Answer:
Step-by-step explanation:
<h3>a)</h3>The function is continuous for x > 0 . The derivative is defined on that interval and is equal to ...
f'(x) = -2x . . . . . for x > 0
Then at x = 1, the derivative is ...
f'(1) = -2(1)
f'(1) = -2
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<h3>b)</h3>The function has a jump discontinuity at x=0, so the derivative does not exist at that point. A condition for the existence of the derivative is that the function is continuous at the point of interest.
Answer:
Step-by-step explanation:
Given that in 1987, the population of country A was estimated at 87 million people, with an annual growth rate of 3.5%
Thus the equation for population for country A would be
The 1987 population of country B was estimated at 243 million with an annual growth rate of 0.6%.
So equation for population for country B would be
where t = time in years and P in millions
a) P(A) = 2*87 when
Take log and solve
ln 2 = 0.005 t
t = 138.63
Thus after 138 years population will double for A
b) P(A) = P(B) when
Approximately after 35.5 years the populations of both countries would be equal.
Given: We have the given figure through which we can see
LK=16,
KJ=10,
LM=24,
MN=15
To Find: Whether KM || JN and the reasoning behind it.
Solution: Yes, KM || JN because
Explanation:
For this solution, we use the concept of Similar Triangles.
Now, KM || JN if ΔLKM ~ ΔLJN (i.e., if ΔLKM is similar to ΔLJN).
Now, ∠MLK=∠NLJ
To prove similarity of the two triangles, we have to show that the sides are proportional. In other words, LK:KJ = LM:LN
which is true as both sides simplify to
Thus, we see that ΔLKM ~ ΔLJN (i.e., if ΔLKM is similar to ΔLJN).
Therefore, KM || JN.
To come to the reasoning, notice that
In other words,
