Answer:
An explicit representation for the nth term of the sequence:
It means, option (B) should be true.
Step-by-step explanation:
Given the geometric sequence
A geometric sequence has a constant ratio, denoted by 'r', and is defined by
Determining the common ratios of all the adjacent terms
As the ratio is the same, so
r = 4
Given that f₁ = -1/2
substituting r = 4, and f₁ = -1/2 in the nth term
Thus, an explicit representation for the nth term of the sequence:
It means, option (B) should be true.
Answer:
4 m
Step-by-step explanation:
The equation can be written ...
y = (x/4)² = (1/16)x²
where the divisor 4 is the horizontal scale factor that makes the parabola 8 m wide at y = 1 m.
This can also be written as ...
y = 1/(4p)x² = (1/16)x²
from which we can see ...
4p = 16
p = 4
In this form, p is the distance from the vertex to the focus, 4 meters.
_____
Another way to find the y-coordinate of the focus is to draw a line with slope 1/2 through the vertex. It will intersect the parabola at the point where the vertical distance to the directrix is the same as the horizontal distance to the focus. The y-coordinate of that point is the y-coordinate of the focus.
The answer in standard form is 86,400
Volume of pyramid = 1/3*AH, where A is the area of the base and H is the height
Since we are given three sides of the triangle (the base of the pyramid), we should use Heron formula: Area of a triangle = sq.root of(s(s - a)(s - b)(s - c)), where s is the semi-perimeter (ie. the perimeter divided by 2) and a, b and c are side lengths.
s = (5 + 12 + 13)/2
= 30/2 = 15
A = sq,root of(15(15 - 5)(15 - 12)(15 - 13))
= sq.root of (15*10*3*2)
= sq.root of 900
= 30 m^2
Volume = 1/3*AH
= 1/3*30*9
= 90 m^3
Answer:
Yes.
The relation is a function because every element in the domain (the x's) is mapped to one element in the range (the y's).
Step-by-step explanation:
For a relation that is a set of points all you have to look for while igorning any duplicate points is that all of the x's are different. If there are any 2 (or more) x's that are the same, then it is not a function.
So there are no duplicate points.
For example the set {(1,5),(2,5)(1,5)} is really just {(1,5),(2,5)}.
Anyways the x's in the points are (in order from left to right):
1
-4
3
0
2
All of these are different, I did not list a value for x that was same anywhere in that list. So it is a function.
The relation is a function because there is no x that gets mapped to more than one y.