Algebra 1 question :D
Medal + Fan!

Question

Algebra 1 question :D
Medal + Fan!

henrietepurina · Answer

A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, ft, in feet, at different times t in seconds:

f(t) = -16t^2 + 48t + 100

The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is _____feet per second.

misty1212 · Answer

HI!!!

henrietepurina · Answer

heya :D

misty1212 · Answer

you never quit doing math!

swissgirl · Answer

#MathisLyfe

henrietepurina · Answer

no, I work on it all day :)

henrietepurina · Answer

really! :D

misty1212 · Answer

for this problem we need a couple numbers 
we are going to compute 
$$\frac{f(5)-f(3)}{5-3}$$

henrietepurina · Answer

that's how I spend my weekends practically :D

henrietepurina · Answer

ok, i'll try doing that :)

misty1212 · Answer

so we need to find $f(5)$ and $f(3)$ because we already know that $5-3=2$

henrietepurina · Answer

f(2)/2

henrietepurina · Answer

f is the answer?

misty1212 · Answer

oh no dear you could not be farther from the truth
first off, $f(5)f(3)\neq f(2)$ we have to compute those numbers

henrietepurina · Answer

ah ok then :D

misty1212 · Answer

secondly, $f$ is a function, not a variable, so $\frac{f(2)}{2}\neq f$ that is just silly

henrietepurina · Answer

ok sorry :|

misty1212 · Answer

you have $f(t) = -16t^2 + 48t + 100$ so what is $f(5)$? feel free to use a calculator

henrietepurina · Answer

give me a second ok?

misty1212 · Answer

take your time

henrietepurina · Answer

umm... could it be −6060?

misty1212 · Answer

idk let me check

henrietepurina · Answer

kk

misty1212 · Answer

that is not even close to what i got $$f(t) = -16t^2 + 48t + 100$$
$$f(5)=-16\times 5^2+48\times 5+100$$ use a calculator

henrietepurina · Answer

I did... ohhh! 16*((5)^2) not ((16*5)^2)

misty1212 · Answer

or better yet, use this http://www.wolframalpha.com/input/?i=+-16*5^2+%2B+48*5+%2B+100

henrietepurina · Answer

-60 it is

misty1212 · Answer

lol yeah don't forget the old "order o' operations"

henrietepurina · Answer

sorry, messed up on my behalf

misty1212 · Answer

that's ok dear, let me know when you get $-60$

henrietepurina · Answer

yeah, I already typed that I got -60

misty1212 · Answer

ok now then next number we need is $f(2)$ 
think we can get that ?

henrietepurina · Answer

yes I can

henrietepurina · Answer

132

misty1212 · Answer

got it !!

henrietepurina · Answer

yay...

misty1212 · Answer

TOO BAD I MADE A MISTAKE

henrietepurina · Answer

what do you mean?

misty1212 · Answer

lol we need $f(3)$ not $f(2)$ doe

henrietepurina · Answer

it's ok i'll redo it :D

henrietepurina · Answer

100

misty1212 · Answer

we got the $f(5)$ so that is ok, we need $f(3)$ let me check

henrietepurina · Answer

its 100

misty1212 · Answer

$$100$$ it is !

henrietepurina · Answer

ok then :)

misty1212 · Answer

final job is 
$$\frac{-60-100}{2}$$

henrietepurina · Answer

haha ok...

misty1212 · Answer

i.e.
$$\frac{f(5)-f(3)}{5-3}$$

henrietepurina · Answer

i got -80

misty1212 · Answer

once we compute it and get the correct answer, we have to have a brief explanation of why this question was written by a moron who knows no math and should not be writing questions for unsuspecting students

misty1212 · Answer

ok good, $-80$ is correct
at least that is what the idiot wants
do you have an actual teacher for this class, or is it on line

henrietepurina · Answer

class

misty1212 · Answer

so you have a real teacher?

henrietepurina · Answer

yeah

misty1212 · Answer

ok explain to this teacher (who may be a very nice person, but should be teaching gym) that if the question really is 
A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, ft, in feet, at different times t in seconds: 
then the ball hits the ground before 5 seconds has elapsed, ( we know this since $f(5)=-60$ ) so it cannot have been in the air for five seconds

henrietepurina · Answer

(don't worry, she's not one of the best)

misty1212 · Answer

in other words it makes no sense to say the ball is $-60$ 
when it hits the ground, $h=0$ then presumably it does not go underground

henrietepurina · Answer

mhm... so would it be correct to say -60 anyway?

misty1212 · Answer

go ahead and ask how the ball can be $-60$ feet see what she says

henrietepurina · Answer

wait wait, when I divided again, I got -80, but that doesn't make a difference

misty1212 · Answer

believe me the answer she is looking for is $$\frac{f(5)-f(3)}{5-3}=\frac{-60-100}{2}=-80$$

misty1212 · Answer

all i am saying is that the ball does not stay in the air for five seconds, so the word problem aspect of this is stupid
if it was just "find the average rate of change of $f(t)=-16t^2+48t+100$ then $-80$ makes perfect sense

misty1212 · Answer

this is what happens when not too sophisticated math teacher try to make up word problems
i would be better if they just stuck to equations and such

henrietepurina · Answer

thanks so much... sorry for not responding, BATHROOM BREAK!

henrietepurina · Answer

wait wait wait @misty1212 .... remember that this question is asking for the rate of change, so wouldn't the answer actually be logical?

misty1212 · Answer

no, not as a word problem
as a math problem, yes, the average rate of change of that function on the interval $(3,5)$ is $-80$

henrietepurina · Answer

ah yeah, I see where you are going :D

misty1212 · Answer

as a word problem it does not make sense because the ball cannot be 60 feet under ground

henrietepurina · Answer

yeah yeah :D BTW... mind helping me on another one?

misty1212 · Answer

as a pure math problem forgetting the words, then yes the rate of change is -80

misty1212 · Answer

sure why not
but post in a different thread it gets hard to scroll down so much

henrietepurina · Answer

ok can do :D

anonymous · Answer

was this correct?