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.
Here is the website for the answer... I hope this helps...
P.S. I think that if you click on the link, it won't work. So, just copy and paste...
Answer:
528
Step-by-step explanation:
Answer:
Huh?? I have no idea what you said.
Step-by-step explanation:
Answer: the rate of the passenger train is 100 mph.
Step-by-step explanation:
Let x represent the rate of the passenger train.
The rate of the freight train was 10 miles per hour slower than the rate of the passenger train. It means that the rate of the freight train is (x - 10) mph
The passenger train traveled 100 miles. It means that the time it took travel 100 miles is
100/x
In the same amount of time, it took a freight train to travel 90 miles. It means that the time it took travel 90 miles is
90/(x - 10)
Since the time is the same, then
100/x = 90/(x - 10)
Cross multiplying, it becomes
100(x - 10) = 90x
100x - 1000 = 90x
100x - 90x = 1000
10x = 1000
x = 100 mph
