QUESTION 2:
The perimeter of a square P (measured in centimeters) is expanding in size at a constant rate of change of
4 centimeters per centimer with respect to the square's side length s (measured in centimeters).
a) If the length of the side of the square changes from
1. Oto 1.5 centimeters, how does the square's perimeter P change?
2. 3 to 8 centimeters, how does the square's perimeter P change?
b) Express the change in the square's perimeter p in terms of the change in the square's side length s.
AP=
Write a formula and construct a graph that represents the perimeter of the square P (in centimeters)
in terms of the square's side lengths (in centimeters).
x
d) Illustrate the solution to 8 - 4.s on the graph below and describe what this solution represents.
e) P-4.s represents the square's perimeter in terms of the square's side length (in centimeters).
write a formula that represents the perimeter's side lengths in terms of the square's perimeter P.
f) How is the formula you determined in part (e) related to the formula P=4.s?

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facundo3141592 facundo3141592 · Answer 1 · 2021-08-30T16:21:49+02:00

We know that for a square of side length s, the perimeter is given by:

P(s) = 4*s

a) If initially we have s = 1cm, then the initial perimeter is:

P(1cm) = 4*1cm = 4cm

if now s changes to 1.5cm, the new perimeter will be:

p(1.5cm) = 4*1.5cm = 6cm

So the side length increased 0.5cm, and the perimeter increased 4 times that, 2cm.

b) We can define the change in side length as Δs, then if the initial side length is s, the new side length will be written as:

s + Δs

using this in the perimeter equation we get:

P(s + Δs) = 4*(s + Δs) = 4*s + 4*Δs = P(s) + ΔP

We can see that ΔP = 4*Δs

c) We already know the formula, it is P(s) = 4*s, the graph can be seen below.

d) We need to solve 8 = 4*s

To get this, we need to isolate s.

s = 8/4 = 2

s = 2

This means that if the perimeter is 8cm, then the side length must be 2cm

e) P = 4*s

is the perimeter in terms of the side length, we want to get the side length in terms of the perimeter, we just need to divide both sides by 4:

s = P/4

f) The formula we got in (e) is the formula P = 4*s divided on both sides by 4.

That is the relation between the two formulas.

If you want to learn more, you can read:

https://brainly.com/question/18793958