Answer:
Step-by-step explanation:
Let 
denote the half life of our substance 
to be our time, 
is mass at time t and 
as initial mass. Our half life equation can be expressed as:
from which we can obtained mass at any given time.
b. From our equation above,
we can convert our t into mins as 
We then substitute value into the equation
Hence mass after 4hrs is 
c. We can set our final mass to 
then substitute in the equation
. Substitute 
Hence time until mass is 109.83 minutes
Compatible numbers are numbers that are close to the numbers they're replacing that divide evenly into each other
NOTES<span><span> Compatible numbers are numbers that are close to the numbers they're replacing that divide evenly into each other</span><span> <span>When we estimate we're trying to make the problem easier, so we can solve it without doing calculationsDividing is easier when we have numbers that divide evenly into each other, so that's how we'll estimate</span></span><span> <span>56,000 is like 560 times 100800 is like 8 times 100When we divide 56,000 by 800, we can cancel out the 100's, and we're left with 560 divided by 8In other words, since there are two zeroes in the divisor, we cancel out two zeros in the dividend</span></span><span> Since we rounded the dividend and divisor into such nice numbers, we can easily divide the front digits to get a round number!</span><span> Since we canceled a few zeroes, there's only one zero left</span><span> </span><span> <span>There are usually more than just one pair of compatible numbers to choose fromAs long as the numbers are easily divisible and close to the original numbers, they'll be good compatible numbers!<span>We'll get a slightly different answer, but it's still a good estimate of our quotient</span></span></span></span>
Answer:
Write a system of equations to represent the situation.
d: Number of dance songs
r: Number of rock songs
d + r = 1075
d = 4 * r
Answer:
h = 11/9 or 1 2/9
Step-by-step explanation:
(-5/11)h+(7/9)=(2/9)
(-5/11)h=(2/9)-(7/9)
(-5/11)h=(-5/9)
h = (-5/9)(-11/5)
h = 11/9
or
h = 1 2/9
Direction: Opens Down
Vertex:
(
0
,
81
)
(0,81)
Focus:
(
0
,
323
4
)
(0,3234)
Axis of Symmetry:
x
=
0
x=0
Directrix:
y
=
325
4
y=3254
Select a few
x
x
values, and plug them into the equation to find the corresponding
y
y
values. The
x
x
values should be selected around the vertex.
Tap for more steps...
x
y
−
2
77
−
1
80
0
81
1
80
2
77
xy-277-180081180277
Graph the parabola using its properties and the selected points.
Direction: Opens Down
Vertex:
(
0
,
81
)
(0,81)
Focus:
(
0
,
323
4
)
(0,3234)
Axis of Symmetry:
x
=
0
x=0
Directrix:
y
=
325
4
y=3254
x
y
−
2
77
−
1
80
0
81
1
80
2
77
xy-277-180081180277
f
(
x
)
=
8
1
−
x
2
?
?
f(x)=81-x2??
f
(
x
)
=
81
−
x
2
x
?
f(x)=81-x2x?
f
(
x
)
=
81
−
x
2
x
2
?
f(x)=81-x2x2?
f
(
x
)
=
81
−
x
2
x
3
?
f(x)=81-x2x3?
(
)
|
[
]
√
≥
π
7
8
9
Direction: Opens Down
Vertex:
(
0
,
81
)
(0,81)
Focus:
(
0
,
323
4
)
(0,3234)
Axis of Symmetry:
x
=
0
x=0
Directrix:
y
=
325
4
y=3254
Select a few
x
x
values, and plug them into the equation to find the corresponding
y
y
values. The
x
x
values should be selected around the vertex.
Tap for more steps...
x
y
−
2
77
−
1
80
0
81
1
80
2
77
xy-277-180081180277
Graph the parabola using its properties and the selected points.
Direction: Opens Down
Vertex:
(
0
,
81
)
(0,81)
Focus:
(
0
,
323
4
)
(0,3234)
Axis of Symmetry:
x
=
0
x=0
Directrix:
y
=
325
4
y=3254
x
y
−
2
77
−
1
80
0
81
1
80
2
77
xy-277-180081180277
f
(
x
)
=
8
1
−
x
2
?
?
f(x)=81-x2??
f
(
x
)
=
81
−
x
2
x
?
f(x)=81-x2x?
f
(
x
)
=
81
−
x
2
x
2
?
f(x)=81-x2x2?
f
(
x
)
=
81
−
x
2
x
3
?
f(x)=81-x2x3?
(
)
|
[
]
√
≥
π
7
8
9
Direction: Opens Down
Vertex:
(
0
,
81
)
(0,81)
Focus:
(
0
,
323
4
)
(0,3234)
Axis of Symmetry:
x
=
0
x=0
Directrix:
y
=
325
4
y=3254
Select a few
x
x
values, and plug them into the equation to find the corresponding
y
y
values. The
x
x
values should be selected around the vertex.
Tap for more steps...
x
y
−
2
77
−
1
80
0
81
1
80
2
77
xy-277-180081180277
Graph the parabola using its properties and the selected points.
Direction: Opens Down
Vertex:
(
0
,
81
)
(0,81)
Focus:
(
0
,
323
4
)
(0,3234)
Axis of Symmetry:
x
=
0
x=0
Directrix:
y
=
325
4
y=3254
x
y
−
2
77
−
1
80
0
81
1
80
2
77
xy-277-180081180277
f
(
x
)
=
8
1
−
x
2
?
?
f(x)=81-x2??
f
(
x
)
=
81
−
x
2
x
?
f(x)=81-x2x?
f
(
x
)
=
81
−
x
2
x
2
?
f(x)=81-x2x2?
f
(
x
)
=
81
−
x
2
x
3
?
f(x)=81-x2x3?
(
)
|
[
]
√
≥
π
7
8
9
Direction: Opens Down
Vertex:
(
0
,
81
)
(0,81)
Focus:
(
0
,
323
4
)
(0,3234)
Axis of Symmetry:
x
=
0
x=0
Directrix:
y
=
325
4
y=3254
Select a few
x
x
values, and plug them into the equation to find the corresponding
y
y
values. The
x
x
values should be selected around the vertex.
Tap for more steps...
x
y
−
2
77
−
1
80
0
81
1
80
2
77
xy-277-180081180277
Graph the parabola using its properties and the selected points.
Direction: Opens Down
Vertex:
(
0
,
81
)
(0,81)
Focus:
(
0
,
323
4
)
(0,3234)
Axis of Symmetry:
x
=
0
x=0
Directrix:
y
=
325
4
y=3254
x
y
−
2
77
−
1
80
0
81
1
80
2
77
xy-277-180081180277
f
(
x
)
=
8
1
−
x
2
?
?
f(x)=81-x2??
f
(
x
)
=
81
−
x
2
x
?
f(x)=81-x2x?
f
(
x
)
=
81
−
x
2
x
2
?
f(x)=81-x2x2?
f
(
x
)
=
81
−
x
2
x
3
?
f(x)=81-x2x3?
(
)
|
[
]
√
≥
π
7
8
9
vvvvv
