Question

Use the graph below to answer the question that follows.

What is the rate of change between the interval x = π and x = three pi over two?

Answer 1

@VeritasVosLiberabit

Answer 2

Rate of change is the slope of the graph. So you have to find the average slope of the graph in the interval [pi,pi/2]

Answer 3

pi over six

six over pi

4 over pi

pi

Answer 4

how do i do that? @navk

Answer 5

You just use the formula
\[m=\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\]

Answer 6

Use the slope formula \[m=\frac{y_2-y_1}{x_2-x_1}\]For this formula you need two points. These points are the end points of the interval pi to 3pi/2

Answer 7

where you have points
\[(\pi,0),(\frac{ 3\pi }{ 2 },2)\]

Answer 8

\[m=\frac{ 2-0 }{ \frac{ 3\pi }{ 2 }-\pi }\]

Answer 9

solve this equation and this will be your linear rate of change

Answer 10

@VeritasVosLiberabit The points are (pi, -1) and (3pi/2, 2)
@madzfl plug in these points in the formula to get the slope, which is the rate of change in the given interval.

Answer 11

is it 6 over pi? @VeritasVosLiberabit @navk

Answer 12

yes it is 6/pi

Answer 13

wooohoo! thank you so much! :)

Answer 14

Could you help with one more?
@navk

Answer 15

sure ask it

Answer 16

Which of the following is the graph of f(x) = 3 sin (2x)?

Answer 17

@navk

Answer 18

get the amplitude and period of the given function first

Answer 19

how do i do that?

Answer 20

Compare it with Asin(Bx) -- in this function A is the amplitude, so amplitude of 3sin(2x) will be ?

Answer 21

i don't know :,(

Answer 22

i don't really understand this

Answer 23

The number before sin(x) is its amplitude. In the function 3sin(2x), the number before sin is 3 so that is its amplitude

Answer 24

okay so its definitely not A

Answer 25

amplitude is 3. this means the graph should be 3 units above the x-axis and 3 units below the y-axis. in other words the max value of graph should be 3 and min value -3

Answer 26

yes, defntly not A

Answer 27

so that could be b, c or d

Answer 28

how do you know whig one?

Answer 29

now get the period of the function. in the function 3sin(2x), what is the number with 'x' ?

Answer 30

ummm im not sure

Answer 31

it's 2. to find the period, divide 2pi by this number. so period = 2pi/2 = pi.

Answer 32

this means that the graph should complete one cycle in an interval of pi on the x-axis

Answer 33

this rules down the choices to B and D since both of them have amplitude of 3 and period of 2. are you with me so far?>

Answer 34

Ty sm!! The first answer, 6/pi, was correct!! THanks! :D