Let's solve this problem step-by-step.
STEP-BY-STEP SOLUTION:
First let's establish that the problem requires the border to be as long as the total perimeter of the rectangular bulletin board.
Therefore:
Total length of border = Perimeter of rectangular bulletin board
As a rectangle has a total of four sides with two equivalent longer sides and two equivalent shorter sides, we must multiply the value of each of the two sides by two.
Total length of border = 2 ( 2 ) + 2 ( 4 )
Total length of border = 4 + 8
Total length of border = 12 feet
12 > 10
ANSWER:
Therefore, 10 feet of border isn't enough.
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The answer is D, because -2/3/2 = -4/3.
Let's work on the left side first. And remember that
the<u> tangent</u> is the same as <u>sin/cos</u>.
sin(a) cos(a) tan(a)
Substitute for the tangent:
[ sin(a) cos(a) ] [ sin(a)/cos(a) ]
Cancel the cos(a) from the top and bottom, and you're left with
[ sin(a) ] . . . . . [ sin(a) ] which is [ <u>sin²(a)</u> ] That's the <u>left side</u>.
Now, work on the right side:
[ 1 - cos(a) ] [ 1 + cos(a) ]
Multiply that all out, using FOIL:
[ 1 + cos(a) - cos(a) - cos²(a) ]
= [ <u>1 - cos²(a)</u> ] That's the <u>right side</u>.
Do you remember that for any angle, sin²(b) + cos²(b) = 1 ?
Subtract cos²(b) from each side, and you have sin²(b) = 1 - cos²(b) for any angle.
So, on the <u>right side</u>, you could write [ <u>sin²(a)</u> ] .
Now look back about 9 lines, and compare that to the result we got for the <u>left side</u> .
They look quite similar. In fact, they're identical. And so the identity is proven.
Whew !
An expression might be: 2354h / 3hrs. You can make the real division sign if you're using paper. Hope this helped :)
