Question

1. in aerospace engineering, what is the primary reason honeycombs are used in honeycomb structures?

a. to maximize strength while minimizing weight
b. to increase weight
c. to reduce manufacturing time
d. aesthetic design

1. given a parallelogram with vertices a(2,1), b(5,1), c(8,4) and d(5,4), which evidence proves that the diagonals bisect each other?

a. diagonal lengths are equal
b. slopes of the diagonals are equal
c. slopes of opposite sides are equal
d. mid - points of diagonals are equal

1. are two lines perpendicular if their slopes are 1/6 and - 6?

a. yes
b. not enough information
c. it depends on the points
d. no

1. how do you prove that two lines are perpendicular using their slopes?

a. the product of their slopes is 1
b. the sum of their slopes is 0
c. the difference of their slopes is 1
d. the slopes are equal

Explanation:

1. In aerospace engineering, honeycomb structures are used mainly to maximize strength while minimizing weight. This provides a high - strength - to - weight ratio which is crucial for aerospace applications.
2. In a parallelogram, the diagonals bisect each other, which means the mid - points of the diagonals are equal.
3. Two lines are perpendicular if the product of their slopes is - 1. Given slopes $\frac{1}{4}$ and - 4, $\frac{1}{4}\times(-4)=-1$, so they are perpendicular.
4. Two lines are perpendicular if the product of their slopes is - 1.

Answer:

1. a. To maximize strength while minimizing weight
2. d. Mid - points of diagonals are equal
3. a. Yes
4. a. The product of their slopes is - 1