TheLovely1

Whoops.

Thank you so much!~

Thank you!

(-infinity,3] U [3,infinty)

?

Hello, Guest!~

We start off with x-5y=13, and 4x-3y=1.

We can rearrange the first equation: x=5y+13.

We can substitute this first, rearranged equation into the second, giving us:

4(5y+13)-3y=1

1=4(5y+13)-3y

1=20y+52-3y

1=17y+52

0=17y+51

-51=17y

y=-3.

Now that we have y, we can use that to find x:

x+15=13

x=-2

So your ordered pair would be: (-2,-3)

Hope that helps!~

-TheLovely1

:D 

Oh, no, somebody upvoted everything-now it's back to normal!~

Oh, much better. I thought we had a troller hanging about here....

Hewo, Otterstar!~

So we have a triangle, ABC, where Point D is on BC, such that BD=DC=DA. (I had to draw it like seven times to get the scale right (I don't know why I bothered to draw it so perfectly)). Now, we're told that ABC is 50.

So, since DA=DC=BD, I'm going ahead and assuming that DA perfectly chops angle ABC in half, meaning, Angle DAC= 50/2=25. (Also BAD but we don't care about that.)

Great. Now what? We still need one more angle to find ACD.

So we go back to the part where ABC is perfectly chopped down in half. That means that angle ADC is 90 degrees, (also ADB but we don't care about that), and so, we have two angles of a triangle, and we need to find the last one...

DAC+ACD+ADC=180

180=DAC+ACD+ADC

180=ACD+90+25

180=ACD+115

65=ACD

(ACD=ACB( Just different ways of saying it))

Therefore, ACD=65, and by extension, ACB=65.

Reply to my answer if I made a mistake, or have any questions!~

-TheLovely1

Thank you so much, Melody!~

(Could have done with the end of step two but thank you for the help!~)

Thank you so much!~

Only four months?

What are we trying to solve for?

I solved it!~

:D 

Here's the official solution!~

Thank you so much!~

First, we should convert the given information about the real-world context into mathematical terms of the sinusoidal function and its graph.

Then, we should use the given information to find the amplitude, midline, and period of the function's graph.

Finally, we should find aaa, b, and d in the expression \(a*cos(b*t)+d\) by considering the features we found.

At t=0, the swing is 1m, behind the center. This means the graph of the function passes through (0,-1).

We are given that this is the farthest point behind the center, which corresponds to a minimum point of the graph.

\(\frac{\pi}{6}\) seconds later the distance is 0m. This corresponds to the point \((\frac{\pi}{6},0)\).

We are given that this is the middle of the swing, which corresponds to the midline of the graph.

In conclusion, the graph has a minimum point at (0,-1) and then intersects its midline at \((\frac{\pi}{6},0)\).

The midline intersection is at y=0, so this is the midline.

The minimum point is 1 unit below the midline, so the amplitude is 1.

The minimum point is \((\frac{\pi}{6})\) units to the left of the midline intersection, so the period is \(4*\frac{\pi}{6} \\ \\=\frac{2\pi}{3}\). 

The amplitude is -1.

The midline is y=0.

The period is 3.

The answer:

\(D(t)=-cos(3t)\)