At what point do the curves r1(t) = t, 3 − t, 35 + t2 and...
At what point do the curves r1(t) = t, 3 − t, 35 + t2 and r2(s)
= 7 − s, s − 4, s2 intersect? (x, y, z) = Find their angle of
intersection, θ, correct to the nearest degree. θ = °
The curves r1(t) = < t, 4, t2-9 >
and r2(s) = < 3, s2, 4-2s >lie on
surface of f and intersect at ( 3, 4, 0 ). Find a linear
approximation for the # f(3.1, 4.1).
2a. The two space curves
and
r1(t) = <?1 + 5t, 3 − t^2, 2 + t − t^3> and? r2(s)=<
?3s−2s^2,s+s^3 +s^4,s−s^2 +2s^3>?
both pass through the point P(1,3,2). Find the values of t and s
at which the curves pass through this point.
2b. Find the tangent vectors to each curve at the point P (1, 3,
2).
2c. Suppose S is a surface which contains the point P (1, 3, 2),
and both r1(t) and r2(s) lie...
Two spacecraft are following paths in space given by
r1=〈sin(t),t,t2〉r1=〈sin(t),t,t2〉 and
r2=〈cos(t),1−t,t3〉.r2=〈cos(t),1−t,t3〉. If the temperature for the
points is given by T(x,y,z)=x2y(6−z),T(x,y,z)=x2y(6−z), use the
Chain Rule to determine the rate of change of the difference DD in
the temperatures the two spacecraft experience at time t=2.t=2.
(Use decimal notation. Give your answer to two decimal
places.)
dDdt=dDdt=
If the moment-generating function of X is M(t) = exp(3 t + 12.5
t2) = e3 t + 12.5 t2.
a. Find the mean and the standard deviation of
X.
Mean =
standard deviation =
b. Find P(4 < X < 16). Round your answer
to 3 decimal places.
c. Find P(4 < X2 < 16). Round
your answer to 3 decimal places.
Given y 1 ( t ) = t2 and y2 ( t ) = t ^− 1 satisfy the
corresponding homogeneous equation of
t^2 y ' ' − 2 y = − 3 − t , t > 0
Then the general solution to the non-homogeneous equation can be
written as y ( t ) = c1y1(t)+c2y2(t)+yp(t)
Use variation of parameters to find y p ( t ) .
Find the intersection point (if any) of the lines
r1(t)=(17,54,−22)+t(−3,−8,3)r1(t)=(17,54,−22)+t(−3,−8,3) and
r2(s)=(−67,−50,37)+s(12,8,−7)r2(s)=(−67,−50,37)+s(12,8,−7).
Please show full working/steps to help with learning
1. If T2 for gray matter is 100 msec at 1.5 T, it’s value for 3
T is most likely:
a) 50
b) 70
c) 100
d) 140
e) 200
2.If transverse magnetization is Mxy the free induction decay
signal is proportional to:
a) (Mxy)-1
b) (Mxy)-0.5
c) (Mxy)0.5
d) (Mxy)1
e) Independent of Mxy
3) What are indifference curves and how do they relate to a
budget line? Draw a graph showing 3 indifference curves and a
budget line. Why is one indifference curve tangent to the budget
line? What happens if the price of one good changes? (15 points).
please give all three graphs.
Consider the following vector function. r(t) =<3t, 1/2 t2,
t2> (a) Find the unit tangent and unit normal vectors T(t) and
N(t).
(b). Find the curvature k(t).