Answer:
h'(x) = 0.6 and Δx = 1 and 2
h(6001) = h(6000) + h'(6000)(1) = 8000 +0.6 = 8,000.6
h(6002) = h(6000) + h'(6000)(2) = 8000 + 0.6 (2) =8000 +1.2 = 8001.2
Explanation below:
Step-by-step explanation:
Based on the information given we have that when the climber is 6000 meters from the start, his elevation is 8000 meters above sea level.
We know that the function for elevation is given by h(x) where x is the number of meters from the start.
Therefore, h(6000) = 8000.
We also know that the derivative of a function tells us the reason of change at some point (or how fast a function is changing near that point). For this problem we have that h'(x) = 0.6. (<u>meaning that the elevation increases in 0.6 meters for every meter they hike further nearby the 6000 meters</u>)
We need to use the derivative at a point to estimate values of the function at nearby points
We're going to use h'(x)= 0.6. Δx= 1
h(6001) = h(6000) + h'(6000)(1) = 8000 +0.6 = 8,000.6
Therefore h (6001) = 8,000.6
Now for h'(x)= 0.6. Δx= 1
h(6002) = h(6000) + h'(6000)(2) = 8000 + 0.6 (2) =8000 +1.2 = 8001.2
Therefore h(6002) = 8001.2
Answer:
should i add 150 + 4x-5
Step-by-step explanation:
During a research experiment, it was found that the number of bacteria in a culture grew at a rate proportional to its size. At 8:00 AM there were 6,000
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:
To solve inequalities balance both sides of any equation, and if there is a negative coefficient, switch the symbol
