Question

after a vigorous soccer match,Tina and Michael decide to have a glass of their favorite refreshment. They each run in a straight line along the indicated paths at a speed of 10 ft/sec. Parametrize the motion ofTina and Michael individually. Find when and where Tina and Michael are closest to one an-other; also compute this minimum distance. Michael starts at (0,0) and goes to (200,300). Tina starts at (400,50) and goes to (-50,275). Pre-calc. problem, help!

Answer 1

I already parametrized the equations, just how do you compute the minimal distance using pre-calc. skills?

Answer 2

hmm I can't remember this,
what does your parmaterized equation look like?

Answer 3

for michael
x = 20t
y= 30t

for tina
x= 400-45t
y=50+22.5t

Answer 4

oh wait what was the distance formula again hmm

Answer 5

yeah square root of (x-x)^2 + (y-y)^2 something like that hmm

Answer 6

yeah, is that what I use?

Answer 7

yeah, cause we'll be trying to find when that's the smallest

Answer 8

ok, let me see if that works and i'll let you know

Answer 9

So I got 5.59016994 times the sprt of (137t^2- 1688t +5200)

Answer 10

alright cool so that looks like a quadratic I think

Answer 11

https://www.desmos.com/calculator/ejs2rzz2fu

Answer 12

So I guess I could graph it and see what the vertex is or change the equation to vertex/standard form and find the vertex. the x-coor. should tell me when they are closest together and the y-coor. should tell me how far apart they are

Answer 13

yep, I got x= about 6.161 and y= about 3.821

Answer 14

ye

Answer 15

thanks for helping

Answer 16

np

Answer 17

What math are you in?

Answer 18

like 3 years ahead of you

Answer 19

ok then

Answer 20

hey I got another question

Answer 21

ye

Answer 22

so I have the equation ax^2+2xa^2+1=0. I should use the quadratic formula to solve for x in terms of a right. So what would my a, b, and c values be?

Answer 23

is a going to be a. b going to be 2a^2 and c going to be 1?

Answer 24

ye

Answer 25

nvr mind I got it