Answer:
least common denominator=6
Step-by-step explanation:
For the fractions, 1/3 and 1/6th, 3*2=6. making the fraction 2/6 and leaving the other the same 1/6th.
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:
Step-by-step explanation:
Evan spent 20 hours doing homework last week
25 hours were spent this week.
<u>Let's see what 125% of 20 equals:</u>
= (125 / 100) * 20
= (125 / 10) * 2
= 125 / 5
= 25 hours
But,
<u>It is written that Evan thought he spent 125 % more than the last week which means:</u>
= (125% of 20) + 20
= 25 + 20
= 45 hours
He should've said that he has given 25% more time than the last week.
(<u>Note that:</u> 25 % of 20 equals 5 so 25 % more than last week will be equal to (25 % + 20) = (5+20) = 25)
![\rule[225]{225}{2}](https://tex.z-dn.net/?f=%5Crule%5B225%5D%7B225%7D%7B2%7D)
Hope this helped!
<h3>~AH1807</h3>
Answer: £90
Step-by-step explanation:
Pip and Sara get some money. They share it in the ratio 5 : 4.
Pip gets £50 so what did Sara get:
Use direct proportion:
5 : 4
50 : x
5x = 200
x = 200/5
x = £40
Pip got £50 and Sara got £40.
Together they got:
= 50 + 40
= £90
Answer:
<C=48 because 90-42=42 as in the other side of the triangle.
<B=42 because vertical angles are always congruent.
<B+<D=90 because <D is 48 because it is vertical to <C
