hectictar

\(\Large{ \frac{4b}{a^{-10}} = 4ba^{10} }\)

I don't know if you need to write it like this but that is the same thing as:

\(\Large{ 4a^{10}b }\)

Can you say what the function is again because I don't know what " =ht−92t16t2 " is.

You can put ^ to mean that it is raised to the power, or you can use the superscript button that looks like x².

Get the vertex at (2,4):

y = c(x-2)² + 4

Find the coefficient c by just plugging in (6,10) for x and y.

10 = c(6-2)² + 4

6 = 16c

3/8 = c

y = (3/8)(x-2)² + 4

Oh okay, thanks

 Oh okay mine is wrong because I found the displacement not the distance, so when I tried to convert that to air time it just gave me something that was meaningless. I didn't really know what I was doing, heh.

But I'm confused though because when I tried to find the arc length from 0 to 90/49 I got about 8.61142 and then 18 divided by that is about 2.09. Howcome 2.09 seconds isn't the answer?

I also want to attempt the second one because why not haha I have no clue if I'm doing these right though.

So I'm going to work towards getting a position function of the ball.

Acceleration:

y''= -9.8 m/s²

Velocity:

y'=\(\int -9.8 dx\)

y' = -9.8x + c

18sin30° = -9.8(0) + c

c=9

y'= -9.8x + 9

Position:

y=\(\int(-9.8x+9)dx\)

y=\(\int-9.8x dx +\int9dx\)

y=\(-9.8\frac{x^{2}}{2}+9x\)

y= -4.9x² + 9x

So that is the position function of the ball. So we need to find the two places where the ball touches the ground, aka where the y value equals 0.

0 = -4.9x² + 9x

0 = x(-4.9x+9)

Set each factor equal to zero.

-4.9x+9 = 0 and x = 0

-4.9x=-9

x = 90/49

So y is 0 when x is 0 and when x is 90/49. The difference in those x values will be the distance it  traveled. So it traveled 90/49 meters. I just realized that we want the time it is in the air, not the distance traveled. Well it's okay the time it was in the air will just be 18 m/s divided by 90/49 meters. Which is 49/5 or 9.8 seconds. That was probably the longest possible approach to this problem but I kind of think I got the right answer.

For the first one, I'm not really sure but I think that this is how to do it.

Imagine a graph of the velocity of the object.

Its velocity is 4 m/s at x = 0, and its velocity is 0 m/s at x=12 meters.

So if y is the velocity and x is the distance, the equation of that line is: y = (-4/12)x + 4, or

y = (-1/3)x + 4.

The derivative of velocity is acceleration, so the acceleration is -(1/3) m/s/s.

You know the acceleration is going to be negative because the object is slowing down.

I'm not sure if this is right though because I didn't use the information about it being 2 kg at all.

No, 6 + 6 is not equal to 26. lol

I don't read very much but a few of my favorites are Christy by Catherine Marshall, the entire Anne of Green Gables series (My favorite was Anne of the Island), and I know this is a silly one but I love the Diary of a Wimpy Kid series.

\(m = \frac{y_{1}-y_{2}}{x_{1}-x_{2}} \\ x_{1}=3, y_{1}=6, x_{2}=-9, y_{2}=2 \\ m = \frac{6-2}{3-(-9)} \\ m= \frac{4}{12} \\ m=\frac{1}{3}\)