Starting from the point (x0, y0) = (2,3) of the function f (x) =
4x ^ 2 - 4xy + 2y ^ 2, it is to choose to proceed according to the
Steep Descent Method (x2, y2).
Use Lagrange multipliers to show that the shortest distance from
the point (x0,y0,z0)
to the plane ax+by+cz=d
Is it the perpendicular distance?
(Remind yourself of the equation of the line perpendicular to the plane.)
How to solve it
Do 5 steps, starting from x0=[1 1 1]T and
using 6S in the computation. Hint. Make sure that you solve each
equation for the variable that has the largest coefficient (why?).
Show the details
10x1 + x2 + x3 = 6
x1 + 10x2 + x3 = 6
x1 + x2 + 10x3 = 6
Starting from the first and second law of thermodynamics, derive
the fundamental equation for A in its natural variables. a) Derive
the Maxwell relation that s related to this equation. b) Show that
for df= gdx + hdy we have an exact equation if:
6. “Starting from an initial position of equilibrium with X – M
=0, an economy experiences income growth. If this growth is due to
an autonomous increase in investment, then the balance of trade
will move into a deficit, while if it is due to an exogenous
increase in exports then the balance of payments will display a
surplus, although the surplus will be less than the initial
increase in exports.”
A batted baseball is hit with a velocity of 49.7 m/s, starting
from an initial height of 4 m. Find how high the ball travels in
two cases: (a) a ball hit directly upward (b) a ball hit at an
angle of 70 degrees. also find how long the ball is in the air in
both cases
In the shot put, a heavy lead weight—the "shot"—is given an
initial velocity, starting from an initial elevation approximately
equal to the shot putter's height, say, 2.00 m. If v0 = 7.05 m/s,
find the horizontal distance traveled by the shot for the following
initial angles above the horizontal.
theta 0 =?
theta 40.0 = ?
theta 45.0 = ?
A batted baseball is hit with a velocity of 44 m/s, starting
from an initial height of 4 m. Find how high the ball travels in
two cases:
(a) a ball hit directly upward and
(b) a ball hit at an angle of 69° with respect to the
horizontal.
Also, find how long the ball stays in the air in each case.
case a:
case b:
In the shot put, a heavy lead weight—the "shot"—is given an
initial velocity, starting from an initial elevation approximately
equal to the shot putter's height, say, 2.00 m. If
v0 = 7.90 m/s, find the horizontal distance
traveled by the shot for the following initial angles above the
horizontal. (a) θ0 = 0°
(b) θ0 = 40.0°
(c) θ0 = 45.0°
1. Calculate the average of the first 10 second values (initial
velocity) for all concentrations and
draw the curve.
2. Calculate the inverse of initial velocities vs inverse of
concentrations. Draw the Lineweaver- Burk
line.
3. Answer: a.) Vmax; b.) Km.
Table 2
Time (s)
30 µg/µL
50 µg/µL
100 µg/µL
150 µg/µL
500 µg/µL
0
0
0
0
0
0
10
0.021
0.024
0.023
0.039
0.063
20
0.024
0.035
0.024
0.041
0.066
30
0.027
0.034
0.019
0.041
0.074
40
0.026...