Assume that securitization combined with borrowing and irrational exuberance in Hyperville have driven up the value of existing financial securities at a geometric rate, specifically from $4 to $8 to $16 to $32 to $64 to $128 over a six-year time period. Over the same period, the value of the assets underlying the securities rose at an arithmetic rate from $4 to $6 to $8 to $10 to $12 to $14. Instructions: Enter your answer as a whole number. If these patterns hold for decreases as well as for increases, by how much would the value of the financial securities decline if the value of the underlying asset suddenly and unexpectedly fell by $6

$120

Explanation:

Given:

• Geometric growth rate of existing financial security:

$4 to $8 to $16 to $32 to $64 to $128

• Arithmetic growth rate of underlying assests:

$4 to $6 to $8 to $10 to $12 to $14

From the values, when the price of the underlying assests is $14, the price of the existing financial security is $128.

We are told to that when values of financial secrities increased from $4 to $128, that of underlying assests also increased from $4 to $14. If patterns hold for decreases as well as for increases. Therefore to get the value of financial securities decline if the value of underlying assests suddenly and unexpectedly fell by $6, we have:

Price of underlying assests when decreased by $6 =

$14-$6 = $8.

Therefore, price of existing financial security decline wil be:

$128-$8 = $120

bd = 9 cm

step-by-step explanation:

in a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. that is, the longest side (hypotenuse) is twice the length of the shortest side.

all of the triangles in your geometry are 30°-60°-90° triangles. ac is the hypotenuse of δacd, and the short side of δabc.

the short side ad of δacd will be half the length of ac, so 3 cm. the hypotenuse ab of δabc will be twice the length of ac, so 12 cm. segment bd is the difference of the lengths ab and ad, so is

bd = ab -ad

bd = 12 cm - 3 cm = 9 cm

comment on side length ratios

you can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. or you can figure the length of the altitude of an equilateral triangle of side length 2 using the pythagorean theorem.