Let d represent the distance of the destination from the starting point.
After 45 min, Henry has already driven d-68 miles. After 71 min., he has already driven d-51.5 miles.
So we have 2 points on a straight line:
(45,d-68) and (71,d-51.5). Let's find the slope of the line thru these 2 points:
d-51.5 - (d-68) 16.5 miles
slope of line = m = ----------------------- = ------------------
71 - 45 26 min
Thus, the slope, m, is m = 0.635 miles/min
The distance to his destination would be d - (0.635 miles/min)(79 min), or
d - 50.135 miles. We don't know how far his destination is from his starting point, so represent that by "d."
After 45 minutes: Henry has d - 68 miles to go;
After 71 minutes, he has d - 51.5 miles to go; and
After 79 minutes, he has d - x miles to go. We need to find x.
Actually, much of this is unnecessary. Assuming that Henry's speed is 0.635 miles/ min, and knowing that there are 8 minutes between 71 and 79 minutes, we can figure that the distance traveled during those 8 minutes is
(0.635 miles/min)(8 min) = 5.08 miles. Subtracting thix from 51.5 miles, we conclude that after 79 minutes, Henry has (51.5-5.08), or 46.42, miles left before he reaches his destination.
What is the question is the o
Answer:
300 percent change
Step-by-step explanation:
300 is 400 percent of 75.(75x4 is 300.) Therefore, the percent change is
400 - 100 = 300.
Step-by-step explanation:
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
.
