anonymous
  • anonymous
A 26 foot long ladder is leaning against a vertical wall. The foot of the ladder is 10 feet away from the base of the wall. The foot of the ladder is being pulled away from the base of the wall at a rate of 4 feet per second. How fast is the top of the ladder sliding down the wall at this instant? (related rates)
Mathematics
katieb
  • katieb
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

myininaya
  • myininaya
related rates problem awesome!
anonymous
  • anonymous
myininaya
  • myininaya
cyter beat me
1 Attachment

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

myininaya
  • myininaya
lol wrong problem
myininaya
  • myininaya
1 Attachment
anonymous
  • anonymous
could both answers be correct?
myininaya
  • myininaya
lol there are two different answers let me see if i made a mistake
anonymous
  • anonymous
You used 4 instead of 10
myininaya
  • myininaya
cyter is right
myininaya
  • myininaya
i used y' for y my bad
myininaya
  • myininaya
cyter wins
anonymous
  • anonymous
we both win because we spent energy working on the problem
myininaya
  • myininaya
lol
anonymous
  • anonymous
in the writing in the purple, isn't the derivative of s^2 2s, not just 2?
anonymous
  • anonymous
yep
anonymous
  • anonymous
the right hand side should have been 2s ds/dt I knew something was amiss.
myininaya
  • myininaya
since s is a constant (it doesnt change) s'=0 so 2ss'=0
myininaya
  • myininaya
so it doesnt change the answer
anonymous
  • anonymous
yep it makes no difference but it looks logical
myininaya
  • myininaya
right and it is best to be logical during to look crazy
myininaya
  • myininaya
than not during*
anonymous
  • anonymous
but what happens to the 2s? does it cancel out? and how does the x (dx/dt) becomes negative?
myininaya
  • myininaya
2ss'=0
myininaya
  • myininaya
the derivative of s^2 is 2ss' but since s doesnt change s'=0
anonymous
  • anonymous
oo right, sorry
anonymous
  • anonymous
factor out the 2 s and devide both sides by 2 0/2 = 0
myininaya
  • myininaya
cyter did you draw that on the computer? it looks very mechanical like
myininaya
  • myininaya
on some parts
myininaya
  • myininaya
lol looks better than my horrible hand writing
anonymous
  • anonymous
\[\text{2((xdx/dt)+(ydy/dt) = 2sds = 0/dt}\] dividing both sides by 2 we have \[\text{((xdx/dt)+(ydy/dt) = sds/dt = 0}\] now subtract both sides by (xdx/dt) we get \[\text{(ydy/dt) = -(xdx/dt)}\] and then divide both sides by y to get dy/dt alone \[\text{(dy/dt) = -(x/y)dx/dt}\] Then plug and play
anonymous
  • anonymous
yes I used paint which isn't very good
anonymous
  • anonymous
Your handwriting is legible, unlike mine where I have to use a drawing program on my computer
myininaya
  • myininaya
i have a scanner haha
myininaya
  • myininaya
lol
anonymous
  • anonymous
ok i get it now, thank you both of you for your help
anonymous
  • anonymous
glad to help
anonymous
  • anonymous
Using cyter's solution diagram, \[y=x \text{Tan}[\text{ArcCos}[x/26]] \] then \[y=26 \sqrt{1-\frac{x^2}{676}} \] The total derivative of the above is: \[\text{Dt}[y]==-\frac{x \text{Dt}[x]}{26 \sqrt{1-\frac{x^2}{676}}} \] Replace x with 10 and Dt[x] with 4 and simplify, \[\text{Dt}[y]==-\frac{5}{3} \] I hope there are no errors. First DE solved in years.

Looking for something else?

Not the answer you are looking for? Search for more explanations.