Hi there!
We can begin by finding ∠VUY so we can solve for ∠UVY.
∠VUY is supplementary to ∠TUY, so:
180 = 144 + ∠VUY
∠VUY = 36°
In a triangle, angles sum up to 180°, so:
180 = 36° + 79° + m∠UVY
m∠UVY = 65°
Solve for m∠VYZ by comparing the angle to m∠UVY because the angles are alternating interior angles. Thus:
m∠UVY = m∠VYZ = 65°.
I'll assume that's an exponent at the end there:
The first derivative gives the velocity. The second derivative gives the acceleration; increasing velocity is the same as positive acceleration. So we want to find when the second derivative is positive.
Let's see if we can use to avoid multiplying this out.
That worked; let's do it again:
That's a nice parabola. It's zero or negative for so positive everywhere else:
Answer: Increasing velocity when t < 1 or t > 3
If the polygons are similar, then we can set up a similarity ratio using sides AB and EF and any other 2 sides where both side lengths are given. That appears to be true for sides BC and FG. Our similarity ratio would be this then, going from the bigger polygon stuff on top and the smaller polygon stuff on bottom:
.
If we cross multiply we have 8y = 36 and divide both sides by 8 to get that y = 4.5. There you go!