course Mth 151
May 1 around 10:00
" "assignment 29-QA
q001:
there is no question.
q002:
To say that y is proportional to x is to say that there exists some constant number k such that y=kx^2. Using the given values of y and we can determine the value of k: Since y=8 when x=12, y=kx^2 becomes 8=k*12^2, or 8=144k. Dividing both sides by 144 we obtain k=8/144=1/18. Now our proportionality reads y=1/18x^2. Thus when x=9 we have y=1/18*9^2=81/8=4.5.
*2
q003:
To say that y is inversely proportional to x is to say that there exists some constant number k such that y=k/x. Using the given values of y and x we can determine the value of k: Since y=120 when x=200, y=k/x becomes 120=k/200. Multiplying both sides by 200 we obtain k=120*200=24,000. Now our proportionality reads y=24,000/x. Thus when x=500 we have y=24,000/500=480.
*2
q004:
To say that y is inversely proportional to the square of x is to say that there exists some constant number k such that y=k/x^2. Using the given values of y and x we can determine the value of k: Since y=8 when x=12, y=k/x^2 becomes 8=k/12^2, or 8=k/144. Multiplying both sides by 144 we obtain k=8*144=1152. Now our proportionality reads y=1152/x^2. Thus when x=16 we have y=1152/(16)^2=4.5.
*2
q005:
To say that y is proportional to the square of x and inversely proportional to z is to say that the there exists a constant k such that y=kx^2/z. Substituting the given values of x, y and z we can evaluate k: y=kx^2/z becomes 40=k*10^2/4. Multiplying both sides by 4/10^2 we obtain 40*4/10^2=k, or k=1.6. Our proportionality is now y=1.6x^2/z, so that when x=20 and z=12 we have y=1.6*20^2/12=1.6*400/12=53 1/3
*2"
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