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
.
Answer:
B
Step-by-step explanation:
Please mark Brainliest when you’re able.
$270 equals 135% of the original price
270/x=135/100
135*2=270
100*2=200
Final answer: $200
Answer:
![ln \frac{(x^3y^2)}{z^4}](https://tex.z-dn.net/?f=ln%20%5Cfrac%7B%28x%5E3y%5E2%29%7D%7Bz%5E4%7D)
Step-by-step explanation:
![3 ln x + 2 ln y - 4 ln z](https://tex.z-dn.net/?f=3%20ln%20x%20%2B%202%20ln%20y%20-%204%20ln%20z)
m ln(x)= ln x^m
![3 ln x + 2 ln y - 4 ln z](https://tex.z-dn.net/?f=3%20ln%20x%20%2B%202%20ln%20y%20-%204%20ln%20z)
![ln x^3 +ln y^2 - ln z^4](https://tex.z-dn.net/?f=ln%20x%5E3%20%2Bln%20y%5E2%20-%20ln%20z%5E4)
ln(mn)= ln m +ln n
![(ln x^3 +ln y^2)- ln z^4](https://tex.z-dn.net/?f=%28ln%20x%5E3%20%2Bln%20y%5E2%29-%20ln%20z%5E4)
![(ln(x^3y^2)-ln z^4](https://tex.z-dn.net/?f=%28ln%28x%5E3y%5E2%29-ln%20z%5E4)
ln (m)-ln(n)= ln(m/n)
![ln \frac{(x^3y^2)}{z^4}](https://tex.z-dn.net/?f=ln%20%5Cfrac%7B%28x%5E3y%5E2%29%7D%7Bz%5E4%7D)
Answer:
| 1/3 -( -4/3)|
Step-by-step explanation:
Take the absolute value of the second point and subtract the first point
| 1/3 -( -4/3)|