(a) Show that the lines
r 1 (t) = (2,1,−4) + t(−1,1,−1) and r 2 (s) = (1,0,0) +
s(0,1,−2)
are skew.
(b) The two lines in (a) lie in parallel planes. Find equations for
these two planes. Express your
answer in the form ax+by+cz +d = 0. [Hint: The two planes will
share a normal vector n. How would one find n?]
would one find n?]
Please answer in C++
Given 3 numbers T, r and s, where r != s and r > 1 & s
> 1. Print a list of numbers from 1 to T where numbers divisible
by r whose decimal representation does not contain the digit r
should be replaced by the number 555 and any number (int) divisible
by s whose decimal representation does not contain the number s
should be replaced by the number 333. Numbers for which both...
Figure for Ca2+ dynamics. Draw a model with arrows and #’s in
the order
“The scheme of ionic currents within a cardiac cycle for a
mammalian pacemaker cell”
The scheme of ionic currents within a cardiac cycle for a
mammalian pacemaker cell (i.e., SA node) is generally described
with the background [Ca2+]i continually increasing and decreasing.
Starting in diastolic depolarization with a slow release of Ca2+ by
ryanodine receptors (RyR), from the SR, leads to a rise in [Ca2+]i
....
Find the following percentile for the standard normal
distribution. Draw a sketch and show the R code:
a. 91st percentile
b. 9th percentile
c. 75th percentile
d. 25th percentile
e. 6th percentile
r(t)=sinti+costj.
- Sketch the plane curve represented by r and include arrows
indicating its orientation.
- Sketch the position vector r(t), the velocity vector r′(t),
and the acceleration vector r′′(t) for the two times t = π/2, 5π/4
, putting the initial points of the velocity and acceleration
vectors at the terminal points of the position vectors.
- Prove that the vectors r(t) and r′(t) are orthogonal for every
t.
Suppose S = {p, q, r, s, t, u} and A = {p, q, s, t} and B = {r,
s, t, u} are events.
x p q r s t u
p(x) 0.15 0.25 0.2 0.15 0.1
(a) Determine what must be p(s).
(b) Find p(A), p(B) and p(A∩B).
(c) Determine whether A and B are independent. Explain.
(d) Arer A and B mutually exclusive? Explain.
(e) Does this table represent a probability istribution of any
random variable? Explain.
Find T(t), N(t), aT, and aN at the given time t for the space
curve r(t). [Hint: Find a(t), T(t), aT, and aN. Solve for N in the
equation a(t)=aTT+aNN. (If an answer is undefined, enter
UNDEFINED.)
Function Time
r(t)=9ti-tj+(t^2)k t=-1
T(-1)=
N(-1)=
aT=
aN=
The forward price of a currency is given by f(S, t) = S e^(r−rf
) (T −t) ,
a) Show that if f(S, t) < S e(r−rf ) (T −t) , then arbitrage
profits can be made. Hint: because f(S, t) is “too low” and S is
“too high,” today’s arbitrage trades are
i) Enter a long position in the forward contract. (That is,
agree to buy the foreign currency at time T at the price f(S, t)
per unit...