Answer:
Step-by-step explanation:
We have the two functions:
And we wish to find:
First, let’s find f(2) first. So, we will substitute 2 for x for f(x):
Hence, we can now substitute 3 for f(2):
Now, we can find g(6). Substitute 6 for t for g(t):
Therefore:
Answer:
The equation of the quadratic graph is f(x)= - (1/8) (x-3)^2 + 3 (second option)
Step-by-step explanation:
Focus: F=(3,1)=(xf, yf)→xf=3, yf=1
Directrix: y=5 (horizontal line), then the axis of the parabola is vertical, and the equation has the form:
f(x)=[1 / (4p)] (x-h)^2+k
where Vertex: V=(h,k)
The directix y=5 must intercept the axis of the parabola at the point (3,5), and the vertex is the midpoint between this point and the focus:
Vertex is the midpoint between (3,5) and (3,1):
h=(3+3)/2→h=6/2→h=3
k=(5+1)/2→k=6/2→k=3
Vertex: V=(h,k)→V=(3,3)
p=yf-k→p=1-3→p=-2
Replacing the values in the equation:
f(x)= [ 1 / (4(-2)) ] (x-3)^2 + 3
f(x)=[ 1 / (-8) ] (x-3)^2 + 3
f(x)= - (1/8) (x-3)^2 + 3
1) 4
2) 16
3) 16
4) 6
5)12
6) 4
As you can see in the given figure, there are two intersecting chords inside the circle.
Recall that the "Intersecting Chords Theorem" is given by
For the given case, we have
AE = 7
BE = 6
EC = 9
Let us substitute these values into the above equation and solve for DE
Therefore, the length of DE is 10.5 units.
