Answer:
Your equation would be 4x2+3 So it would be 11
Step-by-step explanation:
Answer: The ladder is sliding down the wall at a rate of ![5\dfrac{17}{50}\ ft/sec](https://tex.z-dn.net/?f=5%5Cdfrac%7B17%7D%7B50%7D%5C%20ft%2Fsec)
Step-by-step explanation:
Since we have given that
Length of ladder = 25 foot
Distance from the wall to the bottom of ladder = 15 feet
Let base be 'x'.
Let length of wall be 'y'.
So, by pythagorus theorem, we get that
![x^2+y^2=25^2\\\\15^2+y^2+625\\\\225+y^2=625\\\\y^2=625-225\\\\y^2=400\\\\y=\sqrt{400}\\\\y=20\ feet](https://tex.z-dn.net/?f=x%5E2%2By%5E2%3D25%5E2%5C%5C%5C%5C15%5E2%2By%5E2%2B625%5C%5C%5C%5C225%2By%5E2%3D625%5C%5C%5C%5Cy%5E2%3D625-225%5C%5C%5C%5Cy%5E2%3D400%5C%5C%5C%5Cy%3D%5Csqrt%7B400%7D%5C%5C%5C%5Cy%3D20%5C%20feet)
![\dfrac{dy}{dx}=-4\ ft/sec](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%3D-4%5C%20ft%2Fsec)
Now, the equation would be
![x^2+y^2=625\\](https://tex.z-dn.net/?f=x%5E2%2By%5E2%3D625%5C%5C)
Differentiating w.r.t x, we get that
![2x\dfrac{dx}{dt}+2y.\dfrac{dy}{dt}=0\\\\2\times 15\dfrac{dx}{dt}+2\times 20\times -4=0\\\\30\dfrac{dx}{dt}-160=0\\\\\dfrac{dx}{dt}=\dfrac{160}{30}=5.34\ ft/sec](https://tex.z-dn.net/?f=2x%5Cdfrac%7Bdx%7D%7Bdt%7D%2B2y.%5Cdfrac%7Bdy%7D%7Bdt%7D%3D0%5C%5C%5C%5C2%5Ctimes%2015%5Cdfrac%7Bdx%7D%7Bdt%7D%2B2%5Ctimes%2020%5Ctimes%20-4%3D0%5C%5C%5C%5C30%5Cdfrac%7Bdx%7D%7Bdt%7D-160%3D0%5C%5C%5C%5C%5Cdfrac%7Bdx%7D%7Bdt%7D%3D%5Cdfrac%7B160%7D%7B30%7D%3D5.34%5C%20ft%2Fsec)
Hence, the ladder is sliding down the wall at a rate of ![5\dfrac{17}{50}\ ft/sec](https://tex.z-dn.net/?f=5%5Cdfrac%7B17%7D%7B50%7D%5C%20ft%2Fsec)
Origin (0,0), x-axis left to right, y-axis up and down (vertical)
Все детали на приложенном фото.