Differentiating each function, we have for all x, unless otherwise indicated,
and only h(x) has a strictly positive derivative. (A)
It's a hexagon.
The formula of the sum of internal angles in the polygon:
Therefore
A)
To be similar triangles have to have equal angles
triangle ZDB'
1)angle Z=90 degrees
triangle B'CQ
1) angle C 90 degrees
angle A'B'Q=90
DB'Z+A'B'Q+CB'Q=180, straight angle
DB'Z+90+CB'Q=180
DB'Z+CB'Q=90
triangle ZDB'
DZB'+DB'Z=180-90=90
DB'Z+CB'Q=90
DZB'+DB'Z=90
DB'Z+CB'Q=DZB'+DB'Z
2)CB'Q=DZB' (these angles from two triangles ZDB' and B'CQ )
3)so,angles DB'Z and B'QC are going to be equal because of sum of three angles in triangles =180 degrees and 2 angles already equal.
so this triangles are similar by tree angles
b)
B'C:B'D=3:4
B'D:DZ=3:2
CQ-?
DC=AB=21
DC=B'C+B'D (3+4= 7 parts)
21/7=3
B'C=3*3=9
B'D=3*4=12
B'D:DZ=3:2
12:DZ=3:2
DZ=12*2/3=8
B'D:DZ=CQ:B'C
3:2=CQ:9
CQ=3*9/2=27/2
c)
BC=BQ+QC=B'Q+QC
BQ' can be found by pythagorean theorem
Y=5. Just substitute 1 in for x because a coordinate in (x,y) and then when you do that you get ...
y=3(1) +2
y=3+2
y=5
(1,5)
Now, she writes 4 notes every 1 hour.
so in 2 hours she has written 8 notes, and the remaining is 50 - 8 or 42.
in 3 hours has written 12 notes, and remaining are 50 - 12, or 38, and so on.
now, how many hours will it take her to them all? or, how many times does 4 go into 50? 50 /4 or 12.5.
so it will take her 12 hours and a half to do them all, at that time, the remaining notes are 0, because she's done, and the hours are 12 and a half.