<h3>
Answer: B. 4 units to the right, 5 units down</h3>
The vector notation <4, -5> is the same as writing 
which in my opinion is more descriptive in saying "4 units to the right, 5 units down"
We shift 4 units to the right because of the x+4. Whatever x is, add 4 to it getting x+4. So for instance x = 10 leads to x+4 = 10+4 = 14.
The y-5 is why we shift 5 units down. Eg: y = 37 leads to y-5 = 37-5 = 32.
Anything to the power of 0 equals 1
he volume of the solid under a surface
z
=
f
(
x
,
y
)
and above a region D is given by the formula
∫
∫
D
f
(
x
,
y
)
d
A
.
Here
f
(
x
,
y
)
=
6
x
y
. The inequalities that define the region D can be found by making a sketch of the triangle that lies in the
x
y
−
plane. The bounding equations of the triangle are found using the point-slope formula as
x
=
1
,
y
=
1
and
y
=
−
x
3
+
7
3
.
Here is a sketch of the triangle:
Intersecting Region
The inequalities that describe D are given by the sketch as:
1
≤
x
≤
4
and
1
≤
y
≤
−
x
3
+
7
3
.
Therefore, volume is
V
=
∫
4
1
∫
−
x
3
+
7
3
1
6
x
y
d
y
d
x
=
∫
4
1
6
x
[
y
2
2
]
−
x
3
+
7
3
1
d
x
=
3
∫
4
1
x
[
y
2
]
−
x
3
+
7
3
1
d
x
=
3
∫
4
1
x
[
49
9
−
14
x
9
+
x
2
9
−
1
]
d
x
=
3
∫
4
1
40
x
9
−
14
x
2
9
+
x
3
9
d
x
=
3
[
40
x
2
18
−
14
x
3
27
+
x
4
36
]
4
1
=
3
[
(
640
18
−
896
27
+
256
36
)
−
(
40
18
−
14
27
+
1
36
)
]
=
23.25
.
Volume is
23.25
.
This is closest to your problem
Area of a triangle : 1/2 (length x breadth)
: 1/2 (3 x 4)
: 1/2 of 12
: 6. including units it would be 6m^2 (6 metres squared)
hope I helped
