X intercept is where the line crosses the x axis or where y=0
y intercept is where the line crosses the y axis or where x=0
so
6x-3y=-6
x intercept
y=0
6x-3(0)=-6
6x=-6
x=-1
x intercept at x=-1 or the point (-1,0)
y intercept
x=0
6(0)-3y=-6
-3y=-6
y=2
y intercept at y=2 or the point (0,2)
as you already know, the slope of the tangent line is simply the derivative of the function, so
![r=2cos(3\theta )\implies \cfrac{dr}{d\theta }=2\stackrel{chain~rule}{\left[ -sin(3\theta )\cdot 3 \right]} \\\\\\ \left. \cfrac{dr}{d\theta }=-6sin(3\theta ) \right|_{\theta =\frac{\pi }{6}}\implies -6sin\left( 3\cdot \frac{\pi }{6} \right)\implies -6sin\left( \frac{\pi }{2} \right)\implies -6](https://tex.z-dn.net/?f=r%3D2cos%283%5Ctheta%20%29%5Cimplies%20%5Ccfrac%7Bdr%7D%7Bd%5Ctheta%20%7D%3D2%5Cstackrel%7Bchain~rule%7D%7B%5Cleft%5B%20-sin%283%5Ctheta%20%29%5Ccdot%203%20%5Cright%5D%7D%20%5C%5C%5C%5C%5C%5C%20%5Cleft.%20%5Ccfrac%7Bdr%7D%7Bd%5Ctheta%20%7D%3D-6sin%283%5Ctheta%20%29%20%5Cright%7C_%7B%5Ctheta%20%3D%5Cfrac%7B%5Cpi%20%7D%7B6%7D%7D%5Cimplies%20-6sin%5Cleft%28%203%5Ccdot%20%5Cfrac%7B%5Cpi%20%7D%7B6%7D%20%5Cright%29%5Cimplies%20-6sin%5Cleft%28%20%5Cfrac%7B%5Cpi%20%7D%7B2%7D%20%5Cright%29%5Cimplies%20-6)
Answer:
25.96 feet
Step-by-step explanation:
see attached
Answer:
Bobcats
Step-by-step explanation:
The wins-to-losses ratio for the Cougars is 12:10. This can also be written as 12/10; writing this as a decimal, we would have 1.2.
The wins-to-losses ratio for the Bobcats is 20:10. This can also be written as 20/10, which is the same as 2.0.
The wins-to-losses ratio for the Bulldogs is 8:5. This can also be written as 8/5, which is the same as 1.6.
The wins-to-losses ratio for the Tigers is 3:5. This can also be written as 3/5,l which is the same as 0.6.
The largest of these decimals is 2.0; this means the Bobcats have the greatest ratio of wins to losses.
