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 for...
Hi, I'm having a lot of trouble with the following question:
Homework Statement
(a) Let x,y ∈ Z. Prove that if x>0 and x+y <xy, then y>0
Homework Equations
x+y <xy, then y>0
The Attempt at a Solution
I am very confused with this problem, and am not even sure on how to start...
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?
Homework Equations
The Attempt at a Solution
Im very unsure about my solution method. I have attached...
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.
Homework Equations
The Attempt at a Solution
Find the line of intersection for the two...
ok, how could I find the speed..would I need to divide it by 4s?
yes, thats a typo. is the answer 4.875 correct?
But is my assumption correct? should I just put down that the object is moving away from the origin at t= 3?
Thanks!
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...
Thank you.
Just one more question: when it says to interpret the result geometrically, do I have to graph it? or is it just stating the facts that we discussed above?
Thanks Tedjn
So, there is an intersecting line? because I'm really confused; isn't 0=8 a false statement, meaning that the planes are neither parallel, nor they intersect. Is this an example of planes intersecting in pairs? could you please elaborate a little.
Thanks! :smile:
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
Homework Equations
The Attempt at a Solution
x - y - 2z - 3 = 0…………….(1)
2x - 3y - 3z + 15 = 0……….(2)
x - 2y - z + 10...
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).
Homework Equations
N/A
The Attempt at a Solution
I have no clue on how to start this question...
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)
Homework Equations
The Attempt at a Solution
I have solved the...
Thanks!
So, for the example, could I use the following:
Point A (1,-5,0)
Point B (3,-9,0)
Direction vector:
[3-1,-9-(-5),0]
= [2,-4,0]
So therefore the parametric equation would be:
[x,y,z] = (1,-5,0) + t[2,-4,0]
x = 1 + 2t
y = -5-4t
z = 0
Is my method correct...
Thank you,
ok, so the following are the parametric equations:
x = x1
y = y1
z = z1
Symmetric equations:
x-x1
y-y1
z-z1
Is this correct?, and what exactly does it mean in this context..
Thanks LCKurtz!
so basically, my equations are correct, as they demonstrate that the line is not parallel to any other axis..and could you please explain what you think this result means..
Thanks!
Thanks Mark 44, and LCKurtz
Parametric:
x =x1+at
y =y1+bt
z =z1
Symmetric equation:
t = (x-x1)/a
t = (y - y1)/b
0 = z-z1
So basically, the z value is constant? I came to that conclusion too, but what about it not being parallel to any of the axis? I am fine with the former, but...
EDIT: Sorry I made a spelling error in the title: its supposed to be Planes
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 in...
Thanks tiny-tim,
so basically, I will need to find three points for each line (therefore use three different values for t) so that I get:
[x1, y1, z1]
[x2, y2, z2]
[x3, y3, z3]
Thanks again!
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
Homework Equations
(x+2)/3=(y-1)/2=(z+5)/(-3)
x = -1 + 5t
y = 7 + t
z = 3 - 2t
The Attempt...
Homework Statement
Find the vector/ and parametric equations for the line that passes through A(3, -1, 2) and parallel to the x-axis.
Homework Equations
N/A
The Attempt at a Solution
I know how to find the vector and parametric equations of a line, when given two points. I am just...
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
Homework Equations
The Attempt at a Solution
I tried taking...
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...
add them? I'm really confused, how would we find the value of theta, as well as V when both values are unknown, could you please elaborate on your method.
Thanks!
ok, so I get the following:
note:V is force 2
VH = x component of vector V (force 2)
VV = y component of vector V
VH = V cos 50
VV = V sin 50
Now we add the two vectors to get the resultant:
150 + V cos 50 = 200 cos (theta)
0 + V sin 50 = 200 sin (theta)
We have two...
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.
Homework Equations
The Attempt at a Solution
Over here, I am very...