Answer:
Maximum height is 7 feet
Step-by-step explanation:
Solution:-
- The complete question is as follows:
" The height of a small rise in a roller coaster track is modeled by f(x) = –0.07x^2 + 0.42x + 6.37, where x is the distance in feet from a supported at ground level.
Find the greatest height of the rise "
- To find any turning points ( minimum or maximum ) points of a trajectory expressed as function of independent parameter, we find the critical points of the trajectory where the first derivative of the dependent variable w.rt independent variable is set to zero.
- In our case the height of the roller coaster track (y) is function of the distance (x) from a supported pole at ground level.
f(x) = –0.07x^2 + 0.42x + 6.37
- Now set the first derivative equal to zero, and determine the critical values of x:
0 = -0.14x + 0.42
x = 0.42 / 0.14 = 3 ft
- The critical value for the coaster track is at point 3 feet away from the supported pole at ground level. So the height f(x) at x = 3 ft, would be:
f ( x = 3 ) = max height
max height = –0.07*3^2 + 0.42*3 + 6.37
= 7 ft
9/8 of a meter is 1 1/8 of a meter.
9/8 of a meter is also approximately 3.69 feet.
Total Number of socks = 4 pairs= 8 socks
Number of red socks = 4
Number of black socks = 4
Probability of pulling a red sock from the bag the first time =

Since the sock is placed back in the bag before pulling a sock again, the number of socks remains the same.
So,
Probability of pulling a red sock from the bag the second time =

And
Probability of pulling a red sock from the bag the third time =
Therefore, the probability of pulling a red sock 3 times from the bag =