$\dfrac{1-\sqrt 5}{1+\sqrt 5}\\\\\\=\dfrac{\left( 1- \sqrt 5\right)\left( 1- \sqrt 5\right)}{\left( 1+ \sqrt 5\right)\left( 1- \sqrt 5\right)}\\\\\\=\dfrac{\left( 1-\sqrt 5)^2}{1^2 - \left(\sqrt 5 \right)^2}\\\\\\=\dfrac{1+\left(\sqrt 5 \right)^2 -2 \sqrt 5\cdot 1}{1-5}\\\\\\=\dfrac{1+5-2\sqrt 5}{-4}\\\\\\=-\dfrac{6-2\sqrt 5}{4}\\\\\\=-\dfrac{2\left(3-\sqrt 5 \right)}{4}\\\\\\=-\dfrac{3-\sqrt 5}{ 2}\\\\\\=\dfrac{\sqrt 5 -3}{2}$

4 0

3 years ago

In how many ways can seven runners win first,second,and third places?

kap26 [50]

210 ways. This is a permutation question. Thus, insert 7P3 means 7 runners there is 3 places to be occupied. (7P3=210ways)

4 0

3 years ago

Find a2 and a3 for the geometric sequence 4, a2, a3, 108.

LekaFEV [45]

9514 1404 393

Answer:

a2 = 12

a3 = 36

Step-by-step explanation:

Terms of a geometric sequence have a common ratio. If we call that ratio r, then we have ...

a2 = 4r

a3 = (a2)r = 4r^2

108 = (a3)r = 4r^3

27 = r^3 . . . . . . . . . . . divide by 4

3 = r . . . . . . . . . . cube root

a2 = 4(3) = 12

a3 = 12(3) = 36

3 0

3 years ago

Hola pueden ayudar a=6cm b=8cm c?

Alexxandr [17]

Answer:

c=10cm

Step-by-step explanation:

a²+b²=c²

6²+8²=c²

36+64=c²

100=c²

10=c

6 0

2 years ago