Answer:
No, -6/3 is not an integer if that's what you're asking me.
Step-by-step explanation:
Fractions are not integers.
ok I will help u tomorrow I am busy today
Answer:
-17 ft/s
Step-by-step explanation:
The average rate of change is the difference in height on the interval, divided by the difference in time.
m = (h(4.5) -h(2))/(4.5 -2) . . . . . . . . definition of rate of change on [2, 4.5]
h(4.5) = (-16·4.5 +87)(4.5) = 67.5
h(2) = (-16·2 +87)(2) = 110
Then ...
m = (67.5 -110)/(2.5) = -17
The average rate of change on the interval from 2 to 4.5 seconds is -17 ft/s.
_____
<em>Check</em>
The slope of the curve is given by its derivative:
h'(t) = -32t +87
The midpoint of the interval is (2+4.5)/2 = 3.25.
The slope at the midpoint is ...
h'(3.25) = -32(3.25) +87 = -17 . . . . average rate of change on [2, 4.5]
For a quadratic function. the average rate of change on an interval is the slope of the function at the midpoint of the interval. This calculation confirms that.
Answer:
$24.50
Step-by-step explanation:
Money saved for each shirt:
=$9. 10/2
=$4.55
Original price of the shirt:
=$19. 95 + $4.55
=$24.50
x
4
−
12
x
2
=
64
x
4
-
12
x
2
=
64
Move
64
64
to the left side of the equation by subtracting it from both sides.
x
4
−
12
x
2
−
64
=
0
x
4
-
12
x
2
-
64
=
0
Rewrite
x
4
x
4
as
(
x
2
)
2
(
x
2
)
2
.
(
x
2
)
2
−
12
x
2
−
64
=
0
(
x
2
)
2
-
12
x
2
-
64
=
0
Let
u
=
x
2
u
=
x
2
. Substitute
u
u
for all occurrences of
x
2
x
2
.
u
2
−
12
u
−
64
=
0
u
2
-
12
u
-
64
=
0
Factor
u
2
−
12
u
−
64
u
2
-
12
u
-
64
using the AC method.
Tap for fewer steps...
Consider the form
x
2
+
b
x
+
c
x
2
+
b
x
+
c
. Find a pair of integers whose product is
c
c
and whose sum is
b
b
. In this case, whose product is
−
64
-
64
and whose sum is
−
12
-
12
.
−
16
,
4
-
16
,
4
Write the factored form using these integers.
(
u
−
16
)
(
u
+
4
)
=
0
(
u
-
16
)
(
u
+
4
)
=
0
Replace all occurrences of
u
u
with
x
2
x
2
.
(
x
2
−
16
)
(
x
2
+
4
)
=
0
(
x
2
-
16
)
(
x
2
+
4
)
=
0
Rewrite
16
16
as
4
2
4
2
.
(
x
2
−
4
2
)
(
x
2
+
4
)
=
0
(
x
2
-
4
2
)
(
x
2
+
4
)
=
0
Since both terms are perfect squares, factor using the difference of squares formula,
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
a
2
-
b
2
=
(
a
+
b
)
(
a
-
b
)
where
a
=
x
a
=
x
and
b
=
4
b
=
4
.
(
x
+
4
)
(
x
−
4
)
(
x
2
+
4
)
=
0
(
x
+
4
)
(
x
-
4
)
(
x
2
+
4
)
=
0
If any individual factor on the left side of the equation is equal to
0
0
, the entire expression will be equal to
0
0
.
x
+
4
=
0
x
+
4
=
0
x
−
4
=
0
x
-
4
=
0
x
2
+
4
=
0
x
2
+
4
=
0
Set the first factor equal to
0
0
and solve.
Tap for fewer steps...
Set the first factor equal to
0
0
.
x
+
4
=
0
x
+
4
=
0
Subtract
4
4
from both sides of the equation.
x
=
−
4
x
=
-
4
Set the next factor equal to
0
0
and solve.
Tap for more steps...
x
=
4
x
=
4
Set the next factor equal to
0
0
and solve.
Tap for more steps...
x
=
2
i
,
−
2
i
x
=
2
i
,
-
2
i
The final solution is all the values that make
(
x
+
4
)
(
x
−
4
)
(
x
2
+
4
)
=
0
(
x
+
4
)
(
x
-
4
)
(
x
2
+
4
)
=
0
true.
x
=
−
4
,
4
,
2
i
,
−
2
i
x
=
-
4
,
4
,
2
i
,
-
2
i
x
4
−
1
2
x
2
=
6
4
x
4
-
1
2
x
2
=
6
4