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  1. Q

    Calculating Sum, intro to integration

    Thank you. Do you have any suggestions as to how one would approach the same problem, but going the other way? For example, evaluate: \sum ^{n}_{k=m+1} k^2. Thanks for your help
  2. Q

    Calculating Sum, intro to integration

    I guess I am confused as to why they randomly changed the lower limit from k=1+m to k=1, and how they did it
  3. Q

    Calculating Sum, intro to integration

    n^2-m^2. However, let's say you only have this term \sum ^{n}_{k=m+1} k^2 , how would you know to simplify it to n^2-m^2?
  4. Q

    Calculating Sum, intro to integration

    Homework Statement Can someone please explain the following for me? \sum ^{n}_{k=m+1} k^2 = \sum ^{n}_{k=1} k^2 - \sum ^{m}_{k=1} k^2 The Attempt at a Solution I have not done math in a long time, and for some reason this has me baffled. My textbook randomly does it, and does not...
  5. Q

    More equilibrium

    I don't see how you can get tan(θ/2) from sinθ(secθ - 1). Don't you need (1-cosθ)/sinθ. I cant seem to get it to equal the half angle identity..
  6. Q

    More equilibrium

    Homework Statement The Attempt at a Solution 2Fsin(theta)=45 N Where F=ks=(75N/m)(s-1.2m). Looking at the triangle, we can state that s, the stretched length is equal to 1.2m/cos(theta). Therefore, 2(75N/m)[(1.2m/cos(theta))-1.2m]sin(theta)=45 N...
  7. Q

    Equilibrium and maximum forces

    Homework Statement The Attempt at a Solution I'm not entirely sure how to go about this question, and what to do with the maximum force that each cord can withstand. I tried setting up an equation, then taking a derivative to solve it for the maximum, but I bet there is an easier way...
  8. Q

    Need help simplifying expression

    Ok. Find theta. 2sintheta(75)(x-1.2)=45, where x=1.2costheta
  9. Q

    Need help simplifying expression

    The Attempt at a Solution I'm attempting to solve a question with a few unknowns, and I managed to get it to the following form: tanx(1-cosx)=0.25 I just cant seem to simplify it further and thus solve.. Any ideas?
  10. Q

    Difficult equilibrium problem

    Homework Statement A vertical force P=10 N is applied to the ends of the 0.2 m cord AB and spring AC. If the spring has an unstretched length of 0.2 m. determine the angle theta for equilibrium. Take k = 150 N/m. Homework Equations Fspring=ks Fy=0 Fx=0 The Attempt at a Solution...
  11. Q

    Kinematics: the race that Lance could now win

    Homework Equations v=d/t The Attempt at a Solution VL=VR+2km/h d=6km tL1tR+4min tL2=tR +2 VL= 6km / (2-4) = 3km/min which is OBVIOUSLY WRONG. I have tried numerous things for the past couple hours, but cant seem to figure it out/. Help?
  12. Q

    Gemotry of circle and right angle

    90 degrees. So then the calculations would be correct, would they not? Since the center of the circle is below the metal block, we would just add 0.5 to to answer calculated from the triangle? ps thank u
  13. Q

    Gemotry of circle and right angle

    ALright, just a quick question concerning this diagram. Since the 90 degree angle is directed along the middle ove the circle, does that mean if you draw a line from where the circle is touching the ninety degree angle to the centre of the circle, it would make a 45 degree angle with the...
  14. Q

    Urgent: force vectors and a minimum

    Homework Statement Suppose we have the following forces: F1=[5i]kN F2=[-4j]kN F3= unknown force 30 degrees from + y-axis. How do you determine the magnitude of F3 such that the resultant FR for all three forces is a minimum? Thanks in advance.
  15. Q

    Half life

    Homework Statement The half-life of radioactive carbon 14 is 5700 years. After a plant or animal dies, the level of carbon 14 decreases as the adioactive carbon disintegrates. The decay of radioactive material is given by the relationship A = A0e^(-kt), where A0 is the initial amount of...
  16. Q

    Force vectors

    Wouldnt you want to find the angle that F2 (and F1) makes with the vertical, then add 90 degrees to find theta?
  17. Q

    Force vectors

    The three concurrent forces acting on the post produce a resultant force of 0. If F2 = 0.5F1, and F1 is to be 90 degrees from F2 as shown, determine the required magnitude F3 expressed in terms of F1 and the angle theta. I am having no troubles finding the magnitude of F3, however, I am...
  18. Q

    Resolving Force vector

    I have done so, but again I am getting entirely different answers. Perhaps someone can point me in the right director for vector allignment? I am assuming that its my arrangment of vectors that is corrupting my answer.
  19. Q

    Resolving Force vector

    Homework Statement A resultant vertical force of 1750 N is necessary to held the balloon in place. Resolve this force into components along the tether lines AB and AC, and compute the magnitde of each force. The angle between AB and the vertical force is 40 deg, and the angle between AC...
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