Couple multiple choice: Confirmation needed

[livestrong136]

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.

True
False

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.

True
False

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)?

-4.9t^2-15t+20

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

a. ƒ(x) = x^2?

4+h

b. ƒ(x) = 1/x?

-h/2(2+h)= -1/4

 

[SammyS]

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.

True
False

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.

True
False

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)?

-4.9t^2-15t+20

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

a. ƒ(x) = x^2?

4+h

b. ƒ(x) = 1/x?

-h/2(2+h)= -1/4

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.

 

[Mark44]

It would have been more acceptable if you had broken this up into a few threads, and justified each answer.

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.

 

[livestrong136]

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.

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) doesn't seem right, my teacher also said that it is close but still incorrect so I did another step -h/2(2+h)= -1/4

 

[Infinitum]

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

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?

Do your answers hold now?

And for 9b. I think leaving the answer like -h/2(2+h) doesn't seem right, my teacher also said that it is close but still incorrect so I did another step -h/2(2+h)= -1/4

Your answer of -h/2(2+h) isn't correct. How did you get it?

 

[SammyS]

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) doesn't seem right, my teacher also said that it is close but still incorrect so I did another step -h/2(2+h)= -1/4

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.