The function E(d)=0.25d√ approximates the number of seconds it takes a dropped object to fall d feet on Earth. The function S(d)=0.2⋅E(d) approximates the number of seconds it takes a dropped object to fall d feet on the sun. How long (in seconds) does it take a dropped object to fall 80 feet on the sun? Round your answer to the nearest hundredth.

0.45 second

Step-by-step explanation:

The number of seconds it takes a dropped object to fall d feet on Earth is given as:

E(d)=0.25√d

the number of seconds it takes a dropped object to fall d feet on the sun is given as:

S(d)=0.2⋅E(d)

Therefore

S(d)=0.2 × 0.25√d = 0.05√d

Given that it take a dropped object to fall 80 feet on the sun (i.e d = 80 feet), to calculate the time in seconds we use:

S(d) = 0.05√d

S(d) = 0.05 × √80 = 0.05 × 8.944 ≈ 0.45 s

It takes 0.45 second for a dropped object to fall 80 feet on the sun

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .