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Math Problems
Precalculus
Find the magnitude and direction of a vector sum
Relative to a point
O
O
O
, the position vector of a ship is
(
12
i
+
16
j
)
k
m
(12 i+16 j) \mathrm{km}
(
12
i
+
16
j
)
km
. If the ship sails with a constant speed of
24
k
m
/
h
24 \mathrm{~km} / \mathrm{h}
24
km
/
h
on a bearing of
06
0
∘
060^{\circ}
06
0
∘
, find its position vector after
4
4
4
hours. Give your answer correct to
3
3
3
significant figures.
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One diagonal of a rhombus is decreasing at a rate of
7
7
7
centimeters per minute and the other diagonal of the rhombus is increasing at a rate of
10
10
10
centimeters per minute.
\newline
At a certain instant, the decreasing diagonal is
4
4
4
centimeters and the increasing diagonal is
6
6
6
centimeters.
\newline
What is the rate of change of the area of the rhombus at that instant (in square centimeters per minute)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
1
-1
−
1
\newline
(B)
−
16
-16
−
16
\newline
(C)
16
\mathbf{1 6}
16
\newline
(D)
1
1
1
\newline
The area of a rhombus with diagonals
d
1
d_{1}
d
1
and
d
2
d_{2}
d
2
is
d
1
d
2
2
\frac{d_{1} d_{2}}{2}
2
d
1
d
2
.
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Find the circumference and the area of a circle with radius
4
yd
4\,\text{yd}
4
yd
.
\newline
Use the value
3.14
3.14
3.14
for
π
\pi
π
, and do not round your answers. Be sure to include the correct units in your answers.
\newline
Circumference:
\newline
Area:
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Find the circumference and the area of a circle with radius
4
y
d
4 \mathrm{yd}
4
yd
.
\newline
Use the value
3
3
3
.
14
14
14
for
π
\pi
π
, and do not round your answers. Be sure to include the correct units in your answers.
\newline
Circumference:
\newline
Area:
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What is the volume of a square-based pyramid with base side length of
8
8
8
inches and a height of
12
12
12
inches? Write your answer in the box provided.
\newline
_
_
_
_
_
in
3
.
\_\_\_\_\_ \text{in}^{3}.
_____
in
3
.
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For the following set of data, find the sample standard deviation, to the nearest hundredth.
\newline
146
,
147
,
144
,
117
,
105
,
105
,
89
146,147,144,117,105,105,89
146
,
147
,
144
,
117
,
105
,
105
,
89
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