Answer:
24in
Step-by-step explanation:
2*3*4= 24
Answer:B-70
Step-by-step explanation:
from the figure, In ![\triangle ABC\ \text{and}\ \triangle ADE](https://tex.z-dn.net/?f=%5Ctriangle%20ABC%5C%20%5Ctext%7Band%7D%5C%20%5Ctriangle%20ADE)
![\Rightarrow \dfrac{45}{45}=\dfrac{24}{24}\\\Rightarrow \dfrac{1}{1}=\dfrac{1}{1}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7B45%7D%7B45%7D%3D%5Cdfrac%7B24%7D%7B24%7D%5C%5C%5CRightarrow%20%5Cdfrac%7B1%7D%7B1%7D%3D%5Cdfrac%7B1%7D%7B1%7D)
![\therefore \text{two triangles are similar}](https://tex.z-dn.net/?f=%5Ctherefore%20%5Ctext%7Btwo%20triangles%20are%20similar%7D)
Thus we can write
![\Rightarrow \dfrac{35}{x}=\dfrac{45}{45+45}\\\\\Rightarrow x=35\times \dfrac{90}{45}=35\times 2=70](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7B35%7D%7Bx%7D%3D%5Cdfrac%7B45%7D%7B45%2B45%7D%5C%5C%5C%5C%5CRightarrow%20x%3D35%5Ctimes%20%5Cdfrac%7B90%7D%7B45%7D%3D35%5Ctimes%202%3D70)
So you do length times width and in your case it would be 14 times 14 = 196
Answer:
it's a) 7a/20b
Step-by-step explanation:
![5( \frac{a + 2}{4b} ) - 2( \frac{a - 1}{10b} ) + 4( \frac{a - 3}{5b} ) \\ \\ \frac{5a + 10 - 2a + 2 + 4a - 12}{20b } \\ \\ \\ \frac{7a}{20b}](https://tex.z-dn.net/?f=5%28%20%5Cfrac%7Ba%20%2B%202%7D%7B4b%7D%20%29%20-%202%28%20%5Cfrac%7Ba%20-%201%7D%7B10b%7D%20%29%20%2B%204%28%20%5Cfrac%7Ba%20-%203%7D%7B5b%7D%20%29%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7B5a%20%2B%2010%20-%202a%20%2B%202%20%2B%204a%20-%2012%7D%7B20b%20%7D%20%20%5C%5C%20%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7B7a%7D%7B20b%7D%20)
Answer:
![\frac{dy}{dx} =\frac{4x^3+3x^2y-5y^2}{10xy-3y^2-x^3}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%5Cfrac%7B4x%5E3%2B3x%5E2y-5y%5E2%7D%7B10xy-3y%5E2-x%5E3%7D)
Step-by-step explanation:
solving for dy/dx
multiply the equation out to remove parentheses
![x^4 + x^3y = 5xy^2 -y^3](https://tex.z-dn.net/?f=x%5E4%20%2B%20x%5E3y%20%3D%205xy%5E2%20-y%5E3)
now differentiating in terms of x (
)
![4x^3 +3x^2y + x^3(\frac{dy}{dx} ) = 5y^2 + 10xy(\frac{dy}{dx} )-3y^2(\frac{dy}{dx} )](https://tex.z-dn.net/?f=4x%5E3%20%2B3x%5E2y%20%2B%20x%5E3%28%5Cfrac%7Bdy%7D%7Bdx%7D%20%29%20%3D%205y%5E2%20%2B%2010xy%28%5Cfrac%7Bdy%7D%7Bdx%7D%20%29-3y%5E2%28%5Cfrac%7Bdy%7D%7Bdx%7D%20%29)
isolating dy/dx to one side
![4x^3 +3x^2y - 5y^2= 10xy(\frac{dy}{dx} )-3y^2(\frac{dy}{dx} )-x^3(\frac{dy}{dx} )](https://tex.z-dn.net/?f=4x%5E3%20%2B3x%5E2y%20-%205y%5E2%3D%2010xy%28%5Cfrac%7Bdy%7D%7Bdx%7D%20%29-3y%5E2%28%5Cfrac%7Bdy%7D%7Bdx%7D%20%29-x%5E3%28%5Cfrac%7Bdy%7D%7Bdx%7D%20%29)
![4x^3 +3x^2y - 5y^2= \frac{dy}{dx}(10xy-3y^2-x^3)](https://tex.z-dn.net/?f=4x%5E3%20%2B3x%5E2y%20-%205y%5E2%3D%20%5Cfrac%7Bdy%7D%7Bdx%7D%2810xy-3y%5E2-x%5E3%29)
![\frac{dy}{dx} =\frac{4x^3+3x^2y-5y^2}{10xy-3y^2-x^3}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%5Cfrac%7B4x%5E3%2B3x%5E2y-5y%5E2%7D%7B10xy-3y%5E2-x%5E3%7D)