This looks unrealistic for a scenario but, realism aside, the function looks like it will form a parabola. Like this:
The problem though is that this already doesn’t make sense, so this is probably where the “evil” part is coming from. Because doing the problem the way it’s written seems impossible.
Using -16t^2 instead of 16t^2 will flip the parabola vertically as shown here:
and the other parts of the function (like the +192t) will move the parabola into the positive numbers, which will make the parabola look like this:
Average rate of change sounds like the slope is going from one point to another, but it’s not constant because of the parabola. This is probably where the t=1 and 2, t=10 and 11 comes in.
Plugging in those numbers will get the values for y, since f(x) is basically the y (or h(t) in this case). t would be the values for x.
By plugging in h(1)=-16(1)^2+192(1), it produces 176. Likewise, with h(2)=-16(2)^2+192(2), it produces 320.
Plugging in h(10)=-16(10)^2+192(10) will produce 320 and h(11)=-16(11)^2+192(11) will produce 176 once again.
With these results, the numbers can be seen on the parabola as (1,176), (2,320) for t=1 and t=2, and (10,320), (11,176) for t=10 and t=11.
Since it’s asking for the rate of change, the formula would be the same as finding a slope, except with the functions. Like this:
Plugging in (1,176) as X1,Y1 and (2,320) as X2 ,Y2 will give the rate of change of 144/1 or just 144.
Doing the same with (10,320) as X1,Y1 and (11,176) as X2,Y2 will give the rate of change of -144/1 or -144.
So the rate of change for t=1 and t=2 will be 144, and the rate of change for t=10 and t=11 will be -144.
umbrellasArrows.A score or a barrage?
@Background Pony #C1CB
@thps48
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I’ll have the Spam, spam, spam, spam, spam, spam, baked beans, spam, spam, and spam. :3
(I’ve not committed to memory very many Monty Python jokes. Apologies. X3 )
Bless you sir for being good at math, you happening to by here, and solving all this when you REALLY didn’t have to.
mfw
The problem though is that this already doesn’t make sense, so this is probably where the “evil” part is coming from. Because doing the problem the way it’s written seems impossible.
Using -16t^2 instead of 16t^2 will flip the parabola vertically as shown here:
and the other parts of the function (like the +192t) will move the parabola into the positive numbers, which will make the parabola look like this:
Average rate of change sounds like the slope is going from one point to another, but it’s not constant because of the parabola. This is probably where the t=1 and 2, t=10 and 11 comes in.
Plugging in those numbers will get the values for y, since f(x) is basically the y (or h(t) in this case). t would be the values for x.
By plugging in h(1)=-16(1)^2+192(1), it produces 176. Likewise, with h(2)=-16(2)^2+192(2), it produces 320.
Plugging in h(10)=-16(10)^2+192(10) will produce 320 and h(11)=-16(11)^2+192(11) will produce 176 once again.
With these results, the numbers can be seen on the parabola as (1,176), (2,320) for t=1 and t=2, and (10,320), (11,176) for t=10 and t=11.
Since it’s asking for the rate of change, the formula would be the same as finding a slope, except with the functions. Like this:
Plugging in (1,176) as X1,Y1 and (2,320) as X2 ,Y2 will give the rate of change of 144/1 or just 144.
Doing the same with (10,320) as X1,Y1 and (11,176) as X2,Y2 will give the rate of change of -144/1 or -144.
So the rate of change for t=1 and t=2 will be 144, and the rate of change for t=10 and t=11 will be -144.
You beat me to it you dirty bastard!
that’s what makes it evil
What is a spherical arrow and what would it change? You need to apply a force to get acceleration in vacuum too.
Yeah, if this is a ballistic equation that’s gotta be h(t) = -16t^2 + 192t. Gravity accelerates objects downward.
<Twilight> “Do your own math homework, Daybreaker!”
224, 256, 512, 544 for t=1, 2, 10, 11 respectively.
But that’s impossible, because it would mean that the arrow is constantly accelerating. What the hay? Is this a rocket arrow?
Edited
And what were the odds of it impacting an African and/or European swallow during its flight?