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Nikolay [14]
3 years ago
10

I promise I will mark as brainiest if a speed of a car increase its average speed in a journey of 200 miles by 5 mile/hour the j

ourney will end with a difference of one hour less, so what is the original speed of the car ?
Mathematics
1 answer:
jok3333 [9.3K]3 years ago
7 0

Answer:

\large \boxed{\sf \ \ \ \dfrac{\sqrt{4025}-5}{2}=29.22144... \ \ \ }

Step-by-step explanation:

Hello

<u>Let's note the original speed of the car v</u>

it means that in 1 hour he is going v miles

so to go 200 miles it takes ( in hour)

\dfrac{200}{v}

If the speed of the car is v+5 than to go 200 miles it takes (in hour)

\dfrac{200}{v+5}

and this time is one hour less so we can write

\boxed{\sf \ \ \dfrac{200}{v+5}=\dfrac{200}{v}-1 \ \ }

We can multiply by v(v+5) both parts of the equation so

200v=200(v+5)-v(v+5)\\\\200v=200v+1000-v^2-5v\\\\v^2+5v-1000=0

\Delta=b^2-4ac=5^2+4*1000=4025\\\\ \text{There are potential solutions }\\\\\ \ \ \ \ x_1=\dfrac{-5-\sqrt{4025}}{2}\\\\\ \ \ \ \ x_2=\dfrac{-5+\sqrt{4025}}{2}

Only one is positive and this is is

x_1=\dfrac{\sqrt{4025}-5}{2}=29.22144...

So the original speed is 29.22144... mph

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

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Consider this example: say we want to convert <em>x</em> = 11 0101 1001₂ to base 3.

The binary expansion of <em>x</em> is

<em>x</em> = 1×2⁹ + 1×2⁸ + 1×2⁶ + 1×2⁴ + 1×2³ + 1×2⁰

which in base 10 reduces to

<em>x</em> = 512 + 256 + 64 + 16 + 8 + 1 = 857

Recall the first several powers of 3:

3⁰ = 1; 3¹ = 3; 3² = 9; 3³ = 27; 3⁴ = 81; 3⁵ = 243; 3⁶ = 729

Now it's a matter of computing quotients and remainders. Pick the largest power of 3 that fits into the target number, then check the remainder and repeat.

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• How many times does 81 go into 128? Also 1 time, so

128 = 1×81 + 47 = 1×3⁴ + 47

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20 = 18 + 2 = 2×9 + 2 = 2×3² + 2

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So we found

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which is the ternary expansion of <em>x</em>,

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▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪

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\fbox \colorbox{black}{ \colorbox{white}{volume} \:  \:  \:   \:   \: \colorbox{white}{=}  \:  \:   \:   + \colorbox{white}{462 \: cm³ }}

\large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}

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