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:
A
Step-by-step explanation:
pythagorean theorem
A^2+B^2=C^2 do that for all sides then add
The nickels in the envelope is $0. 12
<h3>How to determine the number</h3>
From the information given, we have that;
Dimes + nickels = $1. 20
1/4 dimes + dimes = $ 1. 35
Let dimes = d
Nickels = n
d + n = 1. 20 equation a
d/4 + d = 1. 35 equation b
Make 'd' subject from equation a
d = 1. 20 - n
Substitute into equation b
1. 20 - n/ 4 + 1. 20 - n = 1. 35
0. 3 - 0. 25n + 1. 20 - n = 1. 35
collect like terms
- 1. 25n = 1. 35 - 1. 5
- 1. 25 = - 0. 15
n = -0. 15/ -1. 25
n = 0. 12
Thus, the number of nickels in the envelope is $0. 12
Learn more about algebraic expressions here:
brainly.com/question/4344214
#SPJ1
Answer:
The answer is 30
Step-by-step explanation:
BC the inside of a triangle equals 180
