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gulaghasi [49]
3 years ago
5

Joseph is driving at an average of 50 miles per hour on a 330-mile road trip. On the way back, Joseph was about to average 60 mi

les per hour. How much faster was the trip back home
Mathematics
1 answer:
pishuonlain [190]3 years ago
7 0

1 second faster was the trip back home .

<u>Step-by-step explanation:</u>

Here we have , Joseph is driving at an average of 50 miles per hour on a 330-mile road trip. On the way back, Joseph was about to average 60 miles per hour.  We need to find  How much faster was the trip back home . Let's find out:

  • Joseph is driving at an average of 50 miles per hour on a 330-mile road trip.

We know that , Speed = \frac{Distance}{time}

⇒ Speed = \frac{Distance}{time}

⇒ 50 = \frac{330}{time}

⇒ time = \frac{330}{50}

⇒ time = 6.6.sec

  • On the way back, Joseph was about to average 60 miles per hour.  

We know that , Speed = \frac{Distance}{time}

⇒ Speed = \frac{Distance}{time}

⇒ 60 = \frac{330}{time}

⇒ time = \frac{330}{60}

⇒ time = 5.5sec

So, Time difference in both trips is 6.5sec-5.5sec=1sec .

Therefore, 1 second faster was the trip back home .

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Answer:

C.

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Step-by-step explanation:

You have the quadratic function 2x^2-x+1=0 to find the solutions for this equation we are going to use Bhaskara's Formula.

For the quadratic functions ax^2+bx+c=0 with a\neq 0 the Bhaskara's Formula is:

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It usually has two solutions.

Then we have  2x^2-x+1=0  where a=2, b=-1 and c=1. Applying the formula:

x_1=\frac{-b+\sqrt{b^2-4.a.c} }{2.a}\\\\x_1=\frac{-(-1)+\sqrt{(-1)^2-4.2.1} }{2.2}\\\\x_1=\frac{1+\sqrt{1-8} }{4}\\\\x_1=\frac{1+\sqrt{-7} }{4}\\\\x_1=\frac{1+\sqrt{(-1).7} }{4}\\x_1=\frac{1+\sqrt{-1}.\sqrt{7}}{4}

Observation: \sqrt{-1}=i

x_1=\frac{1+\sqrt{-1}.\sqrt{7}}{4}\\\\x_1=\frac{1+i.\sqrt{7}}{4}\\\\x_1=\frac{1}{4}+(\frac{\sqrt{7}}{4})i

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x_2=\frac{-b-\sqrt{b^2-4.a.c} }{2.a}\\\\x_2=\frac{-(-1)-\sqrt{(-1)^2-4.2.1} }{2.2}\\\\x_2=\frac{1-i.\sqrt{7} }{4}\\\\x_2=\frac{1}{4}-(\frac{\sqrt{7}}{4})i

Then the correct answer is option C.

x_1=\frac{1}{4}+(\frac{\sqrt{7}}{4})i and x_2=\frac{1}{4}-(\frac{\sqrt{7} }{4})i

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