For the ellipse 6? 2 + 4? 2 = 36, find the eccentricity and sketch the graph showing all main features including axis intercepts, foci and directrices.

b) Using exclusively some part of your answer to part a), determine the foci and directrices for the curve: (? + 2) 2 6 + (? − 3) 2 9 =

Reply to the following Discussion Question with a substantive post - one that demonstrates that you understand the mathematical concepts and provides an explanation rather than just making a simple statement about the topic:

Give an example of a function whose Taylor polynomial of degree 1 about x = 0 is closer to the values of the function for some values of x than its Taylor polynomial of degree 2 about that point.

Taco Smell sells only tacos. They offer three types of tortillas, four types of meat, four types of cheese and seven types of salsa. If you must choose exactly one of each for your taco, how many different kinds of tacos can you order at Taco Smell?​

The Richter Scale gives a mathematical model for the magnitude of an earthquake in terms of the ratio of the amplitude of an earthquake wave (also known as the intensity of an earthquake) to the amplitude of the smallest detectable wave. If we denote the magnitude of the earthquake by R, the intensity (also known as the amplitude of the earthquake wave) of the earthquake by A, and the amplitude of the smallest detectable wave by S, then we can model these values by the formula R=log(A/S) In 1906, San Francisco felt the impact of an earthquake with a magnitude of 7.8. Many pundits claim that the worst is yet to come, with an earthquake 891,690 times as intense as the 1989 earthquake ready to hit San Francisco. If the pundits ability to predict such earthquakes were correct, what would be the magnitude of their claimed earthquake? Round your answer to the nearest tenth.

Express your answer as an integer, or as a fraction in lowest terms if necessary.

1. If g(x) = - 3 f(x),   where f(6) = 10 and f'(6) = - 4,   find g'(6).

2. If g(x) = 5 x + 6 f(x), where f(- 5) = 3 and f'(- 5) = - 10, find g'(- 5).

3. If f(x) = (e^x) / x , find f'(1).

4. If f(x) = - sin x sec x,   find f'(0).

5. If h(x) =   3x f(x) - 11 g(x), where   f(2) = 15,   g(2) = 12,   f'(2) = 4, and   g'(2) = 6, find h'(2).

6. If h(x) = f(x) g(x), where f(1) = 3,   g(1) = - 5,   f'(1) = 7,   and   g'(1) = 10, find h'(1).

7. If h(x) = [f(x)] / [g(x)], where f(- 3) = - 2,   g(- 3) = 3,   f'(- 3) = 6, and   g'(- 3) = - 9, find   h'(- 3).

8. If g(x) = 1 / [f(x)], where   f(3) = 4 and   f'(3) = - 3, find   g'(3).

9. If h(x) = f(x) + [g(x)]^2,   where f(- 7) = 6, g(- 7) = 5, f'(- 7) = - 2, and g'(- 7) = - 4, find   h'(- 7).

10. If   h(x) = f (g(x)), where f(0) = 7,   g(0) = - 1,   f'(0) = 0,   g'(0) = - 3,   f(- 1) = - 3,   g(- 1) = 2,   f'(- 1) = - 5, and   g'(- 1) = 4, find h'(0).

Arrange the following data into a frequency distribution table and explain the solution step-by-step :

41 60 72 72 65 64 48 90

60 75 53 48 63 49 58 39

39 75 55 62 53 59 58 38

72 62 60 59 68 60 70 60

56 80 65 85 71 45 70 55

Find measure central tendency.

Find measure dispersion.

Arrange the following data into a frequency distribution table and explain the solution step-by-step :

41 60 72 72 65 64 48 90

60 75 53 48 63 49 58 39

39 75 55 62 53 59 58 38

72 62 60 59 68 60 70 60

56 80 65 85 71 45 70 55

Find measure central tendency.

.

A company produces and sells 3 types of organic fertilizer. A pound of Brand 1 earns a profit of $3 per pound. Brand II earns a profit of $4 per pound, and Brand III earns a profit of $3 per pound. 1 pound of Brand I requires 3 pounds of raw material and takes 2 hours of labor to produce it. 1 pound of Brand II requires 4 pounds of raw material and takes 3 hours of labor to produce it. 1 pound of Brand III requires 2 pounds of raw material and takes 2 hours of labor to produce it. Each day the company has 250 pounds of raw materials to use and because of union rules must have at least 100 labor hours for its workers. In addition since Brand II is the most popular they need to produce at least 15 pounds of it.

How many pounds of each Brand of fertilizer should they produce each day to maximize their profit? And what is their profit?

The quantity demanded x (in units of a hundred) of the Mikado miniature cameras/week is related to the unit price p (in dollars) by p = −0.2x^2 + 220 and the quantity x (in units of a hundred) that the supplier is willing to make available in the market is related to the unit price p (in dollars) by p = 0.1x^2 + 8x + 110 If the market price is set at the equilibrium price, find the consumers' surplus and the producers' surplus. (Round your answers to the nearest dollar.)

solve for |2x-5|>4x-1

-a) Find the equation of the line in its vector, parametric and symmetrical shapes that passes through the point.

P (5, -2, 4) and it's perpendicular to the plane 4x-3y+5z=0.

b) Find the equation of the plane (Cartesian and vector) that passes through the points. A (1, -1, -1), B (3, 5, 7), C (1, 6, 8).

Use power series to solve the initial value problem

x^2y''+xy'+x^2y=0, y(0)=1, y'(0)=0

f(x,y)=sin(2x)sin(y)

intervals for x and y:

-π/2 ≤ x ≤ π/2 and -π ≤ y ≤ π

find extrema and saddle points

In the solution, I mainly interested how to findcritical points in case of the system of trigonometric equations (fx=0 and fy=0).
,