course Mth 151
May 1 around 10:20
assignment 29-QUERYq7.3.18:
If we multiply both sides by 6*18 we get 6*18*(1/3)/6=6*18*(1/18) or 18*1/3=6. Note that the effect here is the same as that of 'cross-multiplying', but it's a good idea to remember that 'cross-multiplying' is really a shortcut way to think of multiplying both sides by the common denominator. Since 18*1/3=18/3=6, the equation 18*1/3=6 is true, which verifies the original equality
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q7.3.20
Multiply both sides by 8*56 to get 8*56*z/8=8*56*49/56. Simplify to get 56*z=8*49. Divide both sides by 56 to get z=8*49/56. Simplify to get z=7.
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q7.3.42:
45 cents/8oz=5.63 cents/oz.
49 cents/16oz=3.06cents/oz.
159 cents/50oz=3.18 cents/oz.
16 oz for .49 is the best value at 3.06cents/oz.
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q7.3.45:
the 4/3 corresponds to 4, 2 corresponds to 6, and x corresponds to 3.
The ratios of corresponding sides are all equal. So 4/3/4=2/6=x/3. Just using x/3=2/6 we solve to get x=1. We would have obtained the same thing if we had used x/3=4/3/4
q001:
If z varies inversely as x then z=k/x. Then we have 9=k/(2/3). Multiplying both sides by 2/3 we get 2/3*9=k so k=6. Thus z=6/x. So when x=5/4 we have z=6/(5/4)=24/5=4.8. Note that the translations of other types of proportionality encountered in this chapter include: z=kx^2: z varies as square of x. z=k/x^2: z varies inversely as square of x. z=kx: z is proportional to x
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q7.3.72:
Set up the variation equation I=k/r^2, where I stands for illumination and r for distance (you might have used different letters). This represents the inverse proportionality of illumination with the square of distance. Use I=75 when r=4 to get 75=k/4^2, which gives you k=75*4^2=75*16=1200. Now rewrite the proportionality with this value of k: I=1200/r^2.
To get the illumination at distance 9 substitute 9 for r to get I=1200/9^2=1200/81=14.8 approx.. The illumination at distance 9 is about 14.8
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q7.3.66:
Set up the variation equation L=k/w, which is the inverse proportion. Use L=27 when w=10 to get 27=k/10, which gives you k=27*10=270. Now we know that L=270/w. so if w=18 you get L=270/18=15
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