Question

I am trying to find the points on the line y=x+2 that is closet to (2, 1). Do not tell me the answer, but give me a head start on how I should begin

Answer 1

READY SET GO!

Answer 2

you probably want the line perpendicular to the given line that goes through pony (2,1)

Answer 3

The closest point will be on a line perpendicular to the original line that passes through the given point:

Answer 4

so I find the line perpendicular to the equation above

Answer 5

There's lots of lines that are perpendicular to that line:


You find the perpendicular slope, then use the point-slope equation.

Answer 6

ok

Answer 7

Sorry if I am asking a lot of question, so I find the perpendicular slope, then the point-slope equation to give me a new equation?

Answer 8

Yes.

Answer 9

The point will be the intersection of the two equations.

Answer 10

I did it and it does not make any sense. I found the perpendicular slope which is -1 and I found the new line equation which is -x+3. how does this give me the points. I plugged 2 as my x value and it gave me 1 as my y value.

Answer 11

y=-x+3 intersects y=x+2:
-x+3 = x+2
-1 = -2x
x = 1/2

y = -(1/2) + 3
y = 2+1/2

Answer 12

so the point is (.5, 1.5). thanks a lot. what does it mean to approximate percent change

Answer 13

Sorry, not a clue what approximate percent change means.

Answer 14

ok thanks, u've done more than enough.

Answer 15

what is the original question ?

Answer 16

approximate change in area of equilateral triangle if side length changes from 5 to5.1. what is the approximate percent change. I know how to do the first part. but not the second one

Answer 17

write down the area of the triangle as a function of x (side length)= f(x)

take the derivative of f(x)
use the approximation formula
\[ \Delta A = f' \cdot \Delta s \]
percent change will be
\[ \frac{\Delta A}{A} \]
changed to a percent

Answer 18

what did you get for \( \Delta A\) ?

Answer 19

to be more clear, use
\[ \Delta A = f'(5) \Delta x \]
where x is the side

Answer 20

got it. thanks

Answer 21

I need help with this problem. An athelete who is 5'6" walks away from a lamp stand that is 22 foot tall at the rate of 3 feet per seconds. at what rate is the top of her shadow moving when she is 20 feet from the lampstand

Answer 22

Have you seen
http://tutorial.math.lamar.edu/Classes/CalcI/RelatedRates.aspx
?

He gives an example of most types of related rates problems. See example 6