Question

Math ...

Answer 1

@jim_thompson5910

Answer 2

how far did you get with #7?

Answer 3

So we were doing a similar problem like this during class today, but I did not understand much. Basically I didn't get anywhere

Answer 4

Let's place Kyle at (0,0) for the start of the trip. If he moves 10 miles south, then he ends up where?

Answer 5

(0,-10)

Answer 6

yes

Answer 7

Should I plot it on a graph?

Answer 8

now he's going 6 mi east and 3 mi north

basically you will have a slope of 3/6 = 1/2

where does he end up after 1 minute?

Answer 9

Can you please give a minute to draw the graph? I am going to done with it soon :)

Answer 10

alright

Answer 11

Did it

Answer 12

He ends up in (6,-7)

Answer 13

so he goes from (0,0) to (0,-10)

After 1 minute in the plane, he goes from (0,-10) to what point?

Answer 14

`He ends up in (6,-7) `
yes

Answer 15

after 2 minutes, where is Kyle?

Answer 16

(12, -4)

Answer 17

yes. So he starts at point A, moves to B, then to C, then to D

see attached

which means Greenup is at (12,-4)

Answer 18

find the distance from A to D

Answer 19

I will measure it with the distance formula

Answer 20

\(D_{AD} = 4\sqrt{10}\)

Answer 21

yes

Answer 22

now find the equation of line BC. Tell me what you get

Answer 23

\(D_{BC} = 3\sqrt{5}\)

Answer 24

not the distance. I'm looking for the equation of the line

Answer 25

Sorry I misread it

Answer 26

y = 1/2x - 10

Answer 27

yes, we can solve for x to get...

y = (1/2)x - 10
2y = 2*[ (1/2)x - 10 ]
2y = x - 20
2y + 20 = x
x = 2y + 20

agreed?

Answer 28

Why did you multiply everything by 2?

Answer 29

to clear out the fraction

Answer 30

oh

Answer 31

so you see how I went from `y = (1/2)x - 10` to `x = 2y + 20` ?

Answer 32

yes

Answer 33

ok now we don't know where his birthplace is. We just know it's 50 mi away from his home

so it's 50 miles away from (0,0)

we'll have a circle represent all the possible places where his birthplace could be. The equation of the circle is going to be `x^2 + y^2 = 50^2` which turns into `x^2+y^2 = 2500`

Answer 34

once you have x^2+y^2 = 2500, you replace the 'x' with 2y+20 to get

(2y+20)^2 + y^2 = 2500

do you see how to solve for y?

Answer 35

why did you do x^2 + y^2?

Answer 36

recall that `(x-h)^2 + (y-k)^2 = r^2` is the equation of any circle

(h,k) is the center. In this case, (h,k) = (0,0)
r is the radius. In this case, r = 50

Answer 37

Well I haven't learned that in my class and my teacher doesn't want anything that we haven't learned from class

Answer 38

ok then don't use it

Answer 39

use the distance formula instead

Answer 40

let point E be the place of Kyle's birth

we don't know where point E is. Let's just say that E = (x,y)

Answer 41

I would get that \(D_{AE} = x + y\)

Answer 42

using the distance formula, we see that
\[\Large d = \sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}\]
\[\Large 50 = \sqrt{\left(0-x\right)^2+\left(0-y\right)^2}\]
\[\Large 50 = \sqrt{x^2+y^2}\]
\[\Large 50^2 = \left(\sqrt{x^2+y^2}\right)^2\]
\[\Large x^2+y^2 = 2500\]
so it leads back to the previous equation written

Answer 43

Oh I totally forgot about a step

Answer 44

uh oh, you made the mistake in thinking that \[\Large \sqrt{x^2+y^2} = x+y\]

Answer 45

yea

Answer 46

\[\Large \sqrt{x^2+y^2} \ne \sqrt{x^2}+\sqrt{y^2}\]

Answer 47

So i substituted and got
\(2500 = (2y + 20)^2 + y^2\)

Answer 48

now isolate y

Answer 49

0 = 5y^2 + 80y - 2100

Answer 50

yep now use the quadratic formula

Answer 51

ok

Answer 52

I have