Semana 5 Univesp Geometria plana nota 10

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Semana 5 Geometria plana e desenho geométrico 
 
 
3/x = 5/11 5x = 33 x = 33/5 = 6,6 
 
tg (acb) = 1/3 
tg = L/(3 - L) 
1/3 = L/(3 - L) 
3 - L = 3L 
3L + L= 3 
4L = 3 
L = 3/4 = 0,75 
 
 
2/5 = 3/(3+x) 
2*(3+x) = 5* 3 
6 + 2x = 15 
2x = 15 - 6 
2x = 9 
x = 4,5 
 
(2+x)/1 = 1/x 
x*(2+x) = 1 
2x + x^2 = 1 
x^2 + 2x - 1 = 0 
 
delta = 4 - 4*1*-1 
delta = 8 
X2 = (-2-2sqrt2)/2 
X1 = (-2+2sqrt2)/2 
X1 = -2/2 + 2*sqrt2/2 
X1 = -1 + sqrt2 
X1 = sqrt2 - 1 
 
H ^2 = m*n H = sqrt(4*5) H = 2*sqrt(5) 
x = sqrt( (2*sqrt(5))^2 + 4^2 
x = sqrt( 4*5 + 16) 
x = sqrt(36) = 6 
 
 
AB/MB = BC/MC = AC/BC 
3/MB = 2/MC = 4/2 
 MC = 1 
 
 
 
10/160 = 3/x 
 10x = 480 
x = 48 
 
15/10 = (10+x)/x = (y+18)/18 
1,5 = (10+x)/x = (y+18)/18 
(10+x)/x = 1,5 
1,5x = 10 + x 
1,5x - x = 10 
0,5x = 10 
 x = 10/0,5 
 x = 20 
(y+18)/18 = 1,5 
 y + 18 = 27 
y = 27 - 18 
y = 9 
x + y = 20 + 9 = 29 
 
 
6/2 = X/3 
2X = 18 
X = 9