For the following questions:

A. Draw a picture

B. Compute the different lengths

C. Compare lengths or replace into formula for sphere

D. Explain your final results in complete sentences

1. Find the midpoint of the segment connecting the points A(3,5,2) and B(4,8,6).
2. Find the equation of a sphere if one of the diameters has endpoints A(5,4,3) and B(1,6,-9).
3. Determine whether the points A(1,0,1), B(2,1,-1), and C(3,2,1) all lie on the same straight line.
4. Determine whether the triangle with corners at A(1,2,3), B(2,4,5) , C(3,6,7) is a) a right triangle b) an isosceles triangle.
5. Find an equation of the set of all points equidistant from the points A(-1,5,3), and B(6,2,-2).

what is the formular of binomial probability

Evaluate the improper integral or state that it is divergent.

Parameterize the given curves:

a) The ellipse in the plane x=11 centered at the origin and going thru the points (+/- 7,0) and (0,+/- 3) from the perspective of the yz-plane.

b) The circle in the plane z=-2 with radius 7 centered at the origin

. Let f(x) = 3x^2 + 5x. Using the limit definition of derivative prove that f '(x) = 6x + 5

Then, Find the tangent line of f(x) at x = 3

Finally, Find the average rate of change between x = −1 and x = 2

why is agenda setting accurate and fruitfull?

Mary has on her bookshelf 5 novels, 4 biographies, and 8 textbooks.

Mary wants to take a fiction and a non-fiction book with her on a short trip.

(a) How many different ways can she do this?

(b) Mary thinks a little and then decides that she wants instead to take a novel and a biography. How many different ways can she do this?

(c) On a longer trip Mary decides to take three novels and four non-fiction books with at least one of the non-fiction books a biography. How many ways are there to make such a selection?

Calculate the double integral ∫∫Rxcos(x+y)dA∫∫Rxcos⁡(x+y)dA where RR is the region: 0≤x≤π3,0≤y≤π2

A new virus strain starts out with one infected individual and passes on to others in such a
way that the number of infected individuals triples every four days. Assume that there is no
deterrent for the spread of the virus.
(a) Set up an appropriate modelling function to determine the number of infected individuals
t days after the outbreak.
(b) Determine how many individuals will be infected 10 days after the outbreak.
(c) Determine how long it will take for the number of infected individuals to reach 100,000.

The position of a point on a line is given by the equation(t)= t3-6t2+9t-4, where s is measured in metres and t in seconds. What is the velocity of the point after 2 seconds? What is its acceleration after 4 seconds? Where is it when is first stops moving? How far has it travelled when its acceleration is 0?

Answer the following questions:

Part A: Volumes of Revolution

a) Find the volume of the solid obtained when the region bounded by y = 1/x , and the lines x = 1, x = 3 and y = 0 is rotated about the x-axis.

b) Find the volume of the solid obtained by revolving the region bounded by the parabolas y = x^2 and y^2 = 8x about the x-axis.

c) Find the volume of the solid obtained by revolving the region bounded by y^2 = x and y = x^3 about the x-axis.

how do you find the range of the following equations y=(x^2+3x)/(x^2-4) (the range y can't equal zero please explain how to get the answer because I assumed it's the coefficient of x^2 divided by x^2 which is one not zero)

Question 2) find the range of y=(2x^2-5x-3)/(x^2-4x+3) (the range is y can't equal to 2 and 3.5, please explain why when 3.5 is the non permissible value)

Question 3) find the range of y=(x^2-4)/(x^2-5x+6) (the range is y can't equal to 2 and -4) please explain why

thank you very much

You have designed a new style of sports bicycle!

Now you want to make lots of them and sell them for profit.

Your costs are going to be:

• $700,000 for manufacturing set-up costs, advertising, etc
• $110 to make each bike

Based on similar bikes, you can expect sales to follow this "Demand Curve":

• Unit Sales = 70,000 − 200P

Where "P" is the price.

For example, if you set the price:

• at $0, you just give away 70,000 bikes
• at $350, you won't sell any bikes at all
• at $300 you might sell 70,000 − 200×300 = 10,000 bikes

So ... what is the best price? Do NOT enter the DOLLAR sign.

a) do the laplace transform to;

x(t)= e^2t . sin(3t) . sin (t)

b) do the inverse laplace transform to;

x(s) = (3s-5) / ( (s+1).(s^2+2s+5) )