20 people show up to a post-PSTAT 120A party. If everyone shakes hands with everyone else, how many handshakes take place
1 answer:
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Answers:
- Length = 17
- Width = 6
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How to get those answers:
Let w be the unknown width in centimeters. This variable is some positive real number. This means w > 0 which will be useful later.
The length is "1 cm less than 3 times its width" and it tells us the length is defined by the expression 3w-1. Whatever w is, we triple it to get 3w and then subtract 1 to get the final length.
Multiply the length and width to get the area 102
length*width = area
(3w-1)*w = 102
3w^2-w = 102
3w^2-w-102 = 0
We could guess and check our way to factoring this, but that's not very efficient. The quadratic formula is the better option. It may seem a bit messy, but it's a more direct path that doesn't involve guessing.
We ignore the second solution (w = -5.667 approximately) because we stated earlier that w > 0. In other words, a negative length does not make sense, so that's why we ignore it.
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If w = 6 cm is the width, then 3w-1 = 3*6-1 = 18-1 = 17 cm is the length.
Note that length*width = 17*6 = 102 which is the proper area we want. This confirms the answers.
The requested values are found in the attached table
Selected pairs
A(22,160)B(30,172)
find the slope of the line AB
m=(y2-y1)/(x2-x1)=(172-160)/(30-22)=12/8=3/2=1.5m=1.5
one point and slope-------- > A(22.160) m=1.5
y=mx+b
160=1.5(22)+bb=127y=1.5x+127---------- > equation in slope intercept form
<span>If the length of the bone is 12 in------------------ > 12*2.54=30.48 cms
</span>y=1.5x+127- >1.5*30.48+127=172.72 cms
172.72/2.54=68 in
172.72/0.30=575.73 feet
the height estimate of the person before death is 172.72 cms=68 inches=575.73 feet
<span>By the height it could be a man of average height or a tall woman</span>
Selected pairs
A(22,160)B(30,172)
find the slope of the line AB
m=(y2-y1)/(x2-x1)=(172-160)/(30-22)=12/8=3/2=1.5m=1.5
one point and slope-------- > A(22.160) m=1.5
y=mx+b
160=1.5(22)+bb=127y=1.5x+127---------- > equation in slope intercept form
<span>If the length of the bone is 12 in------------------ > 12*2.54=30.48 cms
</span>y=1.5x+127- >1.5*30.48+127=172.72 cms
172.72/2.54=68 in
172.72/0.30=575.73 feet
the height estimate of the person before death is 172.72 cms=68 inches=575.73 feet
<span>By the height it could be a man of average height or a tall woman</span>