A graphic designer wants to create a rectangular graphic that has a 2-inch margin on each side and a 4-inch margin on the top an
1 answer:
The area of a shape is the amount of space the shape can occupy.
The dimension that maximizes the design is 20 inches by 20 inches
From the question, we have:
Let the length and width of the graphic (without the margin) be l and w.
So, the dimension of the whole graphic is:
The area is then calculated as:
Substitute
Make l + 4, the subject
Subtract 4 from both sides
The area of the design is:
So, we have:
Plot the graph of
From the graph (see attachment), the maximum is at:
Substitute in
Divide both sides by 20
Hence, the dimension that maximizes the design (<em>excluding the margin</em>) is 20 inches by 20 inches
Read more about maximizing areas at:
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Answer: _L_TS_OF_FLOURS
Each underscore represents an empty box, i.e. a space
I'm assuming your teacher probably meant to have _LOTS_OF_FLOURS
See the explanation below as to why that first "O" is left out.
I would as your teacher for more clarification if s/he made a typo or not.
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Explanation:
For the stuff in the top row, we simplify the expression to get a single number. For example,
2^5 = 2*2*2*2*2 = 32
We have five copies of "2" multiplied out
The result of 32 means we'll cross off "32" from the list. This is the one with the lettering of "lV"
As another example,
3^4 = 3*3*3*3 = 81
The exponent tells us how many copies of the base to multiply
The result of 81 means we cross off the entry labeled "bT 81"
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For the stuff in the bottom row, we replace the variables with the numbers associated with them.
When it says a = 2, we replace every copy of 'a' with 2
Something like (3a)^2 will then mean (3*2)^2. Use PEMDAS to simplify and you should get 36 as the result.
Check out the diagram below to see which items are crossed off the list. Each red box represents something that is crossed off the list.
The remaining items that weren't crossed off are:
- mU 10
- jG -32
- eS 1/12
- lO 1000 .... the first letter is lowercase L
- hF -1/32
- bL 256
- jF -196
- gO 32
- oS 24
- dT 36
- nR 144
- kL -180
We're given a set of boxes labeled with lowercase letters 'a' through 'p'
We'll write "L" in box "b" since these letters pair together in "bL 256"
Then we have "dT" up next to mean we'll write T in box d
Next letter S goes in box 'e' since we have the code "eS 1/12"
This process is repeated until we end up with _L_TS_OF_FLOURS
where each underscore is an empty box. For example, box 'a' is left empty since none of the remaining codes involve a lowercase 'a'
It appears your teacher made a typo. I'm guessing the answer to the riddle should be "_LOTS_OF_FLOURS", but box c is empty because none of the remaining codes involve lowercase c. We do have the code "cO -32" in the upper left corner, but it has been crossed off the list due to (-2)^5 = -32
