Question

The angles between the tetrahedral bonds of diamond are the same as the lines connecting the center of a cube at (0, 0 , 0) to four of the eight corners, say (1, 1, 1), (1, -1, -1), (-1, 1, -1) and (-1, -1, 1).

(a) Sketch a cube and mark these for corners.

(b) Use vector analysis to find the value of the angle.

Answer #1

The following data are product weights for the same items
produced on two different production lines.
Test for a difference between the product weights for the two
lines. Use .
Line 1 Line 2
13.0 14.5
13.7 14.7
14.1 14.8
13.1 15.2
14.2 14.4
14.0 13.5
13.5 14.4
13.1 14.4
13.6 14.6
14.4 13.8
0 13.7
0 13.7
What is the value of the test statistic? Enter negative value as
negative number. (to 2 decimals) What is the p-value for...

(a) Find the distance between the skew lines l1 and l2 given
with the vector equations l1 : r1(t) = (1+t)i+ (1+6t)j+ (2t)k; l2 :
r2(s) = (1+2s)i+ (5+15s)j+ (−2+6s)k.
(b) Determine if the plane given by the Cartesian equation −x +
2z = 0 and the line given by the parametric equations x = 5 + 8t, y
= 2 − t, z = 10 + 4t are orthogonal, parallel, or neither.

Let L1 be the line passing through the point
P1(3, 5, ?5) with direction vector
d=[?1, 2, 0]T, and let
L2 be the line passing through the point
P2(?3, ?4, ?3) with the same direction
vector.
Find the shortest distance d between these two lines, and
find a point Q1 on L1 and a
point Q2 on L2 so that
d(Q1,Q2) = d. Use
the square root symbol '?' where needed to give an exact value for
your answer.

15.)
a) Show that the real numbers between 0 and 1 have the same
cardinality as the real numbers between 0 and pi/2. (Hint: Find a
simple bijection from one set to the other.)
b) Show that the real numbers between 0 and pi/2 have the same
cardinality as all nonnegative real numbers. (Hint: What is a
function whose graph goes from 0 to positive infinity as x goes
from 0 to pi/2?)
c) Use parts a and b to...

Calculate "d" using the following equation:
d = (m*lamda)/sintheta. d = distance between lines
on grating, m = Order of diffraction, lambda = wavelength converted
to metres) and theta = angle of deviation.
Lambda 1 = 589.0mm and lambda 2 = 589.6mm (use the
average value of 589.3mm)
Data
Sodium light, central position = 180°-0’
Colour
Right θ (° ')
Left θ (° ')
Yellow
190°-1’
170°-5’
Hydrogen light, central position = 180°-0’
Colour
Right θ (° or ° ')...

Exercise 13-13 Algo
Wenton Powersports produces dune buggies. They have three
assembly lines, “Razor,” “Blazer,” and “Tracer,” named after the
particular dune buggy models produced on those lines. Each assembly
line was originally designed using the same target production rate.
However, over the years, various changes have been made to the
lines. Accordingly, management wishes to determine whether the
assembly lines are still operating at the same average hourly
production rate. Production data (in dune buggies/hour) for the
last eight...

Net Present Value Methodand Present Value Index
Diamond and Turf Inc. is considering an investment in one of two
machines. The sewing machine will increase productivity from sewing
170 baseballs per hour to sewing 306 per hour. The contribution
margin per unit is $0.5 per baseball. Assume that any increased
production of baseballs can be sold. The second machine is an
automatic packing machine for the golf ball line. The packing
machine will reduce packing labor cost. The labor cost...

Net Present Value Methodand Present Value Index
Diamond and Turf Inc. is considering an investment in one of two
machines. The sewing machine will increase productivity from sewing
170 baseballs per hour to sewing 306 per hour. The contribution
margin per unit is $0.5 per baseball. Assume that any increased
production of baseballs can be sold. The second machine is an
automatic packing machine for the golf ball line. The packing
machine will reduce packing labor cost. The labor cost...

Using MATLAB
The range of an object shot at an angle θ (with respect to
x-axis), with the initial velocity of V0 (in the absence of air
resistance), is calculated by the following formula:
range=(Vo^2/g)(sin(2theta)) where (0<=theta<=pi/2) And the
trajectory of object is given by:
h=tan(theta).x-(g/2Vo^2*cos^2(theta)).x^2 .Where h is the height of
the object at each x location and g = 9.81 m/s2.
a) Using π/8 increment size for the angle and V0 = 10 m/s, plot
the trajectories of...

ou may need to use the appropriate appendix table or technology
to answer this question.
The following data are product weights for the same items
produced on two different production lines.
Line 1
Line 2
13.6
13.7
13.8
14.1
14.0
14.2
13.9
14.0
13.4
14.6
13.2
13.5
13.3
14.4
13.6
14.8
12.9
14.5
14.4
14.3
15.0
14.9
Test for a difference between the product weights for the two
lines. Use α = 0.05.
State the null and alternative hypotheses.
H0:...

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