9514 1404 393
Eexplanation:
16. Suppose the roots are α and kα. Then we can write the equation as ...
a(x -α)(x -kα) = 0
ax² -ax(α +kα) +akα² = 0
Comparing to the original equation, we can equate coefficients to get ...
Solving the first for α gives ...
α = -b/(a(1+k)
Substituting into the second, we have ...
c = ak(-b/(a(1+k)))²
Multiplying by a(1+k)², we get ...
(1+k)²ac = kb²
Using k=2 gives ...
9ac = 2b² . . . . . as required
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17. Using the previous result with k=1 (equal roots), we have ...
(1+k)²ac = kb²
4ac = b² . . . . . for k=1
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<em>Additional comment</em>
We observed that the problems were similar, but had different factors relating the roots. So, we elected to solve the general case, then fill in the specific values for the two problems.
First we need to turn 1 5/7 into an improper fraction 7x1+5 = 12/7
12 / 7 x 5 / 6 = 60/42 ....reduced.....10/7
10/7 as a mixed number is 1 3/7
Answer: number 3 is 32 number 4 is 40 minutes
Step-by-step explanation:You see in number 3 it says a millipede has 14 more legs than a caterpillar. Also it states the total of the legs are 46. This means you must subtract. 46-14 is equal to 32. And for number 4 it states the total time of all her classes are 1 hour and 10 minutes. The yoga class is 30 minutes longer. This means you must subtract those 30 minutes from the 1 hour and 10 minutes. 1 hour and 10 minutes- 30 minutes is equal to 40 minutes. This is the answer.
Hope this helps!!
Answer:
Step-by-step explanation:
download an app called connects go to the app store and look up geometry and scroll down its blue and has a figure 8 on it
The radius was divided by 2.
31.4 = 2pi * r
31.4/2pi = 15.7/pi
15.7 = 2pi * r
15.7/2pi = 7.85/pi
(7.85/pi) / (15.7/pi) = 1/2
