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chester1
05-12-2009, 08:55 PM
Please help me! I am too far out of college to help my son with this problem!
The fuel efficiency E (in miles per gallon) for a midsized car can be modeled by the equation E=-0.018v squared + 1.476v +3.4 where v is the speed in miles per hour of the car.
1. at what speed should the car travel on the highway to get 30 miles per gallon?

2. does the midsized car ever get 35 miles per gallon? if so at what speeds.

3. Give a value of c for which the equation 5x squared + 10x +c =0 has two solutions one solution and no solutions.

we have a fancy calculator and think you use that to solve but I can't figure out what to do.

galactus
05-12-2009, 09:05 PM
Can you still solve a quadratic?.

For the first part, set the equation equal to 30 and solve for v.

Try answering the second part the same way as the first. -.018v^{2}+1.476v+3.4=35

Does it have real solutions or are they complex?. If they are complex, then it never gets 35 mpg.

For the last one, use the 'discriminant'. b^{2}-4ac.

5x^{2}+10x+c=0

Where a=5, b=10, c=c.

If the discriminant = 0, then it has one solution (well, one solution of multiplicity 2).

If the discriminant > 0, then it has two real solutions.

If it is negative, then it has complex, or no real, solutions.

For instance, what value of c makes the 10^{2}-4(5)c > 0. Find that c value to find when the quadratic has two real solutions.

To find when it has no solutions (two complex solutions), 10^{2}-4(5)c<0

To find when it has one solution, 10^{2}-4(5)c=0

chester1
05-12-2009, 09:32 PM
Is there a quick way to solve the quadratic equation on a test rather then radomly choosing numbers? I get the third part and thank you so much but I am worried about the rest being too time consuming to get answered.

Mrspi
05-12-2009, 10:22 PM
Is there a quick way to solve the quadratic equation on a test rather then radomly choosing numbers? I get the third part and thank you so much but I am worried about the rest being too time consuming to get answered.

The quadratic formula does not involve "randomly choosing numbers." If your son is not familiar with using the quadratic formula to solve a quadratic equation, then perhaps he should check with his teacher about getting some extra help.

stapel
05-13-2009, 12:11 PM
Is there a quick way to solve the quadratic equation on a test rather then radomly choosing numbers?
To learn the various methods for solving quadratics, along with how to recognize which will likely be the quickest way to solve a particular quadratic, try here (http://www.purplemath.com/modules/solvquad.htm). :wink: