When graphing a polynomial function, what determines what the graph will look like at the far left side? Explain your answer.
1 answer:
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Answer:
(a)
(b) 10
(c)
(d) 0
(e) 1024
Step-by-step explanation:
(a)
A = {x ∈ Z | 0 < x, x² ≤ 100}
We need to find all the elements of given set.
The given conditions are
... (1)
Taking square root on both sides.
.... (2)
Using (1) and (2) we get
Since x ∈ Z,
(b)
We need to find the value of | {x ∈ Z | 0 < x, x² ≤ 100}| or |A|. It means have to find the number of elements in set A.
| {x ∈ Z | 0 < x, x² ≤ 100}| = 10
(c)
B = {x ∈ Z | x > 10, x² ≤ 100}
We need to find all the elements of given set.
The given conditions are
... (3)
It means
.... (4)
Inequality (3) and (4) have no common solution, so B is null set or empty set.
(d)
We need to find the value of |{x ∈ Z | x > 10, x² ≤ 100}| or |B|. It means have to find the number of elements in set B.
|{x ∈ Z | x > 10, x² ≤ 100}| = 0
(e)
We need to find the value of | P(A) |. P(A) is the power set of set A.
Number of elements of a power set is
where, n is the number of elements of set A.
We know that the number of elements of set is 10. So the value of |P(A)| is
Therefore |P(A)|=1024.
Answer:
a) It takes 0.0017s for the light to reach San Francisco.
b) It takes 0.033s for the light to reach London.
c) It takes 1.334s for the light to reach Mars.
d) It takes 149.7s for the light to reach Venus.
Step-by-step explanation:
Here we can solve this problem by using this following formula:
In which s is the speed(in km/s), d is the distance(in km) and t is the time(in s).
The light speed is 299 792 458 m / s = 299,792.458 km/s, so
(a) San Francisco (about 500km)
Find t when . So
It takes 0.0017s for the light to reach San Francisco.
b) London(about 10,000km)
Find t when . So
It takes 0.033s for the light to reach London.
(c) the Moon (400,000km)
Find t when . So
It takes 1.334s for the light to reach Mars.
(d) Venus (0.3 A.U. from Earth at its closest approach).
Each A.U. has 149,59,7871 km.
So 0.3 A.U. = 0.3*(149,597,871) = 44,879,361.3. This means that . So:
It takes 149.7s for the light to reach Venus.