Question

Help, don't answer. Guide me through it.

Answer 1

he relationship between the area and perimeter of a square can be expressed as the function y = 4 √x, where y is the perimeter of the square in units and x is its area in square units. Joey is using a computer program that allows him to see how changing the area of a square changes its perimeter. Which statement about the rate of change is true?

A. The rate of change is 0.
B. The rate of change is positive.
C. The rate of change is negative.
D. The average rate of change is the same for all points on the graph.

Answer 2

Rate of change here can be calculated by calculating the slope of the curve.

Answer 3

Teach me? o_o

Answer 4

Well there is electricity cut off here in our town. So, I can post my reply only after half an hour. Till then try to find out and study more about slope of curve.

Answer 5

Oh, ok. :) @Hero

Answer 6

Rate of Change is just another word for slope which is often expressed using the notation

\(\dfrac{\Delta y}{\Delta x}\). You may or may not have seen that before. Either way

\(\dfrac{\Delta y}{\Delta x} = \dfrac{y_2 - y_1}{x_2 - x_1}\) which is something you have seen before. Basically, we can take any two points on the graph of \(y = 4\sqrt{x}\), calculate the slope, and then determine whether or not the slope is zero, positive, negative, or the same or any given set of points. Try taking two sets of the given points:

(4,8) & (9, 12) and calculate the slope of those two points

Then

(16,16) and (25,20) and calculate the slope of these two points.

Compare the slopes and then state your conclusion.

Answer 7

x2=8 or 12? I was thinking 12... @Hero

Answer 8

@CrazyCountryGirl, did you read what I wrote above? If so, how would you summarize what was written in your own words?

Answer 9

I did read it. I'm confused what the 1 and 2 are for after the x and y.

Answer 10

\(\dfrac{y_2 - y_1}{x_2 - x_1}\) is the slope formula. Don't you recognize it? I know you've seen it before.

Answer 11

I know the formula but does it matter where either of the ys or xs go as long as they're in the x and y places? do u understand what im talking about or no?

Answer 12

It doesn't matter the order in which you put \(y_1\) and \(y_2\) as long as you know that the y values go in the numerator and the x values go in the denominator.

Answer 13

oh ok. let me see if i can do it now. :)

Answer 14

However, you do have to be consistent. If you chose \((x_1,y_1)\) as the first point, then you have to be consistent when you apply it in the slope formula.

Answer 15

I did this...

Rate of Change is just another word for slope which is often expressed using the notation

ΔyΔx. You may or may not have seen that before. Either way

ΔyΔx=y2−y1x2−x1 which is something you have seen before. Basically, we can take any two points on the graph of y=4x√, calculate the slope, and then determine whether or not the slope is zero, positive, negative, or the same or any given set of points. Try taking two sets of the given points:

(4,8) & (9, 12) and calculate the slope of those two points

Then

(16,16) and (25,20) and calculate the slope of these two points.

Compare the slopes and then state your conclusion



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I got \[\frac{ 12-8=4 }{ 9-4=5 } and \frac{ 20-16=4 }{ 25-16=9 }\]

Answer 16

@Hero

Answer 17

@Hero @karatechopper @Awesome781 @esshotwired @Whitemonsterbunny17 @Zale101 @vishweshshrimali5

Answer 18

I think you mean you calculated:

\(\dfrac{12 - 8}{9 - 4} = \dfrac{4}{5}\)

\(\dfrac{20 - 16}{25 - 16} = \dfrac{4}{9}\)

Answer 19

Yes that's what I calculated...

Answer 20

So, based on those calculations are the slopes 0, +, -, or =?

Answer 21

I know 4/5>4/9...

Answer 22

Are the slopes zero, positive, negative or equal?

Answer 23

The question is not a difficult one to answer @CrazyCountryGirl

Answer 24

Positive.

Answer 25

Did I get it right?

Answer 26

Correct