Question

calc help

Answer 1

@Vocaloid

Answer 2

a) the red segment is the hypotenuse so naturally it will be longer than the green segment
b) you have to get this using your program
c) assuming he starts at x = 0, goes 1m/4 seconds, use distance = rate*time to calculate the distance after 3 secs.

Answer 3

the program doesn't give me anything unless I have to assume the dashes as a 0.25 meter
so is the distance then 0.75?

Answer 4

@Vocaloid

Answer 5

ah yes

Answer 6

so I'm correct on that part?

Answer 7

for c yes

Answer 8

so I'm correct on that part?

Answer 9

so I'm correct?

Answer 10

yes.

Answer 11

for d use trig and do opp/adj

Answer 12

tan

Answer 13

d. pythagorean theorem
e. once you have the leg lengths, the rate of change wrt t for both legs, take the derivative of the pythagorean theorem wrt t and solve for dc/dt

Answer 14

d=about 2.14?

Answer 15

yeah that's what i got too

Answer 16

so do I still need to do opposite over adjacent and then take derivative?

Answer 17

a^2 + b^2 = c^2

2a * da/dt + 2b * db/dt = 2c * dc/dt
da/dt 0 since the black segment is constant

db/dt should be your solution from part b
you should have a,b,c from the pythagorean theorem

Answer 18

so 1.125x0=0+2*2=4*0.25=1

Answer 19

... what

Answer 20

or wait I still have to take the derivative

Answer 21

trying to plug in all the numbers

Answer 22

no, I gave you the derivative, plug in and solve for dc/dt

Answer 23

okay then
2a*da/dt+2b*db/dt=2c*dc/dt
2*0.75=1.125x0=0
2*2=4*0.25=1
2c=4.28 now to figure out what dc/dt is

Answer 24

you should already know what c is. since you know what the two legs a and b are you can use the pythagorean theorem to solve for c

once everything is plugged in, solve for dc/dt

Answer 25

what I plugged in was the legs and stuff
is d distance and t time?
I am kinda confused now

Answer 26

@Vocaloid

Answer 27

@Hero

Answer 28

@Vocaloid

Answer 29

d means derivative.

Answer 30

am I soling the entre thing wrng then or am I finding the derivative of c?

Answer 31

start with the pythagorean theorem
a^2 + b^2 = c^2

take the derivative of both sides wrt t to get

2a*da/dt+2b*db/dt=2c*dc/dt

plug in everything except dc/dt

Answer 32

da/dt is the rate at which side a changes (notice how side a, the black side, is fixed so the da/dt is 0

db/dt is the rate at which side b changes (the green side) which you should have from step C b)

a, b, and c are the side lengths

therefore you can plug everything in and solve for dc/dt

Answer 33

so 1.125 *0=0

Answer 34

@Vocaloid

Answer 35

what are you plugging in? what do these numbers represent?

Answer 36

2x.75

Answer 37

that's side b not side a

2a * da/dt should be the black side (2m) * da/dt

Answer 38

so .28

Answer 39

1.125*.25

Answer 40

2*2=4*0=0

Answer 41

0 + 2b * rate of change for the green side = 2c * dc/dt

Answer 42

.60?

Answer 43

show me the full equation with everything plugged in

what is your db/dt value?

Answer 44

.25

Answer 45

ok

then 2a*da/dt+2b*db/dt=2c*dc/dt

becomes

0 + 2(0.75)(0.5) = 2(2.14)dc/dt

Answer 46

4.28

Answer 47

don't forget your algebra rules

0 + 2(0.75)(0.5) = 2(2.14)dc/dt

becomes

0.75 = 4.28*dc/dt

then you'd divide both sides by 4.28 to solve for dc/dt

Answer 48

.18

Answer 49

yeah that's what i got too

Answer 50

Which segment, red or green, grows at the fastest speed?

Answer 51

uh

if our calculations are correct then you just need to compare which is greater, dc/dt or db/dt

Answer 52

so c?

Answer 53

wait no db/dt

Answer 54

yeah I think we got db/dt as the greater one so the green one grows a bit faster

Answer 55

At what time will the segments theoretically grow at exactly the same

Answer 56

got interrupted by something but

2b(db/dt) = 2c(dc/dt)

if db/dt are both equal then b and c must both be equal (which is impossible for a right triangle)

so I actually don't think they'll ever grow equally... hm. could be making a logical error here.