Math  /  Calculus

QuestionA ladder 23 ft long rests against a vertical wall. If the top of the ladder is being pulled up the wall at a rate of 19ft/s19 \mathrm{ft} / \mathrm{s}, at what rate is the bottom of the ladder moving towards the wall when the top of the ladder is 7 ft from the ground?

Studdy Solution
Solve for dxdt \frac{dx}{dt} : 830dxdt+266=0 8\sqrt{30} \frac{dx}{dt} + 266 = 0 830dxdt=266 8\sqrt{30} \frac{dx}{dt} = -266 dxdt=266830 \frac{dx}{dt} = -\frac{266}{8\sqrt{30}}
Simplify the expression: dxdt=133430 \frac{dx}{dt} = -\frac{133}{4\sqrt{30}}
Rationalize the denominator: dxdt=13330120 \frac{dx}{dt} = -\frac{133 \sqrt{30}}{120}
The rate at which the bottom of the ladder is moving towards the wall is:
13330120ft/s \boxed{-\frac{133 \sqrt{30}}{120} \, \text{ft/s}}

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord