Answer:
see below
Step-by-step explanation:
1. Semi-circles have an arc/angle measure of 180°.
2. The angle where chords cross is the average of the subtended arcs. Linear angles are supplementary.
3. It is a good idea to be familiar with algebraic manipulation of quadratic equations, including eliminating parentheses and putting in "general form" (answer B). It is also useful to be familiar with squares of integers less than 20.
4. You have run across this before in your other questions. Opposite angles of an inscribed quadrilateral are supplementary. (The opposite arcs are double the angle measures, so sum to 360°.)
5. After the fashion of question 3, fill in the parameters in the circle equation.
Answer:
The dimensions are:
by
Step-by-step explanation:
The area of the rectangle is given as
The factored form of this quadratic trinomial gives the dimensions of the rectangle.
We factor 3 first to obtain;
We split the middle term to get;
We factor within the parenthesis to get;
We factor further to get;
The dimensions are:
by
Then the perimeter will be
Answer:
Step-by-step explanation:
The relevant area and volume formulas are ...
A = 2(LW +H(L +W))
V = LWH
When there are multiple instances of the calculations to be done, it is convenient to let a spreadsheet do them. The results are attached.
Figure A has the larger area.
Figure B has the larger volume.
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<em>Additional comment</em>
The more "cube-like" the prism is, the less area it will have for the same volume. Here, package B is more "cube-like" than package A. (The ratio of largest-to-smallest dimensions is smaller for package B.)
