There is an arcade in the amusement park. A computer game there uses functions to simulate the paths of an archer’s arrows. The
x-axis represents the level ground on which the archer stands, and the coordinate pair (2,5) represents the top of a castle wall over which he is trying to fire an arrow.
In response to user input, the first arrow followed a path defined by the function f(x)=6-x^2, failing to clear the castle wall.
The next arrow must be launched with the same force and trajectory, so the user must reposition the archer in order for his next arrow to have any chance of clearing the wall.
a. How much closer to the wall must the archer stand in order for the arrow to clear the wall by the greatest possible distance?
b. What function must the user enter in order to accomplish this?
c. If the user can only enter functions of the form f(x+k), what are all the values of k that would result in the arrow clearing the castle wall?
In response to user input, the first arrow followed a path defined by the function f(x)=6-x^2, failing to clear the castle wall.
The next arrow must be launched with the same force and trajectory, so the user must reposition the archer in order for his next arrow to have any chance of clearing the wall.
a. How much closer to the wall must the archer stand in order for the arrow to clear the wall by the greatest possible distance?
b. What function must the user enter in order to accomplish this?
c. If the user can only enter functions of the form f(x+k), what are all the values of k that would result in the arrow clearing the castle wall?
1 answer:
You might be interested in
Answer:
Speed of first plane is 350 miles per hour
Speed of second plane is 100 miles per hour
Step-by-step explanation:
Let the speed of the second plane be X
Then the speed of the first plane will be 3.5 X
Distance travelled by first plane is 9.5 *X
Distance travelled by second plane is 9.5 * 3.5 X
Difference of distance between the two plane is
miles per hour
Speed of first plane is 3.5 *100 = 350 miles per hour
Speed of second plane is 100 miles per hour
Answer:
Required Probability = 0.1283 .
Step-by-step explanation:
We are given that at Meadow brook Hospital, the mean weight of babies born to full-term pregnancies is 7 lbs with a standard deviation of 14 oz.
Firstly, standard deviation in lbs = 14 ÷ 16 = 0.875 lbs.
Also, Birth weights of babies born to full-term pregnancies follow roughly a Normal distribution.
Let X = mean weight of the babies, so X ~ N()
The standard normal z distribution is given by;
Z = ~ N(0,1)
where, X bar = sample mean weight
n = sample size = 4
Now, probability that the average weight of the four babies will be more than 7.5 lbs = P(X bar > 7.5 lbs)
P(X bar > 7.5) = P( >
) = P(Z > 1.1428) = 0.1283 (using z% table)
Therefore, the probability that the average weight of the four babies will be more than 7.5 lbs is 0.1283 .