1. Is it possible for a rational function to have no vertical asymptotes? If yes the how? If no then why?

2. What is the fundamental difference between a rational function and a polynomial function?

3. Can a rational function have no x - intercepts? If so then how?

4. Can a rational function have two y-intercepts? Why or why not?

5. Can the graph of a rational function cross the vertical asymptote? Why or why not?

Please TYPE out answer, just need detailed explanations to these answers please!

Estimating the time of a victim’s death during homicide investigations is a complex problem that cannot be solved by analysising simple equations or functions of one variable. However, many mathematical texts examine time of death estimation based around analysis of Newton’s Law of Cooling. Such analysis is based on implicit simplifying assumptions that: the only dependent variable of interest in determining the time of death is the victim’s body temperature, T(t); the victim’s baseline body temperature when alive, T0, is known; and the air temperature of the victim’s surroundings, Ts, is constant. Here we will examine such a problem.

(a) Assume that immediately following death, a victim’s body begins to cool from a standard healthy body temperature of 37◦ Celsius. Further, assume that experimental work has determined that the rate constant in Newton’s Law of Cooling for a human body is approximately k = 0.1947 when time t is measured in hours. Determine a function derived from Newton’s Law of Cooling, T(t), that models the temperature of a victim’s body t hours after death, assuming that the temperature of the body’s surroundings is a constant 15.5◦ Celsius

. (b) If the temperature of the victim’s body is now 22.2◦, how long ago was their time of death? (c) If the victim’s body temperature at death had instead been 36.3◦ Celsius (within the range of normal body temperatures for a healthy adult), what time of death would be estimated via a Newton’s Law of Cooling model? By what duration does this estimate differ to the time that you determined in part

(b)? (d) In reality, how might the modelling assumptions made to address this problem be violated?

Instructions: Identify the common ratio and first term and fill in the recursive formula for each of the following geometric sequences. 4,8,16,32,64… 4 , 8 , 16 , 32 , 64 … Common Ratio: ?= r = Answer First Term: Answer ??=??−1⋅ a n = a n − 1 ⋅ Answer ?1= a 1 = Answer 2,6,18,54,164 2 , 6 , 18 , 54 , 164 Common Ratio: ?= r = Answer First Term: Answer ??=??−1⋅ a n = a n − 1 ⋅ Answer ?1= a 1 = Answer −1,5,−25,125 − 1 , 5 , − 25 , 125 Common Ratio: ?= r = Answer First Term: Answer ??=??−1⋅ a n = a n − 1 ⋅ Answer ?1= a 1 = Answer

Match the slope field related to the eigenvectors of the followiing systems of differential equations:

x1'=x1+x2

x2'=-x1-x2

In recent months, two new stores have opened in town. Each claims to have the best selection for the best price! Use the shopping list below to make a decision about which grocery store you would choose to patron if you were interested in maximizing the number of items you can buy for the least amount of money.

Shopping List:Tide Original High Efficiency Liquid Laundry Detergent, 100 oz;

Bounce Fabric Softener Dryer Sheets, Outdoor Fresh, 240 sheets;

Pantene Pro-V Classic Clean Shampoo, 20.1 fl oz;

Listerine Cool Mint Antiseptic Mouthwash Oral Care And Breath Freshener, 1.5 L;

Olay Moisturizing Face Lotion for Sensitive Skin, 6.0 fl oz;

Opti-Free Pure Moist Contact Solution, 20 fl oz;

Windex Original Glass Cleaner Spray, 23 fl oz;

Febreze Fabric Refresher with Gain Original, 27 oz;

Folgers Gourmet Supreme Dark Roast Ground Coffee, 24.2 oz;

LEGO Creator Mighty Dinosaurs 31058

Find the median of money spent on items ON THE SHOPPING LIST for both Company A and Company B.

Important!: The shopping list only has 10 items; whereas, the entire list has 30 items.

Median cost of items for Company A on the shopping list: (Go to two decimal places):$

Median cost of items for Company B on the shopping list: (Go to two decimal places):$

*****

A Ferris wheel is 25 meters in diameter and boarded from a platform that is 1 meter above the ground. The six o’clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 10 minutes. The function h(t) gives a person’s height in meters above the ground t minutes after the wheel begins to turn.

1. Find the amplitude, midline, and period of h(t).
2. Find the domain and range of the function h(t) and
3. Find a formula for the height function h(t).
4. State the phase shift and vertical translation
5. How high off the ground is a person after 5 minutes?
6. what would happen if the diameter of the Ferris wheel increases?
7. The time it takes the ferris wheel to complete one full revolution decreases?

The point P(x,y) is 4/5 of the way from the point A(8, -1) to the point B(-2, 4). Find the ordinate of point P.

1. The percentage of automobile consumers who are under 50 years of age decreased approximately linearly from 56.1% in 1990 to 51.3​% in 2005.

a. Predict when the percentage will be 42​%.

b. Predict the percentage in 2014.

(3) (1.1: Geometry) For each part below, give an example of a linear system of
equations in two variables that has the given property. In each case, draw the lines
corresponding to the solutions of the equations in the system.
(a) has no solution
(b) has exactly one solution
(c) has infinitely many solutions
(i) Add or remove equations in (b) to make an inconsistent system.
(ii) Add or remove equations in (b) to create infinitely many solutions.
(iii) Add or remove equations in (b) so that the solution space remains unchanged.
(iv) Can you add or remove equations in (b) to change the unique solution you had
to a different unique solution?
In each of (i) - (iv) justify your action in words.

Help with B and i - iv especially please

Subject to

2x+6y<= 36

4x+2y<= 32

x>= 0

y>= 0

Maximum is ___________ at

x = ______

y = ______

A population of 50 mice was introduced into a field where there haven't been any mice before. Even though they had to deal with predators, the population grew at 2% per month.

1. Create an exponential model where p in the population of mice and m is the number of months that have passed since the initial population was introduced.

2. How many months does your model say it will take the population to reach 100? How about 200? Fill in the blanks and explain how you did it

It will take ________ months from the initial introduction for the population to reach 100, and _______ months from the initial introduction for the population to reach 200.

3. The "rule of 70" says that if a number grows at p% per time period, it will take about 70/p time periods to double. For example, a population that grows at 1% per year should take about 70/1=70 years to double. Explain how your work in the previous problem shows that this "rule" was followed by the mouse population.

Given that in a triangle a=26 b=21 and c=14, choose the order or orders you should find the angles using the Law of Cosines to find the first angle, followed by the Law of Sines to find the second angle. It is possible to have more than one right answer.

_____B C A

_____A C B
_____B A C

_____A B C
_____C A B

_____C B A
  

Thank you! A big thumbs up awaits!

Solve the system of equations:

x+y^2=6y

x-2y=-5

Prove that, in hyperbolic geometry, for each point P and a line l not containing P, there are infinitely many lines through P parallel to l.

Given the conic section written in general form:  25x^2 + y^2 + 50x - 10y + 25 = 0

FIND:

Part a) Identify which type of graph the conic section has.

Part b) Now rewrite the equation in Standard Form for that particular type of Conic section.

Part c) Use its Standard Form to graph the conic section.

Part d) Label any vertices, focal points, center, radius, directrix or asymptotes as is appropriate for each graph.