Math Challenges

Submissions for Problem #2

Problem #2

A 6 foot ladder slides down a wall at a rate of 2 feet per second. How fast is the foot of the ladder sliding away from the wall at the moment when the top of the ladder is 4 feet from the ground?

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billy

Solution: \( 6\pm\pi^2\pi x_{\imaginaryI}\exists\forall\int_0^{\infty}\!\exponentialE^{x}\,\mathrm{d}x \)

Explanation:
Testing Line breaks are working, as is mobile!

samwise

Solution: \( \pi^2 \)

Explanation:
no?

zapwai

Solution: \( \displaylines{x^2+y^2=6^2\Rightarrow2xx^{\prime}+2yy^{\prime}=0\Rightarrow y^{\prime}=-\frac{xx^{\prime}}{y}\ y^{\prime}=-\frac{x}{y}\cdot2\\ y^2=36-\left(4\right)^2\Rightarrow y=\sqrt{20}\approx4.47\\ \Rightarrow y^{\prime}=-1.79} \)

Explanation:
Pythagorean theorem gives us a relation which we can differentiate. When x = 4, we can solve for y and evaluate.