- dan's math@home - problem
of the week - archives
-
-
- Problem Archives
page 28
- Problems Only.
For answers & winners click here.
-
- 1-10
. 11-20
. 21-30
. 31-40
. 41-50
. 51-60
. 61-70
. 71-80
. 81-90
. 91-100 . 101-110
- 111-120 . 121-130
. 131-140 . 141-150 . 151-160
. 161-170 . 171-180
. 181-190 . 191-200
- 201-210 . 211-220
. 221-230 . 231-240
. 241-250 . 251-260
. 261-270 . 271+ . index
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- 271 - Dan's Directriconix
- 272-StockProfits2daMax
- 273 - Best Best-Fit Curve
-
-
- problem #271 - posted
wednesday, december 19, 2007
- Dan's Directriconix (back to top)
- The points equidistant
from (0, 0) and (1, 1) form the perpendicular bisector
- of the segment joining
the given points, which has the equation x + y = 1.
- The distance from a point
to a line or curve is defined as the shortest distance.
- Call the equidistant point
(x, y) and the closest point on the curve (a, b).
- a) The set
(locus) of points equidistant
from (0, 0) and the line x + y = 1 forms a familiar shape.
- Name the shape, and find
its equation.(as a relation between
x and y or as parametric equations of a)
- b) Determine the locus of
points equidistant from the origin and the hyperbola
x y = 1, x > 0.
- (as a relation between x and
y or as param. eqns of a) . . . c) Find the locus of points equidistant
from
- the origin and the circle
through (1, 1) that's
tangent to both axes. (in {x, y} or a form)
- These are possible with or without
calculus; your choice! . . . Show
your steps and reasoning.
-
-
- problem #272 - posted
saturday, january 12, 2008
- Stock Profits to the Max ! (back to top)
- The price of dansmathcorp stock (DMC) is initially $100 per share.
The stock can go up
- or down each month, from
$0-10, whole # $. Starting
after the first month, you invest
- $1000 per month in DMC.After six months you've put in $6000,
the stock price is again
- $100, and you sell off all the shares you have bought in
the six months.
- a) What sequence of stock
prices will yield the maximum profit (if any)?
- b) If the total price change
(the sum of absolute values of monthly changes) is limited to
- $40, then what sequence of
prices gives the max profit?
- In each case find the maximum profit
and explain how you calculated it. Show
your steps and reasoning.
-
- problem #273 - posted
sunday, february 10, 2008
- Best Best-Fitting Curve ? (back to top)
- We at DVC feel that more
experienced teachers can derive the quadratic formula faster!
- Here is a table of years
of experience (x) vs.
minutes to formula (y), for a dozen
teachers:
| x years |
1 |
2 |
4 |
7 |
9 |
10 |
| y minutes |
8 |
6 |
5 |
3 |
2 |
2 |
| x years |
1 |
3 |
6 |
8 |
13 |
15 |
| y
minutes |
10 |
4 |
2 |
2 |
1 |
1 |
- There are four types of curves
we might try to fit to this data set :
- Linear: y = a + bx
Logarithmic: y
= a + b ln(x) Exponential: y = a*b^x Power: y =
a*x^b
- i) Find the best "a"
and "b" for each type of curve.
- (measured by the least squares deviation
method)
- ii) Which is the best curve
choice, for these data?
- (measured by the largest abs value
of correlation coeff rxy)
-
- Use either the TI-8x, Excel, or the
sample Pearson correlation formula
- where sx and sy are the sample standard
deviations for the x and y data values.
- Show your steps, formulas, and reasoning;
one point penalty for resubmissions.
-
- THANKS to all of you who
have entered, or even just clicked and looked.
- My website is now in its
ninth season - over 97,000 hits
so far! (Not factorial.)
- Help it grow by telling
your friends, teachers, and family about it.
- YOU CAN ALWAYS FIND ME AT dansmath.com - Dan the Man Bach
- 2007 A.D.
-
-
-
- Problem Archives
Index
-
- Probs &
answers . 1-10
. 11-20
. 21-30
. 31-40
. 41-50
. 51-60
. 61-70
. 71-80
. 81-90
. 91-100 .
101-110
- Problems only . .
. 1-10
. 11-20
. 21-30
. 31-40
. 41-50
. 51-60
. 61-70
. 71-80
. 81-90
. 91-100 . 101-110
- Probs &
ans . 111-120
. 121-130
. 131-140
. 141-150
. 151-160
. 161-170
. 171-180
. 181-190 . 191-200
- Probs only . . .
111-120 . 121-130 . 131-140
. 141-150 . 151-160
. 161-170 . 171-180
. 181-190
. 191-200
- Problems &
answers .
. .
. 201-210
. 211-220
. 221-230
. 231-240
. 241-250
. 251-260
. 261-270 . 271+
- Problems only . .
. . . . . . . . 201-210 . 211-220 . 221-230
. 231-240 . 241-250
. 251-260 . 261-270
. 271+
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- Browse the complete
problem list, check out the weekly
leader
board,
- or go back and work on
this week's problem!
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