Two angles are said to be suplementary when the aum of the two angle is 180*
The rest would be 8/10 but to simplify it would be 4/5
Answer:3, 25
Step-by-step explanation:
The seconds should be the x-axis and the height is y axis. Also thinking about how a kicked ball makes an arch, the max is 25, and the mid point between 0 and 6 is 3.
Answer:
![\frac{dy}{dx}=\frac{x(1-2lnx)}{x^{4}}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7Bx%281-2lnx%29%7D%7Bx%5E%7B4%7D%7D)
Step-by-step explanation:
To solve the question we refresh our knowledge of the quotient rule.
For a function f(x) express as a ratio of another functions u(x) and v(x) i.e
, the derivative is express as
![\frac{df(x)}{dx}=\frac{v(x)\frac{du(x)}{dx}-u(x)\frac{dv(x)}{dx}}{v(x)^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7Bdf%28x%29%7D%7Bdx%7D%3D%5Cfrac%7Bv%28x%29%5Cfrac%7Bdu%28x%29%7D%7Bdx%7D-u%28x%29%5Cfrac%7Bdv%28x%29%7D%7Bdx%7D%7D%7Bv%28x%29%5E%7B2%7D%20%7D)
from ![y=lnx/x^{2}](https://tex.z-dn.net/?f=y%3Dlnx%2Fx%5E%7B2%7D)
we assign u(x)=lnx and v(x)=x^2
and the derivatives
.
Note the expression used in determining the derivative of the logarithm function.it was obtain from the general expression of logarithm derivative i.e ![y=lnx\\\frac{dy}{dx}=\frac{1}{x}](https://tex.z-dn.net/?f=y%3Dlnx%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7B1%7D%7Bx%7D)
If we substitute values into the quotient expression we arrive at
![\frac{dy}{dx}=\frac{(x^{2}*\frac{1}{x})-(2x*lnx)}{x^{4}}\\\frac{dy}{dx}=\frac{x-2xlnx}{x^{4}}\\\frac{dy}{dx}=\frac{x(1-2lnx)}{x^{4}}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7B%28x%5E%7B2%7D%2A%5Cfrac%7B1%7D%7Bx%7D%29-%282x%2Alnx%29%7D%7Bx%5E%7B4%7D%7D%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7Bx-2xlnx%7D%7Bx%5E%7B4%7D%7D%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7Bx%281-2lnx%29%7D%7Bx%5E%7B4%7D%7D)