Given a projectile's maximum horizontal range on level ground is r = vo^2sin 20/g, keeping
the initial velocity vo constant, at what launch angle or angles will the projectile land a
distance r/2 ? (2 points)

15°, 75°

Step-by-step explanation:

The range of a projectile on level ground is:

R = v₀² sin(2θ) / g

For a range of R/2 at the same initial velocity:

R/2 = v₀² sin(2A) / g

Dividing the second equation by the first:

(R/2) / R = sin(2A) / sin(2θ)

1/2 = sin(2A) / sin(2θ)

sin(2A) = 1/2 sin(2θ)

The maximum range is when θ = 45°.

sin(2A) = 1/2 sin(90°)

sin(2A) = 1/2

2A = 30°, 150°

A = 15°, 75°

tangent

step-by-step explanation:

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.