Answer:9/16
Step-by-step explanation:
Since we know it's 3/4 use
r=(3/4)² .... 
=
Answer:
First Number: 2
Step-by-step explanation:
You need to work backwards, as an algebraic equation.
24 ÷ 3 = 8
8 ÷ 2 = 4
4 × 2 = 8
8 - 6 = 2
The first number is 2.
- Educationist
First, let's add 30 to both sides:
4x - 30 +30 ≥ -3x + 12+30
4x ≥ -3x + 42
Now, let's add 3x to both sides
4x +3x ≥ -3x+3x + 42
7x ≥ 42
Let's divide both by 7:
x ≥ 6
This is a linear relationship. The slope-intercept form of the linear equation is:
Where,
- m is the rate of change (positive if increasing rate and negative if decreasing rate)
- c is the y intercept, or the initial value
<u><em>Rate of change is 2.5 quarts per minute (it is decreasing so m is -2.5)</em></u>
<u><em>Initial value is 50 quarts, so c is 50.</em></u>
Plugging in the values we get 
.
Changing variables to w instead of y and t instead of x, gives us,
. Where w is warts of water left in the tub and t is the time in minutes.
There is no viable solution when t=30 because at t=20, w=0 (
). It means after 20 minutes, there is no water left. So t=30 minutes doesn't make sense.
ANSWER:
Modelling equation:
When 
, there is no VIABLE solution
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
.
