A park ranger uses two drones to observe wildlife. After letting the drones hover at the same height for a while, she decreases the height of the first drone by

Question

feet in order to take pictures. She also decreases the height of the second drone, but only by
of the decrease in height of the first drone.

Which THREE methods could be used to find the change in height, in feet, of the second drone?

A.
Multiply
by
.

B.
Multiply

by

. Then multiply by

.

C.
Multiply

by

.

D.
Multiply
by
. Then add
.

E.
Multiply
by

. Then multiply

by

. Add the products.

Answer 1

To determine how to find the change in height of the second drone, we need to understand what the problem is saying.

1. Let \( x \) be the decrease in height of the first drone in feet.
2. The second drone’s decrease in height is a fraction of the height decrease of the first drone. Let’s denote this fraction as \( r \). Therefore, the decrease in height of the second drone will be \( r \cdot x \).

Now let's analyze the answer options based on this understanding:

• Option A: Multiply \( x \) by \( r \). This is correct because it directly computes the change in height for the second drone as \( r \cdot x \).

• Option B: Multiply \( x \) by \( r \). Then multiply by \( p \). This option sounds incorrect unless there is another context for \( p \). Normally, we just need \( r \cdot x \).

• Option C: Multiply \( x \) by \( r \). This is the same as option A and is correct since it directly computes the decrease for the second drone.

• Option D: Multiply \( x \) by \( r \). Then add \( k \). The mention of adding \( k \) does not seem relevant to the problem as it specifically asks for the height decrease. Hence this option is incorrect.

• Option E: Multiply \( x \) by \( r \). Then multiply by \( k \). Add the products. Similar to option B, if \( k \) does not relate to the problem context that was given, this option seems irrelevant and incorrect.

Based on the above analysis, the three valid methods to find the change in height of the second drone could be:

1. A: Multiply \( x \) by \( r \).
2. C: Multiply \( x \) by \( r \).
3. Any method that directly computes \( r \cdot x \) without introducing unrelated elements.

Assuming you are allowed to consider only unique operations or combinations, the answer would be A and C as valid methods. If the question requires three distinct approaches, please clarify if there is an additional aspect to consider (like units or further operation conditions).