Answer:
41.5 ft
Step-by-step explanation:
From the information given, and definition of midpoint, we know that:
AB = BC = ½ AC
AC = CE = ½ AE
CD = DE = ½ CE
GF = FE = ½ GE
HG = GE = ½ HE
AI = IH = ½ AH
AJ = JI = ½ AI
We also know:
AH = 20
HE = 14
GD = 4
Therefore:
AI = IH = 10
HG = GE = 7
AJ = JI = 5
GF = FE = 7/2
Next, since JB and IC are parallel with HE, we know that AJB and AIC are similar to AEH. So:
JB / 5 = 14 / 20
JB = 7/2
IC / 10 = 14 / 20
IC = 7
And since DF and CG are parallel to AH, then DFE and DGE are similar to AHE. So:
DF / (7/2) = 20 / 14
DF = 5
CG / 7 = 20 / 14
CG = 10
Next we know that AIB and AHC are similar, and DEG and CEH are similar.
IB / 10 = CH / 20
CH / 14 = 4 / 7
CH = 8, IB = 4.
We've found all the lengths inside triangle AEH. Adding them up:
JB + IB + IC + CH + CG + DG + DF
7/2 + 4 + 7 + 8 + 10 + 4 + 5
41.5
The total length of the inside bars is 41.5 ft.
Answer:
88kg
Step-by-step explanation:
Mean= sum of weights/ Number of people
or, 68= 58+58+x/3
or, 68 * 3= 58+58+x
or, 204=116+x
or, x= 204-116
or,x= 88
Therefore, the weight of third person was 88 kg
10x^5 + 5x^3 - 14x^2 - 7
= 5x^3(2x^2 + 1) - 7(2x^2 + 1)
= (5x^3 - 7)(2x^2 + 1)
Answer is D
(5x^3 - 7)(2x^2 + 1)
I will use the letter x instead of theta.
Then the problem is, given sec(x) + tan(x) = P, show that
sin(x) = [P^2 - 1] / [P^2 + 1]
I am going to take a non regular path.
First, develop a little the left side of the first equation:
sec(x) + tan(x) = 1 / cos(x) + sin(x) / cos(x) = [1 + sin(x)] / cos(x)
and that is equal to P.
Second, develop the rigth side of the second equation:
[p^2 - 1] / [p^2 + 1] =
= [ { [1 + sin(x)] / cos(x) }^2 - 1] / [ { [1 + sin(x)] / cos(x)}^2 +1 ] =
= { [1 + sin(x)]^2 - [cos(x)]^2 } / { [1 + sin(x)]^2 + [cos(x)]^2 } =
= {1 + 2sin(x) + [sin(x)^2] - [cos(x)^2] } / {1 + 2sin(x) + [sin(x)^2] + [cos(x)^2] }
= {2sin(x) + [sin(x)]^2 + [sin(x)]^2 } / { 1 + 2 sin(x) + 1} =
= {2sin(x) + 2 [sin(x)]^2 } / {2 + 2sin(x)} = {2sin(x) ( 1 + sin(x)} / {2(1+sin(x)} =
= sin(x)
Then, working with the first equation, we have proved that [p^2 - 1] / [p^2 + 1] = sin(x), the second equation.
