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?
In: Math
Calculate the double integral
∫∫Rxcos(x+y)dA∫∫Rxcos(x+y)dA where RR is the region:
0≤x≤π3,0≤y≤π2
In: Math
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.
In: Math
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?
In: Math
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.
In: Math
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
In: Math
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:
Based on similar bikes, you can expect sales to follow this "Demand Curve":
Where "P" is the price.
For example, if you set the price:
So ... what is the best price? Do NOT enter the DOLLAR sign.
In: Math
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) )
In: Math
a) Find the equation of the normal line at the point (−2, 1 − 3) to the ellipsoid x2 /4 + y2 + z2 / 9 = 3
b) Find a plane through P (2, 1, 1) and perpendicular to the line of intersection of the planes: 2x+y−z = 3 and x+2y+z = 2.
In: Math
can you find a linear homogeneous constant-coefficient DE and such that x.e^(-2x).sinx is a solution.
Write the answer in a.y''' + by'' +cy'+dy=0
In: Math
Maximize 250 + 7x − 5y subject to:
2x + 3y ≤ 90
2x+ y≤62
x+ y≥20
x ≥ 0, y ≥ 0
In: Math
(27) Give an example of an infinite incidence geometry (i.e. an incidence geometry with an infinite number of points and an infinite number of lines).
In: Math
How do I find the missing sides of an isosceles trapezoid?
In: Math
Find the Radius and center of the sphere. 2x2 +2y2 + 2z2 + x + y + z = 9
In: Math
For f(x)=9x+5 and g(x)=x2 find the following composite functions and state the domain of each
a) f o g b) g o f c) f o f d) g o g
a. the domain of f o g is
b. (g o f )(x)=
a. the domain of g o f is
c. ( f o f )(x)=
the domain of f o f is
d. ( g o g)(x)=
the domain of g o g is
In: Math