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Homework Help: Couple multiple choice: Confirmation needed

  1. May 31, 2012 #1
    1. For which following condition, will the cross product of two vectors be zero?

    a. If the angle between them is 90°.
    b. If the angle between them is 0°.
    c. If the angle between them is 45°.
    d. If the vectors have the same magnitude.

    2. If a = (5, 2) and b = (-3, 1), then which of the following vectors represent 3a - 2b?

    a) (9, 4)
    b) (9, 8 )
    c) (21, 8 )
    d) (21, 4)

    3. Given the vectors a = (1, 3, 4) and a = (4, 5, -4), which of the following represent a × b?

    a) (8, -20, 7)
    b) (-32, 20, -7)
    c) (4, 15, 16)
    d) -3

    4. In the previous question, what is the angle between the two given vectors to the nearest degree?

    a) 94°
    b) 86°
    c) 36°
    d) 24°

    5. If ƒ'(c) < 0 then ƒ(x) is decreasing and the graph of ƒ(x) is concave down when x = c.


    6. If ƒ′(x) > 0 when x < c and ƒ′(x) < 0 when x > c, then ƒ(x) has a maximum value when x = c.


    7. Which of the following would best represent the statement "the plane is flying to the left of me, but is slowing down to come around for another pass?"

    a) v(t) > 0 and a(t) > 0
    b) v(t) > 0 and a(t) < 0
    c) v(t) < 0 and a(t) > 0
    d) v(t) < 0 and a(t) < 0

    8. A ball is thrown downward from the top of a 20 m tall building with an initial velocity of 15 m/s. What equation could be used to model its height, h(t)?


    9. What is the simplified average rate of change between x = 2 and x = 2 + h for the function:

    a. ƒ(x) = x^2?


    b. ƒ(x) = 1/x?

    -h/2(2+h)= -1/4
  2. jcsd
  3. May 31, 2012 #2


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    That's an awful lot of stuff for one post !

    I didn't check #4 numerically, but it seems reasonable. (Why isn't the answer 94°? You can't tell merely with the cross product.)

    #s 5 & 6 don't necessarily follow. (Aren't necessarily true.)

    Why simplify the answer to #9b that way?

    The others looked OK.

    It would have been more acceptable if you had broken this up into a few threads, and justified each answer.
  4. Jun 1, 2012 #3


    Staff: Mentor

    Echoing what Sammy said...
    Many homework helpers won't bother jumping in if there is a whole laundry list of problems. It's better to include at most two or three in a post.
  5. Jun 1, 2012 #4
    Ok, from now on i'll post one question at a time. I didn't get what you really mean for #5 and 6. They both looked true to me.. can you clear it, are they true or false. And for 9b. I think leaving the answer like -h/2(2+h) doesnt seem right, my teacher also said that it is close but still incorrect so I did another step -h/2(2+h)= -1/4
  6. Jun 1, 2012 #5
    For (5), think what would happen if y=(-x)

    For (6), Are the local maximum's the same as the global max for any function? :wink:

    Do your answers hold now?

    Your answer of -h/2(2+h) isn't correct. How did you get it?
  7. Jun 1, 2012 #6


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    For #5, Can the first derivative tell you anything about concavity ? Why or why not?

    For #6, Is f(x) continuous at x = c ?

    For #9 b , See Infinitum's comment.
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