Question

The height of a ball dropped from a tall building is modeled by the equation d(t) = 16t2 where d equals the distance traveled at time t seconds and t equals the time in seconds. What does the average rate of change of d(t) from t = 2 to t = 5 represent?
a.)The ball falls down with an average speed of 336 feet per second from 2 seconds to 5 seconds.
b.)The ball falls down with an average speed of 48 feet per second from 2 seconds to 5 seconds.
c.)The ball travels an average distance of 336 feet from 2 seconds to 5 seconds.
d.)The ball travels an average distance of 48 feet from 2 seconds

Answer 1

i think its B.

Answer 2

why?

Answer 3

umm.... ok just a sec

Answer 4

its either A or B because its being dropped

Answer 5

so its falling

Answer 6

umm... so either A or B

Answer 7

find d 1. when t=2 s
2.when t=5s
3. find difference
4.this gives distance covered in (5-2)=3 s
5.divide by ( 5-2)=3s
this gives average speed

Answer 8

@ranga

Answer 9

d(t) = 16 * t^2
when t = 2:
d(2) = 16 * 2^2 = ?
when t = 5:
d(5) = 16 * 5^2 = ?
Distance traveled between t = 2 and t = 5 is: d(5) - d(2) = ?
Average speed = { d(5) - d(2) } / ( 5 - 2 ) = ?

Answer 10

d(3)

Answer 11

Just plug the numbers into a calculator and fill out all the question marks in my previous reply.

Answer 12

d(2) = 16 * 2^2 = 64
when t = 5:
d(5) = 16 * 5^2 = 400
Distance traveled between t = 2 and t = 5 is: d(5) - d(2) = 336
Average speed = { d(5) - d(2) } / ( 5 - 2 ) = 112

Answer 13

@ranga

Answer 14

Yes. See which choice fits the answer.

Answer 15

You found the average SPEED to be 112 feet / sec.
You found the average DISTANCE traveled to be 336 feet.
Which choice is the correct answer?

Answer 16

The first two choices deal with average SPEED.
The last two choices deal with average DISTANCE.

Answer 17

c? @ranga

Answer 18

Yes.

Answer 19

thanks. can you help me with one more?

Answer 20

I can guide you but I cannot give the answer.

Answer 21

functions 1 and 2 are shown below function 1 f(x)=-3x^2+2

Answer 22

function 2

Answer 23

which function has a larger maximum?

Answer 24

The general equation of a parabola is ax^2 + bx + x.
The maximum or minimum occurs at x = -b/(2a)
For function 1) find at what value of x the maximum occurs by finding -b/(2a)
Then put that x value in the function and find the maximum value of the function.
What do you get?

Answer 25

It is ax^2 + bx + c (not x)

Answer 26

im confused :/

Answer 27

Compare ax^2 + bx + c to
-3x^2 + 2
what is a, b and c?

Answer 28

a=-3x^2
b= 1x
c=2

Answer 29

a,b,c are coefficients. So a = -3, b = 0 and c = 2
Maximum/minimum for a parabola occurs at x = -b/(2a)
plug the values for a and b and find what x value the max/min occurs.

Answer 30

x=1?

Answer 31

a = -3, b = 0, c = 2
What is -b/(2a)?

Answer 32

-0/2-3?

Answer 33

-0 / (2 * -3) = -0 / (-6) = ?

Answer 34

0?

Answer 35

Yes, the maximum occurs at x = 0
Put x = 0 in the first function to find what the maximum value is.

Answer 36

f(x)=-3x^2+2
f(0)=-3(0)^2+2?

Answer 37

simplify above. what is the max value?

Answer 38

2

Answer 39

Yes. The max value of function 1 is 2.
From the graph, what is the max value of function 2?

Answer 40

4

Answer 41

I think

Answer 42

Yes. So which function has the larger maximum?

Answer 43

function 2?

Answer 44

Yes.

Answer 45

thanks for all your help :)

Answer 46

you are welcome.