The cities of Abnarca and Bonipto have populations that are growing exponentially. In 1980, Abnarca had a population of 23,000 people. In 1990, its population was 28,000. Bonipto had a population of 35,000 in 1980. The population of Bonipto doubles every 55 years.
(a) How long does it take the population of Abnarca to double?
(b) How long will it take for Abnarca's population to equal that of Bonipto?
In: Math
In: Math
1. A manufacturing company manufactures a cardboard box with a square base and a height of 15 inches. Suppose the equation x2 +60x- 7,200 = 0 can be used to find the length and width of the base of the box, each measuring x inches.
Write the equation in factored form.
Use the zero product property to solve the equation. Show all the steps needed to find both answers.
Explain how the solution relates to this situation
2. City engineers decide to build a rectangular dog park that has an area of 3,600 square yards, where the length of the park is 10 more yards than twice its width. The equation x2 +5x-1,800 = 0 can be used to find the width of the dog park.
Write the equation in factored form
Use the zero product property to solve the equation. Show all the steps needed to find both answers.
Explain how the solution relates to this situation.
3. A graphic designer uses a photo editing program to increase both the height and width of a square image by 3 inches. Suppose the equation x2 +6x-55 = 0 can be used to find the height and width of the original image.
Write the equation in factored form.
Use the zero product property to solve the equation. Show all the steps needed to find both answers.
Explain how the solution relates to this situation.
In: Math
Which of the following statements are TRUE or False. (Explain why it’s true or false?)
Subtracting a positive number from a negative number always gives you a negative number.
Subtracting two negative numbers always gives you a negative number.
Subtracting a - b is the same as adding a + (-b).
A positive number minus a negative number is always a positive number.
The difference of a number and its opposite gives you zero.
Zero minus a number is the same as a number minus zero.
In: Math
Roots of a complex number
Find all the solutions to the equation
(a) z^ 4 − 1 = 0
(b) z ^5 + 2^5 i = 0
(c) z^ 6 − 16z^ 3 + 128 = 0
In: Math
On the standard coordinate grid at initial moment, ship Tiger is at the position (0, 352), ship Lion is at the position (511, 0). Tiger sails along the straight line to the position (724, 0). At the same time, Lion sails along the straight line to the position (0, 565). Lion will reach her destination in one hour, Tiger – in two hours.
Task:
In: Math
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
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