MA 3972-MA-Book April 11, 2018 16:32
368 STEP 5. Build Your Test-Taking Confidence
- The correct answer is (C).
Remember,a(t)=v′(t). Using the TI-89
graphing calculator, finda(t), and evaluate it
att=
π
4
:
d(cos(t)∗e∧(sin(t)),t)|t=π/ 4
=− 0. 420036 ≈− 0. 420
- The correct answer is (A).
x = k
0 π
2
x
y
y = cos x
Since the areas of the two regions are equal, set
∫k
0
cos(x)dx=
∫ π
2
k
cos(x)dx, and obtain
−sin(x)]k 0 =−sin(x)]
π 2
k. Evaluating the definite
integrals, you have
−sin(k)−(−sin( 0 ))=−sin
(
π
2
)
−(−sin(k)),
or 2 sin(k)=1, which yields sin(k)=
1
2
,or
k=sin−^1
(
1
2
)
=
π
6
.
- The correct answer is (C).
LetR(t) be the function representing the
number of bacteria in the petri dish, so∫
r(t)dt=R(t). The net change in the
number of bacteria between day two and day
five is
∫ 5
2
r(t)dt=R(5)−R(2), or
∫ 5
2
2
√
t(e^1.^02 t)dt=R(5)−150. Thus,
623. 227 =R(5)−150, or
R(5)= 773. 227 ≈773.
