Sense this string would only be 11 (in), and we are cutting it into 3 pieces, this would show us that we would then be dividing the 11 (in) string into 3 pieces. The expression would be below.
Adjacent angles<span> are two </span>angles<span> that have a common vertex and a common side.
<OPN and <TSP have a common side but do not have a common vertex.
<OPN and <RSU do not have a common side or a common vertex.
<OPN and <QPN are adjacent angles. They have a common side and a common vertex.
<OPN and <QPS have common vertex but do not have a common side.</span>
The volume of a rectangular prism is (length) x (width) x (height).
The volume of the big one is (2.25) x (1.5) x (1.5) = <em>5.0625 cubic inches</em>.
The volume of the little one is (0.25)x(0.25)x(0.25)= 0.015625 cubic inch
The number of little ones needed to fill the big one is
(Volume of the big one) divided by (volume of the little one) .
5.0625 / 0.015625 = <em>324 tiny cubies</em>
=================================================
Doing it with fractions instead of decimals:
The volume of a rectangular prism is (length) x (width) x (height).
Dimensions of the big one are:
2-1/4 = 9/4
1-1/2 = 3/2
1-1/2 = 3/2
Volume = (9/4) x (3/2) x (3/2) =
(9 x 3 x 3) / (4 x 2 x 2) =
81 / 16 cubic inches.
As a mixed number: 81/16 = <em>5-1/16 cubic inches</em>
Volume of the tiny cubie = (1/4) x (1/4) x (1/4) = 1/64 cubic inch.
The number of little ones needed to fill the big one is
(Volume of the big one) divided by (volume of the little one) .
(81/16) divided by (1/64) =
(81/16) times (64/1) =
5,184/16 = <em>324 tiny cubies</em>.
First, let me introduce the general equation of the parabola:
(x-h)^2 = +/- 4a(y-k) or (y-k)^2=+/- 4a(x-h), where
(h,k) are the coordinates of the vertex
a is the distance of the vertex to the focus
4a = length of lactus rectum or the focal width
If the equation contains (x-h)^2, then the parabola passes the x-axis twice. Similarly, (y-k)^2 passes the y-axis twice. If the sign is (-), it opens to the left(if y-axis) or downward (if x-axis). If the sign is (+), it opens to the right(if y-axis) or upward (if x-axis).
The equation of the parabola is -1/12 x^2 = y. Rearranging to the general form:
x^2 = -12y
Therefore,
-4a = -12
4a = 12
a = 3, and the parabola is facing downwards.
The vertex is (0,0) at the origin.
The focus is (0,-3). Since it is negative, the focus is situated downwards, hence -3.
The directrix is the mirror image of the focus. Hence, it is a line passing +3 on the y-axis. y=3
Focal width is 4a which is equal to 12 units.
