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    Proof involving linear algebra

    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...
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    Problem with Sets

    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...
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    Trig derivative applications answer check!

    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...
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    Plane Intersections-Answer check

    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...
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    Velocity/acceleration using derivatives (answer check)

    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!
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    Velocity/acceleration using derivatives (answer check)

    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...
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    Planar Intersections (Answer Check)

    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?
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    Planar Intersections (Answer Check)

    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:
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    Planar Intersections (Answer Check)

    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...
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    Planar intersection question

    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...
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    Plane intersections

    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...
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    Lines and Plains

    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...
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    Lines and Plains

    Thanks Mark 44! what would this result mean?, other than that the z is constant.. are there any connections between this, and the other two planes?
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    Lines and Plains

    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!
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    Lines and Plains

    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!
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    Lines and Plains

    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...
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    Lines and Plains

    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...
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    Equations of Lines and Vectors

    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!
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    Equations of Lines and Vectors

    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...
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    Parametric/vector equations

    ok, so something like (1,0,0) would work? your point makes sense, just want to confirm..
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    Parametric/vector equations

    so would the (0,1,1) work?
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    Parametric/vector equations

    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...
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    Linear Intersections

    Thanks lanedance, could you elaborate a little more. what points would I need to pick, in order to solve for the equations. Thanks,
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    Linear Intersections

    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...
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    Vector Application

    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...
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    Cartesian vector calculus

    still don't understand how to find the magnitude of the second force..could you please elaborate on this method.. Thanks!
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    Cartesian vector calculus

    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!
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    Cartesian vector calculus

    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...
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    Cartesian vector calculus

    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...
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