(Type an integer or decimal rounded to the nearest hundredth as needed.)

In: Math

W=e^x^2+sin(xy) where x=2s-t and y= t-s.

how to write generic chain rule

find when s=, t=1

In: Math

Iterative method of solving large systems

In: Math

Find the equation of the tangent plane to the surface,

(4x^2)(y^3) + (5yz) + (2xz^3) = 7

at the point P(-1,1,1). Also nd the parametric equation of the normal

line to that surface at that point . Sketch a picture that illustrates what this

is all about.

In: Math

1. A 10 ft chain weighs 25 lb and hangs from a ceiling with a 5 lb weight attached to the end. Find the wok done lifting the lower end of the chain and the weight to the ceiling so that they are level with the upper end.

2. Use the method of cylindrical shells to find the volume formula for a sphere with radius r. (in our example we used the disk method. You formula should be the same, but the integral you use to get there should be different.

In: Math

**( NO HAND WRITING PLEASE )**

**Q1**: **Suppose that a and b are
integers, a ≡ 11 (mod 19), and**

**b ≡ 3 (mod 19). Find the integer c with 0 ≤ c ≤ 18
such**

**that**

**a) c ≡ 13a (mod 19).**

**b) c ≡ 8b (mod 19).**

**c) c ≡ a − b (mod 19).**

**d) c ≡ 7a + 3b (mod 19).**

**e) c ≡ 2a ^{2} + 3b^{2} (mod
19).**

**Q2**:

**List all the steps used to search for 10 in the
sequence 1,3, 4, 5, 6, 8, 9, 11 using**

**a) A linear search.**

* b) A binary search*.

In: Math

Utilize identities to calculate the exact value of the five remaining trigonometric functions if:

csc(α)= √3, π/2, < α < π

Calculate the equivalent algebraic expression for:

sec(arcsin(x - 1)

In: Math

x' = x − y

y' = 4y − x^2*y

Linearize the system about the point (2, 2). Classify the type and stability of the critical point at (2, 2) by examining the linearized system.

In: Math

a) A salt-water tank has pure water flowing into it at 5 L/min.
The contents of the tank are kept thoroughly mixed, and the
contents flow out at 5 L/min. Initially, the tank contains 1 kg of
salt in 10L of water. How much salt will be in the tank after 20
minutes? Let ?? represent the amount of salt in the tank at time t
and let ?? represent the volume of saltwater in the tank at time
t.

b) Now assume that salt is added into the tank at a rate of 0.1 kg/min with pure water still flowing into it at 5 L/min. The contents of the tank are kept thoroughly mixed, and the contents flow out at 5 L/min. Initially, the tank contains 1 kg of salt in 10L of water. How much salt will be in the tank after 20 minutes?

In: Math