Given that

, we have for

the Taylor series expansion about 0 as

Replace

with

, so that the series is equivalent to

and notice that

Recall that for

, we have

which means

Answer:
0.016
Step-by-step explanation:
Answer:
For the yes/no bit:
step 1: no
step 2: no
step 3: yes
step 4: yes
step 5: no
for the final answer bit: a = 2 3/5 (the last option)
Step-by-step explanation:
yes/no bit:
step 1 is wrong because she didn't multiply
by -2
step 2 is wrong because she subtracted 1/2 instead of adding it
step 3 is correct because 6 - 1/2 = 11/2
step 4 is correct because she correctly multiplied both sides by 4
step 5 is wrong because she added 5 instead of dividing by -5.
for the final answer bit, I've attached an image below with my working out. hope this helps!
V=πr^2h/3=π·3^2·11.5/3≈108.38495 or 108.40 rounded
638-243 = 395 miles
rounding up, it would be 400 miles