Friday

October 31, 2014

October 31, 2014

Posted by **Meg** on Friday, July 8, 2011 at 10:06am.

- Math Calculus -
**Reiny**, Friday, July 8, 2011 at 10:17amLet the foot of the ladder be x ft from the wall, and let the top of the ladder by y ft above the ground

x^2 + y^2 = 30^2

2x dx/dt + 2y dy/dt = 0

x dx/dt + y dy/dt = 0

when y = 6

x^2 + 36 = 900

x = √864

given: dx/dt = 1 , x = √864 , y = 6

√864(1) + 6dy/dt = 0

dy/dt = -√864/6 ft/min or appr. -4.9 ft/min

(the negative sign shows that y is decreasing or the ladder is moving down the wall)

- Math Calculus -
**Meg**, Friday, July 8, 2011 at 10:59amReini - How did you ended up getting x dx/dt + y dy/dt=0?

my professor said something with

a^2 + b^2 = c^2

then differentiate it so 2a(da/dt) + 2b(db/dt) = 2c(dc/dt)

so a^2+b^2=c^2

a^2 + 6^2 = 30^2

so a=sqrt(864)

then I differentiate

let da/dt = 1

b = 6

c=30

2a(da/dt)+2b(db/dt)=2c(dc/dt)

2sqrt(864)(1)+2(6)(db/dt)=2(30)(0)

=24sqrt(6)+12db/dt = 0

but how do i sold for db/dt?

is this way correct?

thanks

- Math Calculus -
**Reiny**, Friday, July 8, 2011 at 11:55amthat is exactly what I did, except I used x and y instead of a and b

remember that your c is a constant, so its derivative is zero (I used the actual 30^2)

I had defined x as the distance along the ground, and we were told the base of the ladder moved out"at a rate of 1 foot per minute"

this is the same as saying dx/dt = 1

from your

24sqrt(6)+12db/dt = 0

12db/dt = -24√6

db/dt = -24√6/12 = -4.9 , the same answer as I had

so yes, you are correct

- Math Calculus -
**Megan**, Friday, July 8, 2011 at 3:03pmThank you very much for your help :)

**Answer this Question**

**Related Questions**

Calculus - a 5m ladder rests against a vertical wall. The top of the ladder ...

Calculus - related rates: a ladder, 12 feet long, is leaning against a wall. if ...

math - A ladder 10 m long rests on horizontal ground and leans against a ...

Calculus - A 10 foot ladder leans against a 20 foot wall. Someone begins pushing...

Calculus - A 17 foot ladder is leaning on a 6 foot fence. The base of the ladder...

Calculus - A 25 foot ladder is leaning on a 9 foot fence. The base of the ladder...

Calculus - A 23 foot ladder is leaning on a 6 foot fence. The base of the ladder...

Calculus--Please Help! - A 13-foot ladder is leaning against a vertical wall. If...

College Calculus - A 13-foot ladder is leaning against a vertical wall. If the ...

Calculus - A ladder of length 10 metres is being drawn up a wall. The top of the...