1. Homework Statement
Hi, I'm supposed to solve the following question using proof by induction, and am very confused with it. It would be greatly appreciated if someone could help me solve this problem:
Let an = 2 and an+1\frac{4a_n -3}{a_n} for n >=1. Show that 1\leq a_n \leq a_(n+1)\leq3...
Hi, I'm having a lot of trouble with the following question:
1. Homework Statement
(a) Let x,y ∈ Z. Prove that if x>0 and x+y <xy, then y>0
2. Homework Equations
x+y <xy, then y>0
3. The Attempt at a Solution
I am very confused with this problem, and am not even sure on how...
1. Homework Statement
Hello, I'm having some trouble with the following problem:
Solve y = x+\frac{1}{x} for 0 < x \leq 1
2. Homework Equations
y = x+\frac{1}{x} for 0 < x \leq 1
3. The Attempt at a Solution
I am not sure on how to start. I've spent a lot of time thinking...
1. Homework Statement
Please find all ordered pairs of integers (x,y) such that x2 + 2x + 18 = y2
2. Homework Equations
x2 + 2x + 18 = y2
3. The Attempt at a Solution
Im not sure on how to begin. I tried square-rooting the expression, to solve for y, turning it into y = \sqrt{x + 2x +...
1. Homework Statement
Solve for x for 0\leq x\leq 2 \pi in the following equation:
sin x tan x + tan x - 2sinx + cos x =0
2. Homework Equations
N/A
3. The Attempt at a Solution
I tried making tan x = \frac{cos x}{sin x}, but did not have any luck, and am very confused on how to solve...
1. Homework Statement
The base of an isosceles triangle is 20 cm and the altitude is increasing at the rate of 1 cm/min. At what rate is the base angle increasing when the area is 100 cm^2?
2. Homework Equations
3. The Attempt at a Solution
Im very unsure about my solution method. I...
1. Homework Statement
Find the equation of the plane that passes through the line of intersection of the planes x - 3y - 2z - 1 = 0 and 2x + 4y + z - 5 = 0 and parallel to the x-axis.
2. Homework Equations
3. The Attempt at a Solution
Find the line of intersection for...
Hey everyone!
I got accepted to the university of waterloo for computer science honours (BCS), and was wondering about the university's reputation. I know that its considered to be a very good school in Canada (one of the best), but what about international reputation? is it known to be a...
1. Homework Statement
An object is traveling along a linear path according to the equation
s(t) = 4t^3 - 3t^2 + 5 where t is measured in seconds and s(t) measured in meters.
1. How fast is the object moving at t = 4 seconds?
2. What is the position of the object when it stops...
1. Homework Statement
Solve the following systems and interpret the result geometrically
x - y - 2z - 3 = 0
2x - 3y - 3z + 15 = 0
x - 2y - z + 10 = 0
2. Homework Equations
3. The Attempt at a Solution
x - y - 2z - 3 = 0…………….(1)
2x - 3y - 3z + 15 = 0……….(2)
x -...
1. Homework Statement
Find the equation of the plane that passes through the line of intersection of the planes 4x - 3y - z - 1 = 0 and 2x + 4y + z - 5 = 0 and passes through A(1, -3, 2).
2. Homework Equations
N/A
3. The Attempt at a Solution
I have no clue on how to start this...
1. Homework Statement
Find out if the following planes and lines intersect. If they intersect, state the point of intersection
Plane: 2x + y + 3z = 10
Line: Passing through the point A(1, 5, 1) and B(0, 4, 2)
2. Homework Equations
3. The Attempt at a Solution
I have solved...
EDIT: Sorry I made a spelling error in the title: its supposed to be Planes
1. Homework Statement
Recall that there are three coordinates planes in 3-space. A line in R3 is parallel to xy-plane, but not to any of the axes. Explain what this tells you about parametric and symmetric equations...
1. Homework Statement
Find the coordinates of three points on each of the following lines.
a. (x+2)/3=(y-1)/2=(z+5)/(-3)
x = -1 + 5t
b.y = 7 + t
z = 3 - 2t
2. Homework Equations
(x+2)/3=(y-1)/2=(z+5)/(-3)
x = -1 + 5t
y = 7 + t
z = 3 - 2t
3. The...
1. Homework Statement
Find the vector/ and parametric equations for the line that passes through A(3, -1, 2) and parallel to the x-axis.
2. Homework Equations
N/A
3. The Attempt at a Solution
I know how to find the vector and parametric equations of a line, when given two points. I am...
1. Homework Statement
Find the vector, parametric and symmetric equations of a line that intersect both line 1 and line 2 at 90°.
L1 :
x = 4 + 2t
y = 8 + 3t
z = -1 - 4t
L2 :
x = 7 - 6t
y = 2+ t
z = -1 + 2t
2. Homework Equations
3. The Attempt at a Solution
I...
1. Homework Statement
A pilot wishes to fly form city A to city B, a distance of 720 km on a bearing of 070°. The speed of the plane is 700 km/h. An 60 km/h wind is blowing on a bearing of 110°. What heading should the pilot take to reach his or her destination? How long will the trip take...
1. Homework Statement
Two forces act on an object at an angle of 50°. One force is 150 N. The resultant force is 200 N. Find the second force and the angle that it makes with the resultant, using only cartesian vectors.
2. Homework Equations
3. The Attempt at a Solution
Over here, I am...
1. Homework Statement
The displacements of two ships, A and B, two hours after leaving from the same port can be represented with position vectors \vec{OA} [20, 50, 0] and
(\vec{OB}) [60, 10, 0]. Assume that the port is located at the origin and that all units are in kilometres.
a...
1. Homework Statement
Use Cartesian vectors in two-space to prove that the line segments joining midpoints of the consecutive sides of a quadrilateral form a parallelogram.
2. Homework Equations
We could say vectors a and b
a = [a1, a2]
b = [b1, b2]
3. The Attempt at a...
1. Homework Statement
Prove that If \vec{a}x \vec{b} = 0, then \vec{a}is parallel to \vec{b}.
2. Homework Equations
3. The Attempt at a Solution
I tried attempting the solution by using the following:
\vec{a} = [a1, a2, a3]
\vec{b} = [b1, b2, b3]
When I took the cross product of a...
1. Homework Statement
Given triangle ABC with vertices A(4, 1, 7), B(-2, 1, 1) and C(-3, 5, -6)..is ABC a Right triangle
2. Homework Equations
3. The Attempt at a Solution
I took the dot product of vertices A(4, 1, 7).B(-2, 1, 1), and it gives 0..but however I am a little...
1. Homework Statement
Expand and simplify:
(2\vec{a} + 3\vec{b}) .(5\vec{a} - \vec{b}
2. Homework Equations
3. The Attempt at a Solution
I tried expanding it, but was a little confused, and would really appreciate any help..would it be (2\vec{a})(\vec{a}) = 2 \vec{a}2...
1. Homework Statement
Prove that vectors \vec{u}, \vec{v}and \vec{w} are coplanar if and only if vectors \vec{u}, \vec{v}and \vec{w}are linearly dependent
2. Homework Equations
3. The Attempt at a Solution
This may sound like an awkward question, but I am having much...