Answer:
a) -13.9 ft/s
b) 13.9 ft/s
Step-by-step explanation:
a) The rate of his distance from the second base when he is halfway to first base can be found by differentiating the following Pythagorean theorem equation respect t:
(1)

(2)
Since:

When x = 45 (the batter is halfway to first base), D is:

Now, by introducing D = 100.62, x = 45 and dx/dt = 31 into equation (2) we have:

Hence, the rate of his distance from second base decreasing when he is halfway to first base is -13.9 ft/s.
b) The rate of his distance from third base increasing at the same moment is given by differentiating the folowing Pythagorean theorem equation respect t:

(3)
We have that D is:

By entering x = 45, dx/dt = 31 and D = 100.63 into equation (3) we have:

Therefore, the rate of the batter when he is from third base increasing at the same moment is 13.9 ft/s.
I hope it helps you!
Answer:
A. 200 packages
Step-by-step explanation:
The number of packages per roll can be found by dividing the length of a roll by the length of tape needed for each package.
__
For each package:
(2.375 in/piece)×(4 piece/package) = 9.5 in/package
Per roll:
(1900 in/roll) / (9.5 in/package) = (1900/9.5) packages/roll
= 200 packages/roll
The machine can seal 200 packages with a roll of tape 1900 inches long.
Hello!
I believe the answer is 58°.
Explanation: In order to find this answer, we must first add up the two numbers; 87+35. After adding, your solution should be 122. In order to be a triangle, all of the degrees must all add up to 180°. Next we must subtract 122 from 180. After subtracting, the answer is 58. Therefor your answer is 58°.