By Pythagorean theorem
x²+GF²=EF² ( where G is the point of intersection of perpendicular lines)
now, GF=1/2 EF= 12
x²+12²=24²
x²=24²-12²
x²=432
x=√432
x=12√3
x≈20.78
When x=1/4 x²=1/16 so f(1/4)=y=2 1/16 last answer
<h2>3w + 6 (w - 4) = 156</h2><h2 /><h2>3w + 6w - 24 = 156</h2><h2 /><h2>9w - 24 = 156</h2><h2 /><h2>9w = 180</h2><h2>÷9 ÷9 ← divide by 9 on both sides</h2><h2 /><h2> w = 20</h2>
![z=2x^4+8x \\ dz=(8x^3+8)\ dx=8(x^3+1)\ dx \\ \int\limits^0_{-1} {(2x^4+8x)^3*(4x^3+4)} \, dx =4* \int\limits^0_{-6} { \dfrac{z^3}{2}} \, dz \\ = 2* \left[\begin{array}{ccc} \dfrac{z^4}{4}\end{array}\right] ^0_{-6}= \left[\begin{array}{ccc} \dfrac{z^4}{2}\end{array}\right] ^0_{-6}=0-648=-648](https://tex.z-dn.net/?f=%20z%3D2x%5E4%2B8x%20%5C%5C%0Adz%3D%288x%5E3%2B8%29%5C%20dx%3D8%28x%5E3%2B1%29%5C%20dx%20%5C%5C%0A%0A%20%5Cint%5Climits%5E0_%7B-1%7D%20%7B%282x%5E4%2B8x%29%5E3%2A%284x%5E3%2B4%29%7D%20%5C%2C%20dx%20%3D4%2A%20%5Cint%5Climits%5E0_%7B-6%7D%20%7B%20%5Cdfrac%7Bz%5E3%7D%7B2%7D%7D%20%5C%2C%20dz%20%5C%5C%0A%3D%202%2A%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%20%5Cdfrac%7Bz%5E4%7D%7B4%7D%5Cend%7Barray%7D%5Cright%5D%20%5E0_%7B-6%7D%3D%0A%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%20%5Cdfrac%7Bz%5E4%7D%7B2%7D%5Cend%7Barray%7D%5Cright%5D%20%5E0_%7B-6%7D%3D0-648%3D-648)