1
Differential Equations Group Project #1
Azum Beg
Amir Shalabi
Each member of this group has abided by the guidelines regarding this project.
Azum Beg: _
Amir Shalabi: _
2
26.
If A(t) is the number of gallons of alcohol in the tank at time t,
dA
then
is
Azum Beg
Mailbox #88
WP #1
DEQ Mangum
46. Suppose M(x, y) dx + N(x, y) dy = 0 is a homogeneous equation. Show that
the substitution x = r cos(), y = r sin() reduce the equation to one with
separable variables.
x r cos
dx cos dr rsin d
y r sin
dy sin dr r
Metal NameCharge (Cation) Category Family (Cation) Anion Charge (Anion)
Family (Anion)
Aluminum
3
Main
NA
Phosphate
3
Polyatomic
Antimony
3
Main
NA
Phosphate
3
Polyatomic
Barium
2
Main
Alkaline
Phosphate
3
Polyatomic
Cadmium
2
Transition
NA
Phosphate

Amir Shalabi #95
Vector Calculus
Ms. Jennifer Mangum
2215
Writing Prompt One
1) Prove a + (b + c) = (a + b) + c in R2.
Proof:
Let a, b, and c be vectors in R2 such that a = (a1, a2), b = (b1, b2), and c
= (c1,c2). Note that a1, a2, b1, b2, c1, and c2 ar
1
Calibration of a 50mL Buret
by Azum Beg, Aryiana Moore
September 2, 2015
Mailbox #88
2
Abstract:
3
Data:
Tria
l
Flask w/ water
(g)
015 mL Titrations
Flask w/o water
volume of water
(g)
(mL)
1
33.2432
18.1569
15.0863
2
3
33.7929
33.3980
18.9059
18.4241
Azum Beg
Mailbox #88
VCMangum
WP #1
February 2, 2015
1. Suppose a, b, and c are vectors in R2, such that a = (a1, a2), b = (b1, b2), and c = (c1,
c2), where a1, a2, b1, b2, c1, and c2 are elements of R. Consider:
a + (b + c) = (a1, a2) + [(b1, b2) + (c1,