Let a, b, c the last three digits of your QUID. Find the
dimension of the...
Let a, b, c the last three digits of your QUID. Find the
dimension of the rectangular box of maximum volume that can be
inscribed in the ellipsoid (x/a)^2+(y/b)^2+(z/c)^2=1 a=4, b=8,
c=9
Let A be the sum of the last four digits and let B be the last
digit of your 8-digit student ID. (Example: For 20245347, A = 19
and B = 7) On a road trip, a driver achieved an average speed of
(48.0+A) km/h for the first 86.0 km and an average speed of
(43.0-B) km/h for the remaining 54.0 km. What was her average speed
(in km/h) for the entire trip? Round your final answer to three
significant...
-Let O (0,0,0) be the origin and A(a+1,b,c) where a,b and c are
the last three digits of your student ID. Find, describe and sketch
the set of points P such that OP is perpendicular to AP
- Let u=<a , b+1 , c+1> find and describe all vectors v
such that |u x v|=|u|
a=1 , b=1 , c=9
a) Write C code initialize an array of ints to the last four
digits of your phone number. Use a loop to add the digits.
Calculate and display the average of the digits.
b) Write C code using a struct to hold student information:
integer id
integer number of hours taken
integer number of hours passed
double gpa
7. Let A = (−1,3,0), B = (3,2,4) and C = (1,−1,5).
(a) Find an equation for the plane that passes through these three
points.
(b) Find the area of the triangle determined by these three
points.
8). Find an equation of the tangent plane to the surface z = x
at (−4, 2, −1).
(A) Let a,b,c∈Z. Prove that if gcd(a,b)=1 and a∣bc, then
a∣c.
(B) Let p ≥ 2. Prove that if 2p−1 is prime, then p
must also be prime.
(Abstract Algebra)
Calculus #3:
1.
a) Let A = (2,4,6),B = (1,2,3) and C = (5,5,5). Find point D so
that ABCD is a parallelogram.
b). Two points X and Y are colinear if they lie on the same
line. Are the points A = (3,6,−1), B = (2,0,3) and C = (−1, 3, −4)
colinear? Justify your answer.
Let A = (3, 4), B = (0, −5), and C = (4, −3). Find equations for
the perpendicular bisectors of segments AB and BC, and coordinates
for their common point K. Calculate lengths KA, KB, and KC. Why is
K also on the perpendicular bisector of segment CA?
5. Write a C++ statement or statements that
will:
Print the first two digits and the last two digits of
any 4 digit number stored in an integer variable
n.
For example, given int n = 5623, print
56 23.
6. Write C++ statements that will align the following
three lines as printed in two 20 character columns.
Name Years
President
Abraham
Lincoln 1860-1865
Thomas
Jefferson 1801-1809
7. Write a C++ statement or statements that will
Output if a string has a length greater than 10, equal...
Let?:?2(R)⟶?1(R)bedefinedby?(?+?x+?x2)=(?+?)+(?−?)x,where
?, ?, ? are arbitrary constants.
a. DeterminethetransformationmatrixforT.(6pts)
b. Find the basis and the dimension of the Kernel of T. (10pts)
c. Find the basis and the dimension of the Range of T. (10pts)
d. Determine if T is one-to-one. (7pts)
e. DetermineifTisonto.(7pts)