A:93
B: slope
the slope is the rate of change of the line.
this line models the distance between cop and the driver. note that the
cop is standing still while the sports car is moving away at 93 mph
if
the x-axis is in hours and the y-axis is in miles, then slope =
rise/run = km/h, which is kilometers per hour. the slope is the rate of
change of distance for the distance vs time graph
therefore the slope is 93 mph
I'll give you an example from topology that might help - even if you don't know topology, the distinction between the proof styles should be clear.
Proposition: Let
S
be a closed subset of a complete metric space (,)
(
E
,
d
)
. Then the metric space (,)
(
S
,
d
)
is complete.
Proof Outline: Cauchy sequences in (,)
(
S
,
d
)
converge in (,)
(
E
,
d
)
by completeness, and since (,)
(
S
,
d
)
is closed, convergent sequences of points in (,)
(
S
,
d
)
converge in (,)
(
S
,
d
)
, so any Cauchy sequence of points in (,)
(
S
,
d
)
must converge in (,)
(
S
,
d
)
.
Proof: Let ()
(
a
n
)
be a Cauchy sequence in (,)
(
S
,
d
)
. Then each ∈
a
n
∈
E
since ⊆
S
⊆
E
, so we may treat ()
(
a
n
)
as a sequence in (,)
(
E
,
d
)
. By completeness of (,)
(
E
,
d
)
, →
a
n
→
a
for some point ∈
a
∈
E
. Since
S
is closed,
S
contains all of its limit points, implying that any convergent sequence of points of
S
must converge to a point of
S
. This shows that ∈
a
∈
S
, and so we see that →∈
a
n
→
a
∈
S
. As ()
(
a
n
)
was arbitrary, we see that Cauchy sequences in (,)
(
S
,
d
)
converge in (,)
(
S
,
d
)
, which is what we wanted to show.
The main difference here is the level of detail in the proofs. In the outline, we left out most of the details that are intuitively clear, providing the main idea so that a reader could fill in the details for themselves. In the actual proof, we go through the trouble of providing the more subtle details to make the argument more rigorous - ideally, a reader of a more complete proof should not be left wondering about any gaps in logic.
(There is another type of proof called a formal proof, in which everything is derived from first principles using mathematical logic. This type of proof is entirely rigorous but almost always very lengthy, so we typically sacrifice some rigor in favor of clarity.)
As you learn more about a topic, your proofs typically begin to approach proof outlines, since things that may not have seemed obvious before become intuitive and clear. When you are first learning it is best to go through the detailed proof to make sure that you understand everything as well as you think you do, and only once you have mastered a subject do you allow yourself to omit obvious details that should be clear to someone who understands the subject on the same level as you.
Answer:
1962.5 m^2
Step-by-step explanation:
area of the entire circle = pi (50^2)
subtract the large area
pi 50^2 - 4.71 /2pi pi 50^2 =
Like terms are when you have 2 of the same coefficent disregarding the amount of numbers. you can add or subtract them to simplify in other words.
Answer: units = 6198
Step-by-step explanation:
expected consumer demand is 5000, the units that must be planned given shrinkage percentage levels in different stages of the supply chain we have to use the trial and error method.
lets try 6200 units
6200 x 95% = 5890, 5890 x 96% = 5654.4, 5654.40 x 97% = 5484.768, 5484.768 x 96% = 5265.37728, 56265 x 95% = 5002.108416 ≈ 5002
6198 units
(6198 x 95% = 5888.10) (5888.10 x 96% = 5652.576) (5652.576 x 97% = 5482.99872) (5482.99872 x 96% = 5263.6787712) (5263.6787712 x 95% = 5000.4948326) ≈ 5000
using the same procedure for 6197 units the answer will be 4999.688041
units that should be produced to cover the demand of 5000 = 6198
