Step-by-step explanation:
WYXV is quadrilateral.
the reason are the undefined angles at W and V (they are equal, but not necessarily 90°, so the shape could shrink or extend between W and V)
ABCD is a rectangle.
AB and CD are parallel and equally long. and C is 90°.
that means then that the other angles must be 90° too, or either the parallel or equally long criteria would be violated.
PQSR is a parallelogram.
PQ and RS are parallel and equally long.
that means that PR and QS must also be parallel and equally long. we just don't know the angles, they could be anything. and therefore this is not a rectangle but a more generic parallelogram.
V = 1/3s^2h; where V is the volume, s is the side length of the square base, and h is the height.
s/h = 6/10 = 3/5
s = 3h/5
V = 1/3(3h/5)^2 h = 1/3(9h^2/25)h = 3h^3/25
dV/dt = 9h^2/25 dh/dt = 0.2 = 1/5
dh/dt = 5/(9h^2)
When h = 2
dh/dt = 5/(9(2)^2) = 5/(9 * 4) = 5/36 = 0.1389 inches per seconds.
You don't need to understand the construction or why it works. You only need to accept the fact that it does. You can figure out the answers to this question by looking at the picture.
RT is tangent to circle Q -- TRUE. That is the point of the construction.
QT is a radius of circle Q -- TRUE. Q is the center and T is on the circle. A line segment from the center to a point on the circle is a radius.
m∠QSR = 90° -- FALSE. Those points lie on the same line. The measure of the angle is 180°.
QS = QT -- FALSE. S lies inside circle Q, so is closer to the center than T, which lies on the circle. (For some choice of point R, S might lie on the circle, but because this statement is not always true, it must be considered false.)
ΔRTQ is a right triangle -- TRUE. A tangent line is always perpendicular to the radius to the point of tangency. The construction succeeds because RTQ is inscribed in semicircle RTQ (centered at S). Such a triangle is always a right triangle.
