Question

help

Answer 1

@Vocaloid

Answer 2

for 1: consider the sign and the magnitude of -pi/4 (whether the absolute value of -pi/4 is >1 or <1

Answer 3

b?

Answer 4

good, I'm still working on 2 but you would have to resolve the force into its vertical and horizontal components I believe and calculate F*distance in both directions

Answer 5

b again?

Answer 6

I think so :S technically it should be closer to 28 but that's not an option

Answer 7

oops i was looking at 3 lol

Answer 8

3 is something other than b, check your calculations again

Answer 9

d?

Answer 10

just look at the y-coordinates

-u - v = -3 - (-4) = ?

Answer 11

1

Answer 12

good so the y-coordinate must be 1 making a the only possibility

4) just calculate the magnitude and divide the vector by the magnitude

Answer 13

d?

Answer 14

good

Answer 15

5 is just a dot product, it may be helpful to convert to vector notation <,>

Answer 16

d?

Answer 17

@Vocaloid

Answer 18

keep in mind u = 13j = <0,13>

<0,13> dot <1,3> = ?

Answer 19

c

Answer 20

good

for 6) since u is the line RS and v is the line OP

you will need to find the length of RS and OP by subtracting S - R and P - O respectively, then finding the magnitudes of each segment

Answer 21

are you looking at 6 or 7 i think you are looking at 7

Answer 22

oh duh that's 7)


6) the horizontal component is just initial velocity * cos(theta)

Answer 23

c

Answer 24

good, lmk if you need help w/ 7

Answer 25

well done

as a minor nitpick, when you square a negative number you need to write that number in parentheses

(-4)^2 not -4^2

Answer 26

anyway for 8 to find PQ, subtract Q - P and to find RS, subtract S - R, then perform the indicated operation PQ + 3RS

Answer 27

a

Answer 28

good

Answer 29

part b d?

Answer 30

good

part 9 is basically the same thing just with PQ + 4RS instead

Answer 31

c

Answer 32

awesome then for part 9B you'd just calculate the magnitude based on that

Answer 33

b

Answer 34

good

10A is just the same steps from 8 and 9 except with PQ + 5RS

Answer 35

c

Answer 36

good

guessing part 10B is going to ask for the magnitude

Answer 37

am i seriously getting them all correct?

Answer 38

c? for b

Answer 39

10B I got something a little different

magnitude = sqrt(18^2 + 26^2) = ?

Answer 40

b

Answer 41

good

for 11: magnitude = sqrt(x^2 + y^2) as usual, angle is given by tan(theta) = y/x, lmk what you get

Answer 42

b

Answer 43

check the magnitude again

[ 3cos(123) ] ^2 + [3 sin(123)] ^ 2 = ?

Answer 44

d

Answer 45

good

for 12) follow the usual angle formula:

Answer 46

c

Answer 47

I got something a little different, what did you get as your denominator

Answer 48

b?

Answer 49

may I see your calculations so I can see where you might have made a mistake?

Answer 50

trying to multiply both u and v and then I'm lost

Answer 51

first convert the notation to <,> to make it a little easier

<-1, sqrt(7)> dot <-1, -4> = ?

Answer 52

wait

Answer 53

<1, sqrt(7)> dot <-1, -4> = ?

Answer 54

should be a positive 1 at the beginning

Answer 55

2,-7

Answer 56

1. multiply the x-coordinates
2. multiply the y-coordinates
3. add the results from steps 1 and 2

Answer 57

let me check

Answer 58

d

Answer 59

may I know what you got for the dot product?

Answer 60

I did cos(97)
I got about -12

Answer 61

let's try to take it one step at a time
<1, sqrt(7)> dot <-1, -4>

we multiply the x-coordinates to get -1
we multiply the y-coordinates to get -4sqrt(7)

adding them together gives -1 - 4sqrt(7) as the dot product

Answer 62

then, simply find the magnitudes of the vectors <1, sqrt(7)> dot <-1, -4> to put in the denominator of our angle expression

lmk what you get, you can leave things in radical form instead of decimals

Answer 63

-10.58

Answer 64

magnitudes are always positive so something must be amiss

Answer 65

that's for- 4* square root 7

Answer 66

let's leave things in radical form for now

please calculate the magnitudes of <1, sqrt(7)> and <-1, -4>

Answer 67

18
23 took out all -

Answer 68

1^2 + sqrt(7) ^ 2 = ?
(-1)^2 + (-4)^1 = ?

Answer 69

last exponent should be a 2

Answer 70

1+7=8
-1+-16=-17

Answer 71

good so your magnitudes are sqrt(8) and sqrt(17)

putting everything together

cos(theta) = (-1-4sqrt(7)) / (sqrt(8*17)) solve for theta

Answer 72

its a

Answer 73

well done

Answer 74

use the graph to determine what u would be in vector notation then see which dot product is 0

Answer 75

b?

Answer 76

check carefully
the dot product of <-6,-5> and <5,6> is not 0

Answer 77

c

Answer 78

good

Answer 79

14?

Answer 80

try sketching the path of the plane (160 mph east and 30 mphs south) and calculate the magnitude of the vector

Answer 81

what's the magnitude of this vector?

Answer 82

d

Answer 83

good

Answer 84

15

Answer 85

try to write what vector v would be based on the graph (hint - try finding the horizontal and vertical distance between the tip and tail and put those into a vector)

then find u - 2v

Answer 86

a

Answer 87

check your calculations again

what did you get for vector v?

Answer 88

d

Answer 89

may I ask what you got for vector v? it's easier to pinpoint mistakes and speed up the process if I know what steps you're doing

Answer 90

6*2=12
-4*2=-8

Answer 91

2--8=10

Answer 92

good, that's 2u, but what about vector v?

Answer 93

7-12=-5

Answer 94

vector v = <12,2>

then v - 2u = <12, 2> - <12, -8> = ?

Answer 95

so it is 10

Answer 96

c

Answer 97

good, <0,10> = C

Answer 98

16: magnitude = sqrt of dot product as usual

Answer 99

a

Answer 100

awesome

for 17: tan(theta) = y/x, solve for theta

Answer 101

as a hint for tan angles, you might need to add 180 once you get the angle

Answer 102

also a

Answer 103

6.77
and i had 6.75

Answer 104

hm, not quite

tan(theta) = -27/4 so

theta = arctan(-27/4) = ?

Answer 105

b

Answer 106

good

Answer 107

my calculator is putting the same thing but b and d are negative?

Answer 108

can we open a new question, this one has over 120 posts

Answer 109

anyway, for tan, you might get a negative angle but we can convert negative angles to positive angles by adding 180 (this only works for tan)