Submitting Discussion Board Postings and Replies
MAT 113 Online-Spring 2017 (Revised)
A. Directions: Preparing / submitting postings in the DB Forum
NOTE: First choice is to use f(x) icon in the Description/Dialogue box on
Blackboard. The templates for ty
Solution
Week 30 (4/7/03)
Dierence of Powers
A value of 26 is obtainable with m = n = 1. By considering the remainder when
33m 7n is divided by certain numbers, we will show that no value smaller than 26
is possible. We will use the mod notation for conve
Solution
Week 20
(1/27/03)
Collinear points
Draw all the lines determined by the points. From the assumption of the problem,
there are at least three points on each of these lines. Consider all of the distances
between any of the points and any of the lin
Solution
Week 19
(1/20/03)
Block and bouncing ball
(a) Consider one of the collisions. Let it occur at a distance from the wall, and
let v and V be the speeds of the ball and block, respectively, after the collision.
We claim that the quantity (v V ) is i
Solution Week 17 (1/6/03) Icosahedron of resistors First Solution: We will calculate the eective resistance between vertices 1 and 2 in the gure below. When the icosahedron is viewed from the angle shown, four vertices lie directly behind four other verti
Solution
Week 15
(12/23/02)
Maximal gravity
Assume that the material has been shaped and positioned so that the eld at
P is maximum. Let this eld point in the x-direction. The key to this problem
is to realize that all the small elements of mass dm on the
Solution
Week 13
(12/9/02)
Unchanged velocity
Our strategy will be to produce (and equate) two dierent expressions for the
total change in the angular momentum of the ball (relative to its center). The rst
comes from the eects of the friction force on the
Solution
Week 8
(11/4/02)
Sub-rectangles
Put the rectangle in the x-y plane, with its sides parallel to the x and y axes,
and consider the function,
f (x, y) = e2ix e2iy .
(1)
Claim: The integral of f (x, y) over a rectangle, whose sides are parallel to t
Solution
Week 6
(10/21/02)
Flipping a coin
(a) There is a 1/2 chance that you win one dollar, a 1/4 chance that you win two
dollars, a 1/8 chance that you win three dollars, etc. Therefore, the average
value of your winnings is
1 2 3
4
+ + +
+ .
2 4 8 16
Edexcel Maths FP1
Topic Questions from Papers
Series
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2.
(a) Show, using the formulae for
n
(6 r
2
r and r
2
, that
+ 4r 1) = n(n + 2)(2n + 1)
r =1
(5)
20
(b) Hence, or otherwise,
Edexcel Maths FP1
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Matrices
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7.
2
Given that X =
1
a
, where a is a constant, and a 2,
1
(a) find X1 in terms of a.
(3)
Given that X + X1 = I, where
Edexcel Maths FP1
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Proof by Induction
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4.
Prove by induction that, for n Z + ,
n
r =1
1
n
=
r (r + 1)
n +1
(5)
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Edexcel Maths FP1
Topic Questions from Papers
Coordinates
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3.
The rectangular hyperbola, H, has parametric equations x = 5t, y =
5
, t 0.
t
(a) Write the cartesian equation of H in
Solution
Week 45
(7/21/03)
Sliding along a plane
The normal force from the plane is N = mg cos . Therefore, the friction force on
the block is N = (tan )N = mg sin . This force acts in the direction opposite to
the motion. The block also feels the gravita
Week 49
(8/18/03)
Falling chimney
A chimney initially stands upright. It is given a tiny kick, and it topples over. At
what point along its length is it most likely to break?
In doing this problem, work with the following two-dimensional simplied model
of
Edexcel Maths FP1
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Numerical Solutions
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f(x) = 3 x +
5.
18
20
x
(a) Show that the equation f(x) = 0 has a root in the interval [1.1, 1.2].
(2)
(b) Find f
Solution
Week 60
(11/3/03)
Cereal box prizes
First Solution: Assume that you have collected c of the colors, and let Bc be the
number of boxes it takes to get the next color. The average value of Bc , which we
will denote by B c , may be found as follows.
Solution
Week 50
(8/25/03)
Equal segments
The construction will proceed inductively. Given a segment divided into N equal
segments, we will show how to divide it into N + 1 equal segments. For purposes
of concreteness and having manageable gures, we will