Let S be a surface in the 3-D space (but we don’t have an
equation
for...
Let S be a surface in the 3-D space (but we don’t have an
equation
for S). Suppose that there are two curves
r _1(t) = < cos(t), sin(t), t >
and
r_ 2(s) = < (s + 1)^2, 2s, se^s >
that both lie on S. Find an equation of the tangent plane to the
surface S at the
point (1, 0, 0).
In the right-half tx plane (t ≥ 0), plot the nullclines of the
differential equation x′...
In the right-half tx plane (t ≥ 0), plot the nullclines of the
differential equation x′ = 2x2(x − 4√t). Determine the sign of the
slope field in the regions separated by the nullclines. Sketch the
approximate solution curve passing through the point (1,4). Why
can’t your curve cross the x = 0 axis?
Determine how the following lines interact.
(x, y, z) = (-2, 1, 3) + t(1, -1,...
Determine how the following lines interact.
(x, y, z) = (-2, 1, 3) + t(1, -1, 5) ; (x, y, z) =
(-3, 0, 2) + s(-1, 2, -3)
(x, y, z) = (1, 2, 0) + t(1, 1, -1) ; (x, y, z) =
(3, 4, -1) + s(2, 2, -2)
x = 2 + t, y = -1 + 2t, z = -1 – t ; x = -1 - 2s,
y = -1 -1s, z = 1...
Consider the following recursive equation s(2n) = 2s(n) + 3;
where n = 1, 2, 4,...
Consider the following recursive equation s(2n) = 2s(n) + 3;
where n = 1, 2, 4, 8, 16, ...
s(1) = 1
a. Calculate recursively s(8)
b. Find an explicit formula for s(n)
c. Use the formula of part b to calculate s(1), s(2), s(4), and
s(8)
d Use the formula of part b to prove the recurrence equation
s(2n) = 2s(n) + 3
The builder of a new movie theater complex is trying to decide
how many screens she...
The builder of a new movie theater complex is trying to decide
how many screens she wants. Below are her estimates of the number
of patrons the complex will attract each year, depending on the
number of screens available.
Number of screens
Total number of patrons
1
40,000
2
70,000
3
95,000
4
115,000
5
130,000
After paying the movie distributors and meeting all other
noninterest expenses, the owner expects to net $3 per ticket sold.
Construction costs are $1,000,000...