anonymous
  • anonymous
Water coming out from a fountain is modeled by the function f(x) = -x2 + 5x + 4 where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds. What does the average rate of change of f(x) from x = 3 to x = 5 represent? The water falls down with an average speed of 3 feet per second from 3 seconds to 5 seconds. The water falls down with an average speed of 5 feet per second from 3 seconds to 5 seconds. The water travels an average distance of 3 feet from 3 seconds to 5 seconds. The water travels an average distance of 5 feet from 3 seconds
Mathematics
schrodinger
  • schrodinger
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freckles
  • freckles
average rate of change is given by the change of y over the change of x. \[\frac{ f(5)-f(3)}{5-3} \]
freckles
  • freckles
you are dividing a change of height by a change in time
anonymous
  • anonymous
So x = 2?

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dumbcow
  • dumbcow
also "rate of change" = speed
anonymous
  • anonymous
So, I know its either A or B, right?
dumbcow
  • dumbcow
yes
anonymous
  • anonymous
So its either 5 or 3 feet per 3-5 seconds?
freckles
  • freckles
just used the formula I gave above to figure out between A and B
anonymous
  • anonymous
I dont understand the formula you gave me.
anonymous
  • anonymous
f(5) - f(3) = f(2) ----- 2 ??????????????
freckles
  • freckles
...how did you get f(5)-f(3)=f(2)?
freckles
  • freckles
f(5)=-5^2+5(5)+4 and f(3)=-3^2+5(3)+4
anonymous
  • anonymous
So f(5) = 3154 And f(3) = 110
freckles
  • freckles
-5^2+5(5)+4 ------ first we know 5^2=5(5)=25 so -5^2+5(5)+4 can be written as -25+25+4
freckles
  • freckles
-25+25 is 0 though so you have -5^2+5(5)+4 can be written as 0+4 which is just 4
freckles
  • freckles
can you try doing f(3)
anonymous
  • anonymous
f(3) = 25?
freckles
  • freckles
are you guessing?
anonymous
  • anonymous
No
freckles
  • freckles
f(x)=-x^2+5x+4 just plug in 3 where x is
anonymous
  • anonymous
OH there is a negative, my bad
freckles
  • freckles
f(3)=-3^2+5(3)+4 3^2 means 3(3) which is 9 5(3) is 15 f(3)=-9+15+4
anonymous
  • anonymous
so 10?
freckles
  • freckles
\[\frac{f(5)-f(3)}{5-3}=\frac{4-10}{5-3}\]
anonymous
  • anonymous
so its 3
anonymous
  • anonymous
So the answer is a?
freckles
  • freckles
well -3 where the units is distance/time which is a speed unit which just means going down at a speed of 3ft/sec
freckles
  • freckles
and yes a sounds great
anonymous
  • anonymous
Thx for the help! Ima submit my test now, lets see :D
anonymous
  • anonymous
Oh no! I got a %62 on my test :(. 5 questions wrong out of 13. But the one you helped me with was right, ty so much!

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